素数桁のレピュニットが持つ素因数

(予想)

$p, q$ を奇素数、 $b$ を $|b|\ge 2$ の整数とする。

基数 $b$ の $p$ 桁のレピュニット $\displaystyle{R_p^{(b)}=\frac{b^p-1}{b-1}}$ を割り切れる素数 $q$ は以下のような形となる。

$p,q\text{ is odd prime},\quad$ $p\ge 3,\quad$ $q\ge 3,\quad$ $b\text{ is integer},\quad$ $|b|\ge 2$

q\mid\frac{b^p-1}{b-1}\implies\begin{cases} q\equiv 1(\operatorname{mod}2p)\text{ or }q=p&\left\{p\mid (b-1)\right\}\\ q\equiv 1(\operatorname{mod}2p)&\left\{p\nmid (b-1)\right\}\\ \end{cases}

$p\mid (b-1)$ の意味 : $(b-1)$ を $p$ で割り切れる時
$p\nmid (b-1)$ の意味 : $(b-1)$ を $p$ で割り切れない時

以下は $|b|\le 50,\ p\lt 50$ においてレピュニット $\displaystyle{R_p^{(b)}=\frac{b^p-1}{b-1}}$ を素因数分解した時の素因数の形を示したリスト。

Mizar/みざー

$b=-50, p=2,$ $\bigl[$ $\color{magenta}\bm{(3p+1)^{2}}$ $\bigr]$
$b=-50, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(6p+1)^{1}$ , $(14p+1)^{1}$ $\bigr]$
$b=-50, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(111408p+1)^{1}$ $\bigr]$
$b=-50, p=7,$ $\bigl[$ $(870p+1)^{1}$ , $(359280p+1)^{1}$ $\bigr]$
$b=-50, p=11,$ $\bigl[$ $(8p+1)^{1}$ , $(97795119069078p+1)^{1}$ $\bigr]$
$b=-50, p=13,$ $\bigl[$ $(2434p+1)^{1}$ , $(581860501220512p+1)^{1}$ $\bigr]$
$b=-50, p=17,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(13847228706p+1)^{1}$ , $(21989242474200p+1)^{1}$ $\bigr]$
$b=-50, p=19,$ $\bigl[$ $(24p+1)^{1}$ , $(174p+1)^{1}$ , $(8464p+1)^{1}$ , $(809886116546300584p+1)^{1}$ $\bigr]$
$b=-50, p=23,$ $\bigl[$ $(246p+1)^{1}$ , $(110295144p+1)^{1}$ , $(70792649308527687408824p+1)^{1}$ $\bigr]$
$b=-50, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(18p+1)^{1}$ , $(3674360p+1)^{1}$ , $(3830262553829613289849808933814818p+1)^{1}$ $\bigr]$
$b=-50, p=31,$ $\bigl[$ $(279448p+1)^{1}$ , $(3399973364552178761343783162519639474827518p+1)^{1}$ $\bigr]$
$b=-50, p=37,$ $\bigl[$ $(34p+1)^{1}$ , $(43768p+1)^{1}$ , $(52474800p+1)^{1}$ , $(1883090000095578p+1)^{1}$ , $(1398004336844168504698170p+1)^{1}$ $\bigr]$
$b=-50, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(18p+1)^{1}$ , $(37484799639819896471237661066p+1)^{1}$ , $(23070370206462280725880783336968p+1)^{1}$ $\bigr]$
$b=-50, p=43,$ $\bigl[$ $(891426742p+1)^{1}$ , $(1085509454811286p+1)^{1}$ , $(2897446159919802661487725736589014196330342p+1)^{1}$ $\bigr]$
$b=-50, p=47,$ $\bigl[$ $(14p+1)^{1}$ , $(38p+1)^{1}$ , $(316056928016896781924033067729080p+1)^{1}$ , $(1694529095375327796989529787561720158p+1)^{1}$ $\bigr]$
$b=-49, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{4}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=-49, p=3,$ $\bigl[$ $(4p+1)^{1}$ , $(60p+1)^{1}$ $\bigr]$
$b=-49, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(56p+1)^{1}$ , $(804p+1)^{1}$ $\bigr]$
$b=-49, p=7,$ $\bigl[$ $(1937780208p+1)^{1}$ $\bigr]$
$b=-49, p=11,$ $\bigl[$ $(60p+1)^{1}$ , $(128p+1)^{1}$ , $(7632762308p+1)^{1}$ $\bigr]$
$b=-49, p=13,$ $\bigl[$ $(12p+1)^{1}$ , $(91989028296401316p+1)^{1}$ $\bigr]$
$b=-49, p=17,$ $\bigl[$ $(8p+1)^{1}$ , $(3491844p+1)^{1}$ , $(7828708198450724p+1)^{1}$ $\bigr]$
$b=-49, p=19,$ $\bigl[$ $(136773485733813705386496995472p+1)^{1}$ $\bigr]$
$b=-49, p=23,$ $\bigl[$ $(1160p+1)^{1}$ , $(28260p+1)^{1}$ , $(674520p+1)^{1}$ , $(2420954015733063644p+1)^{1}$ $\bigr]$
$b=-49, p=29,$ $\bigl[$ $(8p+1)^{1}$ , $(4719072p+1)^{1}$ , $(1921243707252p+1)^{1}$ , $(4024642759619777301428p+1)^{1}$ $\bigr]$
$b=-49, p=31,$ $\bigl[$ $(1095084816p+1)^{1}$ , $(2403311250599459812p+1)^{1}$ , $(6349881464815873900p+1)^{1}$ $\bigr]$
$b=-49, p=37,$ $\bigl[$ $(186244404035294113902558370990468780134013945058340435676128p+1)^{1}$ $\bigr]$
$b=-49, p=41,$ $\bigl[$ $(825416p+1)^{1}$ , $(132917760394997528p+1)^{1}$ , $(5253657974556289804196077149512596219296p+1)^{1}$ $\bigr]$
$b=-49, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(24p+1)^{1}$ , $(12412136890304948050288111833254978910105955082256813345265067332p+1)^{1}$ $\bigr]$
$b=-49, p=47,$ $\bigl[$ $(2040p+1)^{1}$ , $(97337388p+1)^{1}$ , $(26670907805367151649309936911206161636210491098582321908070300p+1)^{1}$ $\bigr]$
$b=-48, p=2,$ $\bigl[$ $\color{magenta}\bm{(23p+1)^{1}}$ $\bigr]$
$b=-48, p=3,$ $\bigl[$ $(12p+1)^{1}$ , $(20p+1)^{1}$ $\bigr]$
$b=-48, p=5,$ $\bigl[$ $(1040016p+1)^{1}$ $\bigr]$
$b=-48, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(244509930p+1)^{1}$ $\bigr]$
$b=-48, p=11,$ $\bigl[$ $(330p+1)^{1}$ , $(1592350237626p+1)^{1}$ $\bigr]$
$b=-48, p=13,$ $\bigl[$ $(714p+1)^{1}$ , $(1214250533876802p+1)^{1}$ $\bigr]$
$b=-48, p=17,$ $\bigl[$ $(45756841037179073428036560p+1)^{1}$ $\bigr]$
$b=-48, p=19,$ $\bigl[$ $(78p+1)^{1}$ , $(87690p+1)^{1}$ , $(2383830p+1)^{1}$ , $(842868560922p+1)^{1}$ $\bigr]$
$b=-48, p=23,$ $\bigl[$ $(6p+1)^{1}$ , $(554837895254064p+1)^{1}$ , $(233193151484603310p+1)^{1}$ $\bigr]$
$b=-48, p=29,$ $\bigl[$ $(12p+1)^{1}$ , $(11496784186179610142865690166216031619074772p+1)^{1}$ $\bigr]$
$b=-48, p=31,$ $\bigl[$ $(18858p+1)^{1}$ , $(2074398p+1)^{1}$ , $(230042845544690162059745399479145796p+1)^{1}$ $\bigr]$
$b=-48, p=37,$ $\bigl[$ $(267366p+1)^{1}$ , $(133708522598998813459296p+1)^{1}$ , $(1810753018800779483847868854p+1)^{1}$ $\bigr]$
$b=-48, p=41,$ $\bigl[$ $(268367415132p+1)^{1}$ , $(38583103306510968276960938792150625995642370434565636p+1)^{1}$ $\bigr]$
$b=-48, p=43,$ $\bigl[$ $(382032p+1)^{1}$ , $(8927154p+1)^{1}$ , $(147896863546535935622271278622538087790143993322558562p+1)^{1}$ $\bigr]$
$b=-48, p=47,$ $\bigl[$ $(1229628p+1)^{1}$ , $(25949253474831630408p+1)^{1}$ , $(305469175423368246276p+1)^{1}$ , $(4475943878616478472321880p+1)^{1}$ $\bigr]$
$b=-47, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(11p+1)^{1}}$ $\bigr]$
$b=-47, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(34p+1)^{1}$ $\bigr]$
$b=-47, p=5,$ $\bigl[$ $(955604p+1)^{1}$ $\bigr]$
$b=-47, p=7,$ $\bigl[$ $(840p+1)^{1}$ , $(256386p+1)^{1}$ $\bigr]$
$b=-47, p=11,$ $\bigl[$ $(35396p+1)^{1}$ , $(12025261458p+1)^{1}$ $\bigr]$
$b=-47, p=13,$ $\bigl[$ $(10p+1)^{1}$ , $(952p+1)^{1}$ , $(5397602233854p+1)^{1}$ $\bigr]$
$b=-47, p=17,$ $\bigl[$ $(649934p+1)^{1}$ , $(2955664998684725214p+1)^{1}$ $\bigr]$
$b=-47, p=19,$ $\bigl[$ $(64545276034955575995024916278p+1)^{1}$ $\bigr]$
$b=-47, p=23,$ $\bigl[$ $(260184642827957962630982799621016394p+1)^{1}$ $\bigr]$
$b=-47, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(1052p+1)^{1}$ , $(17652p+1)^{1}$ , $(501800p+1)^{1}$ , $(51873728p+1)^{1}$ , $(110268572368127558p+1)^{1}$ $\bigr]$
$b=-47, p=31,$ $\bigl[$ $(3052p+1)^{1}$ , $(9610p+1)^{1}$ , $(72178p+1)^{1}$ , $(8168258031856p+1)^{1}$ , $(287829589290074406p+1)^{1}$ $\bigr]$
$b=-47, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(11096771180062750p+1)^{1}$ , $(678567661924550192776344242171165604414p+1)^{1}$ $\bigr]$
$b=-47, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(18p+1)^{1}$ , $(66p+1)^{1}$ , $(1100972052284408596944943070291057058776722461045083764218p+1)^{1}$ $\bigr]$
$b=-47, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(22p+1)^{1}$ , $(92903832250126208566p+1)^{1}$ , $(236139622528679004133671691556104908958660p+1)^{1}$ $\bigr]$
$b=-47, p=47,$ $\bigl[$ $(14p+1)^{1}$ , $(330p+1)^{1}$ , $(1394p+1)^{1}$ , $(450618p+1)^{1}$ , $(223812548p+1)^{1}$ , $(1297089860p+1)^{1}$ , $(53332168394p+1)^{1}$ , $(75391785622320208980636p+1)^{1}$ $\bigr]$
$b=-46, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{2}}$ , $(2p+1)^{1}$ $\bigr]$
$b=-46, p=3,$ $\bigl[$ $(6p+1)^{1}$ , $(36p+1)^{1}$ $\bigr]$
$b=-46, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(14p+1)^{1}$ , $(36p+1)^{1}$ $\bigr]$
$b=-46, p=7,$ $\bigl[$ $(1324673730p+1)^{1}$ $\bigr]$
$b=-46, p=11,$ $\bigl[$ $(90p+1)^{1}$ , $(36338p+1)^{1}$ , $(9528338p+1)^{1}$ $\bigr]$
$b=-46, p=13,$ $\bigl[$ $(16102p+1)^{1}$ , $(32283852341344p+1)^{1}$ $\bigr]$
$b=-46, p=17,$ $\bigl[$ $(216p+1)^{1}$ , $(6299635634011346426118p+1)^{1}$ $\bigr]$
$b=-46, p=19,$ $\bigl[$ $(78p+1)^{1}$ , $(84p+1)^{1}$ , $(27204p+1)^{1}$ , $(458892p+1)^{1}$ , $(4104402384p+1)^{1}$ $\bigr]$
$b=-46, p=23,$ $\bigl[$ $(162033358841136164361412492057211490p+1)^{1}$ $\bigr]$
$b=-46, p=29,$ $\bigl[$ $(12054p+1)^{1}$ , $(85473698p+1)^{1}$ , $(1405142415102317774230673314250p+1)^{1}$ $\bigr]$
$b=-46, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(136p+1)^{1}$ , $(68358834151390p+1)^{1}$ , $(867187280460308178438029542p+1)^{1}$ $\bigr]$
$b=-46, p=37,$ $\bigl[$ $(951101134p+1)^{1}$ , $(28009158378790p+1)^{1}$ , $(524577891637309763328029730320334p+1)^{1}$ $\bigr]$
$b=-46, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(398p+1)^{1}$ , $(76826852p+1)^{1}$ , $(18118442180649795272870145171600511294904489269310p+1)^{1}$ $\bigr]$
$b=-46, p=43,$ $\bigl[$ $(34896p+1)^{1}$ , $(275314p+1)^{1}$ , $(7624612p+1)^{1}$ , $(26778920246520091281361279670516093768772268836p+1)^{1}$ $\bigr]$
$b=-46, p=47,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(14p+1)^{1}$ , $(20627144008917485363248589836812677198797057529693347613363311039312998p+1)^{1}$ $\bigr]$
$b=-45, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $\color{magenta}\bm{(5p+1)^{1}}$ $\bigr]$
$b=-45, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(94p+1)^{1}$ $\bigr]$
$b=-45, p=5,$ $\bigl[$ $(8p+1)^{1}$ , $(19568p+1)^{1}$ $\bigr]$
$b=-45, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(26987538p+1)^{1}$ $\bigr]$
$b=-45, p=11,$ $\bigl[$ $(6p+1)^{1}$ , $(45197283382122p+1)^{1}$ $\bigr]$
$b=-45, p=13,$ $\bigl[$ $(154p+1)^{1}$ , $(194556p+1)^{1}$ , $(1024217974p+1)^{1}$ $\bigr]$
$b=-45, p=17,$ $\bigl[$ $(1725613898p+1)^{1}$ , $(554642864101826p+1)^{1}$ $\bigr]$
$b=-45, p=19,$ $\bigl[$ $(78p+1)^{1}$ , $(3292p+1)^{1}$ , $(112674p+1)^{1}$ , $(148452423233092p+1)^{1}$ $\bigr]$
$b=-45, p=23,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(20p+1)^{1}$ , $(1202p+1)^{1}$ , $(1416p+1)^{1}$ , $(222547691198706519882p+1)^{1}$ $\bigr]$
$b=-45, p=29,$ $\bigl[$ $(12p+1)^{1}$ , $(167774p+1)^{1}$ , $(387310166438717924063391233344564994p+1)^{1}$ $\bigr]$
$b=-45, p=31,$ $\bigl[$ $(21140754180p+1)^{1}$ , $(1901018009927820004484336113347665400p+1)^{1}$ $\bigr]$
$b=-45, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(3766p+1)^{1}$ , $(132318p+1)^{1}$ , $(781498p+1)^{1}$ , $(2949046893370937690500695437048063878p+1)^{1}$ $\bigr]$
$b=-45, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(10680p+1)^{1}$ , $(1787826p+1)^{1}$ , $(3392169615423951094962p+1)^{1}$ , $(86569847971547028577485146p+1)^{1}$ $\bigr]$
$b=-45, p=43,$ $\bigl[$ $(22p+1)^{1}$ , $(1839962706974677665469654p+1)^{1}$ , $(826578966499964720003373659764226347500p+1)^{1}$ $\bigr]$
$b=-45, p=47,$ $\bigl[$ $(22456158366p+1)^{1}$ , $(106550465814021510867296244p+1)^{1}$ , $(43958809966352891663838009507570606p+1)^{1}$ $\bigr]$
$b=-44, p=2,$ $\bigl[$ $\color{magenta}\bm{(21p+1)^{1}}$ $\bigr]$
$b=-44, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(210p+1)^{1}$ $\bigr]$
$b=-44, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(84p+1)^{1}$ , $(348p+1)^{1}$ $\bigr]$
$b=-44, p=7,$ $\bigl[$ $(1013580348p+1)^{1}$ $\bigr]$
$b=-44, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(90p+1)^{1}$ , $(276p+1)^{1}$ , $(392408p+1)^{1}$ $\bigr]$
$b=-44, p=13,$ $\bigl[$ $(1426p+1)^{1}$ , $(213620350739302p+1)^{1}$ $\bigr]$
$b=-44, p=17,$ $\bigl[$ $(530274888p+1)^{1}$ , $(1259169173104700p+1)^{1}$ $\bigr]$
$b=-44, p=19,$ $\bigl[$ $(352p+1)^{1}$ , $(2939500528153313223108460p+1)^{1}$ $\bigr]$
$b=-44, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(1295308905675223436006729105352486p+1)^{1}$ $\bigr]$
$b=-44, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(323302178483828p+1)^{1}$ , $(633371424872120701171229594p+1)^{1}$ $\bigr]$
$b=-44, p=31,$ $\bigl[$ $(229682836p+1)^{1}$ , $(1649521698p+1)^{1}$ , $(954454048236p+1)^{1}$ , $(58902276890710p+1)^{1}$ $\bigr]$
$b=-44, p=37,$ $\bigl[$ $(52391481527728p+1)^{1}$ , $(1990088492601143202803197400328216946130020p+1)^{1}$ $\bigr]$
$b=-44, p=41,$ $\bigl[$ $(37892942p+1)^{1}$ , $(17589766067066p+1)^{1}$ , $(335108904356592p+1)^{1}$ , $(847632184327242853974656p+1)^{1}$ $\bigr]$
$b=-44, p=43,$ $\bigl[$ $(3582p+1)^{1}$ , $(67680p+1)^{1}$ , $(53735130509489363246478901346868691678636523214429667626p+1)^{1}$ $\bigr]$
$b=-44, p=47,$ $\bigl[$ $(171776p+1)^{1}$ , $(7831538p+1)^{1}$ , $(2365532019270628781100907640p+1)^{1}$ , $(249996206365939548395030040078p+1)^{1}$ $\bigr]$
$b=-43, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=-43, p=3,$ $\bigl[$ $(4p+1)^{1}$ , $(46p+1)^{1}$ $\bigr]$
$b=-43, p=5,$ $\bigl[$ $(668220p+1)^{1}$ $\bigr]$
$b=-43, p=7,$ $\bigl[$ $(882527958p+1)^{1}$ $\bigr]$
$b=-43, p=11,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(32642p+1)^{1}$ , $(315458p+1)^{1}$ $\bigr]$
$b=-43, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(4242p+1)^{1}$ , $(1027770462970p+1)^{1}$ $\bigr]$
$b=-43, p=17,$ $\bigl[$ $(289294064p+1)^{1}$ , $(1596885226409024p+1)^{1}$ $\bigr]$
$b=-43, p=19,$ $\bigl[$ $(12992549454139254324052984074p+1)^{1}$ $\bigr]$
$b=-43, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(797901630p+1)^{1}$ , $(42542099555010530269130p+1)^{1}$ $\bigr]$
$b=-43, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(23580p+1)^{1}$ , $(238691948p+1)^{1}$ , $(658725271640078057857090878p+1)^{1}$ $\bigr]$
$b=-43, p=31,$ $\bigl[$ $(121473719148p+1)^{1}$ , $(208474092707356p+1)^{1}$ , $(13075248275875405558p+1)^{1}$ $\bigr]$
$b=-43, p=37,$ $\bigl[$ $(18130p+1)^{1}$ , $(246204154p+1)^{1}$ , $(24385464142029087084p+1)^{1}$ , $(305666912199613032000p+1)^{1}$ $\bigr]$
$b=-43, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(602p+1)^{1}$ , $(16970p+1)^{1}$ , $(26788496135228910p+1)^{1}$ , $(3321204336756327316310206222026068p+1)^{1}$ $\bigr]$
$b=-43, p=43,$ $\bigl[$ $(22p+1)^{1}$ , $(30p+1)^{1}$ , $(156p+1)^{1}$ , $(2016p+1)^{1}$ , $(11300604859819224751884574p+1)^{1}$ , $(26531041957417103595862032p+1)^{1}$ $\bigr]$
$b=-43, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(14p+1)^{1}$ , $(296p+1)^{1}$ , $(530243580p+1)^{1}$ , $(300175131098966243030p+1)^{1}$ , $(31428843381560917113631259151668p+1)^{1}$ $\bigr]$
$b=-42, p=2,$ $\bigl[$ $(20p+1)^{1}$ $\bigr]$
$b=-42, p=3,$ $\bigl[$ $(574p+1)^{1}$ $\bigr]$
$b=-42, p=5,$ $\bigl[$ $(26p+1)^{1}$ , $(4640p+1)^{1}$ $\bigr]$
$b=-42, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(48p+1)^{1}$ , $(78370p+1)^{1}$ $\bigr]$
$b=-42, p=11,$ $\bigl[$ $(2p+1)^{3}$ , $(6p+1)^{1}$ , $(1860470306p+1)^{1}$ $\bigr]$
$b=-42, p=13,$ $\bigl[$ $(1420p+1)^{1}$ , $(88732p+1)^{1}$ , $(106304034p+1)^{1}$ $\bigr]$
$b=-42, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(228p+1)^{1}$ , $(13489241627741917920p+1)^{1}$ $\bigr]$
$b=-42, p=19,$ $\bigl[$ $(804p+1)^{1}$ , $(556514369331443763256602p+1)^{1}$ $\bigr]$
$b=-42, p=23,$ $\bigl[$ $(330p+1)^{1}$ , $(88117034p+1)^{1}$ , $(1420530914086542308030p+1)^{1}$ $\bigr]$
$b=-42, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(60p+1)^{1}$ , $(926215800209687219278453007060927168492p+1)^{1}$ $\bigr]$
$b=-42, p=31,$ $\bigl[$ $(132p+1)^{1}$ , $(1087986p+1)^{1}$ , $(25935796p+1)^{1}$ , $(38600610p+1)^{1}$ , $(1182099290460451318p+1)^{1}$ $\bigr]$
$b=-42, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(34p+1)^{1}$ , $(166p+1)^{1}$ , $(1799355934816p+1)^{1}$ , $(9411140270681435452721628304195314p+1)^{1}$ $\bigr]$
$b=-42, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(80477593770p+1)^{1}$ , $(7403407629116172420716309025565718507965584304466p+1)^{1}$ $\bigr]$
$b=-42, p=43,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(24p+1)^{1}$ , $(2734p+1)^{1}$ , $(5041940274398774618800p+1)^{1}$ , $(3012152713792667022357044120702406p+1)^{1}$ $\bigr]$
$b=-42, p=47,$ $\bigl[$ $(134p+1)^{1}$ , $(1541270005874173287693354763490739005265317137254274747877283793285448p+1)^{1}$ $\bigr]$
$b=-41, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{3}}$ , $(2p+1)^{1}$ $\bigr]$
$b=-41, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(182p+1)^{1}$ $\bigr]$
$b=-41, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(12p+1)^{1}$ , $(822p+1)^{1}$ $\bigr]$
$b=-41, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(10p+1)^{1}$ , $(1332856p+1)^{1}$ $\bigr]$
$b=-41, p=11,$ $\bigl[$ $(210p+1)^{1}$ , $(515442830090p+1)^{1}$ $\bigr]$
$b=-41, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(33276p+1)^{1}$ , $(49578676770p+1)^{1}$ $\bigr]$
$b=-41, p=17,$ $\bigl[$ $(3661232867648144577316160p+1)^{1}$ $\bigr]$
$b=-41, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(28830821619945171558546130p+1)^{1}$ $\bigr]$
$b=-41, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(12p+1)^{1}$ , $(20p+1)^{1}$ , $(42p+1)^{1}$ , $(12674p+1)^{1}$ , $(7598074070725633026p+1)^{1}$ $\bigr]$
$b=-41, p=29,$ $\bigl[$ $(72p+1)^{1}$ , $(116296620648996512p+1)^{1}$ , $(6873548850020877683400p+1)^{1}$ $\bigr]$
$b=-41, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(2586p+1)^{1}$ , $(188302300p+1)^{1}$ , $(3867117996p+1)^{1}$ , $(4364817773389304208p+1)^{1}$ $\bigr]$
$b=-41, p=37,$ $\bigl[$ $(34p+1)^{1}$ , $(240727637702013043907194755255524693437694984108531914p+1)^{1}$ $\bigr]$
$b=-41, p=41,$ $\bigl[$ $(440p+1)^{1}$ , $(497480p+1)^{1}$ , $(2100317099811423767811663198578683726634928645258080p+1)^{1}$ $\bigr]$
$b=-41, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(62802p+1)^{1}$ , $(18831230599240p+1)^{1}$ , $(20618262152087469196p+1)^{1}$ , $(3693450040927541198386p+1)^{1}$ $\bigr]$
$b=-41, p=47,$ $\bigl[$ $(14p+1)^{1}$ , $(26p+1)^{1}$ , $(43008p+1)^{1}$ , $(1965780062605541891766152119457358980089601601169145999433404p+1)^{1}$ $\bigr]$

Mizar/みざー

$b=-40, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ , $(6p+1)^{1}$ $\bigr]$
$b=-40, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(74p+1)^{1}$ $\bigr]$
$b=-40, p=5,$ $\bigl[$ $(2p+1)^{2}$ , $(4128p+1)^{1}$ $\bigr]$
$b=-40, p=7,$ $\bigl[$ $(30p+1)^{1}$ , $(2705550p+1)^{1}$ $\bigr]$
$b=-40, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(40434821170346p+1)^{1}$ $\bigr]$
$b=-40, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(6581440p+1)^{1}$ , $(277659492p+1)^{1}$ $\bigr]$
$b=-40, p=17,$ $\bigl[$ $(38p+1)^{1}$ , $(235760p+1)^{1}$ , $(950525213149806p+1)^{1}$ $\bigr]$
$b=-40, p=19,$ $\bigl[$ $(22p+1)^{1}$ , $(84p+1)^{1}$ , $(5273311647377472348154p+1)^{1}$ $\bigr]$
$b=-40, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(34634p+1)^{1}$ , $(199314647572992975061771920p+1)^{1}$ $\bigr]$
$b=-40, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(14969964p+1)^{1}$ , $(3816024438620718p+1)^{1}$ , $(8552202629106272p+1)^{1}$ $\bigr]$
$b=-40, p=31,$ $\bigl[$ $(43753132p+1)^{1}$ , $(812261388042150p+1)^{1}$ , $(1062394556805118596946p+1)^{1}$ $\bigr]$
$b=-40, p=37,$ $\bigl[$ $(96525394p+1)^{1}$ , $(241891348p+1)^{1}$ , $(37336427031064p+1)^{1}$ , $(2819903542553765079166p+1)^{1}$ $\bigr]$
$b=-40, p=41,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(62p+1)^{1}$ , $(8448p+1)^{1}$ , $(3006123659262246p+1)^{1}$ , $(64629679160048211915695676592084728p+1)^{1}$ $\bigr]$
$b=-40, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(30p+1)^{1}$ , $(70p+1)^{1}$ , $(352720p+1)^{1}$ , $(43027453493359075806161845318558751315787449823652p+1)^{1}$ $\bigr]$
$b=-40, p=47,$ $\bigl[$ $(156p+1)^{1}$ , $(2744p+1)^{1}$ , $(1767268454p+1)^{1}$ , $(11199014900532188p+1)^{1}$ , $(24859523312437141353570596098430150p+1)^{1}$ $\bigr]$
$b=-39, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(9p+1)^{1}}$ $\bigr]$
$b=-39, p=3,$ $\bigl[$ $(494p+1)^{1}$ $\bigr]$
$b=-39, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(8202p+1)^{1}$ $\bigr]$
$b=-39, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(10p+1)^{1}$ , $(160534p+1)^{1}$ $\bigr]$
$b=-39, p=11,$ $\bigl[$ $(1110p+1)^{1}$ , $(59089017600p+1)^{1}$ $\bigr]$
$b=-39, p=13,$ $\bigl[$ $(928616824168231884p+1)^{1}$ $\bigr]$
$b=-39, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(146336p+1)^{1}$ , $(6411385731974726p+1)^{1}$ $\bigr]$
$b=-39, p=19,$ $\bigl[$ $(384p+1)^{1}$ , $(4395828p+1)^{1}$ , $(3668388284626962p+1)^{1}$ $\bigr]$
$b=-39, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(1064p+1)^{1}$ , $(7606020p+1)^{1}$ , $(152761165898049402p+1)^{1}$ $\bigr]$
$b=-39, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(202098738612198499642685536215617362086830p+1)^{1}$ $\bigr]$
$b=-39, p=31,$ $\bigl[$ $(136p+1)^{1}$ , $(580p+1)^{1}$ , $(223750333141880274113611110453350951142p+1)^{1}$ $\bigr]$
$b=-39, p=37,$ $\bigl[$ $(40029310888507776340p+1)^{1}$ , $(33771387716177703514621576506431728p+1)^{1}$ $\bigr]$
$b=-39, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(470586p+1)^{1}$ , $(681538299337802p+1)^{1}$ , $(2333618949970097613499334760341859306p+1)^{1}$ $\bigr]$
$b=-39, p=43,$ $\bigl[$ $(736p+1)^{1}$ , $(2082p+1)^{1}$ , $(1577635705206965738754p+1)^{1}$ , $(787880675935762945385127356219302p+1)^{1}$ $\bigr]$
$b=-39, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(4118022717716p+1)^{1}$ , $(5852017947374583588119043589599871561594904677739857736p+1)^{1}$ $\bigr]$
$b=-38, p=2,$ $\bigl[$ $(18p+1)^{1}$ $\bigr]$
$b=-38, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(22p+1)^{1}$ $\bigr]$
$b=-38, p=5,$ $\bigl[$ $(406334p+1)^{1}$ $\bigr]$
$b=-38, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(34p+1)^{1}$ , $(60468p+1)^{1}$ $\bigr]$
$b=-38, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(30p+1)^{1}$ , $(42p+1)^{1}$ , $(102p+1)^{1}$ , $(140490p+1)^{1}$ $\bigr]$
$b=-38, p=13,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(4p+1)^{1}$ , $(42p+1)^{1}$ , $(28336p+1)^{1}$ , $(4894284p+1)^{1}$ $\bigr]$
$b=-38, p=17,$ $\bigl[$ $(18p+1)^{1}$ , $(17000p+1)^{1}$ , $(2700576p+1)^{1}$ , $(265989540p+1)^{1}$ $\bigr]$
$b=-38, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(134592300562p+1)^{1}$ , $(2865912607818p+1)^{1}$ $\bigr]$
$b=-38, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(14040p+1)^{1}$ , $(411980p+1)^{1}$ , $(16766102518620157940p+1)^{1}$ $\bigr]$
$b=-38, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(612p+1)^{1}$ , $(5527062140p+1)^{1}$ , $(686147186942p+1)^{1}$ , $(1723963892922p+1)^{1}$ $\bigr]$
$b=-38, p=31,$ $\bigl[$ $(430p+1)^{1}$ , $(583448416967865562460243824697797797827476p+1)^{1}$ $\bigr]$
$b=-38, p=37,$ $\bigl[$ $(16p+1)^{1}$ , $(37770p+1)^{1}$ , $(23676801366256264849828545618733221667369705228p+1)^{1}$ $\bigr]$
$b=-38, p=41,$ $\bigl[$ $(165582p+1)^{1}$ , $(6010731848665950561606p+1)^{1}$ , $(22068394685321911280826120338990p+1)^{1}$ $\bigr]$
$b=-38, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(24p+1)^{1}$ , $(40p+1)^{1}$ , $(136p+1)^{1}$ , $(45160p+1)^{1}$ , $(24602934555636p+1)^{1}$ , $(13755446627895042194528342456154p+1)^{1}$ $\bigr]$
$b=-38, p=47,$ $\bigl[$ $(120p+1)^{1}$ , $(281862978p+1)^{1}$ , $(379335421175662990394926974p+1)^{1}$ , $(72786917340099792150593619734p+1)^{1}$ $\bigr]$
$b=-37, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $\color{magenta}\bm{(1p+1)^{2}}$ $\bigr]$
$b=-37, p=3,$ $\bigl[$ $(10p+1)^{1}$ , $(14p+1)^{1}$ $\bigr]$
$b=-37, p=5,$ $\bigl[$ $(364968p+1)^{1}$ $\bigr]$
$b=-37, p=7,$ $\bigl[$ $(356886756p+1)^{1}$ $\bigr]$
$b=-37, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(188p+1)^{1}$ , $(8944464738p+1)^{1}$ $\bigr]$
$b=-37, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(45474p+1)^{1}$ , $(15736652326p+1)^{1}$ $\bigr]$
$b=-37, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(6860559993177359635158p+1)^{1}$ $\bigr]$
$b=-37, p=19,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(10p+1)^{1}$ , $(426142152p+1)^{1}$ , $(29457812651728p+1)^{1}$ $\bigr]$
$b=-37, p=23,$ $\bigl[$ $(17264p+1)^{1}$ , $(65010p+1)^{1}$ , $(67647756p+1)^{1}$ , $(1450669032266p+1)^{1}$ $\bigr]$
$b=-37, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(12p+1)^{1}$ , $(1362p+1)^{1}$ , $(3352778509681095704437293763081652p+1)^{1}$ $\bigr]$
$b=-37, p=31,$ $\bigl[$ $(22p+1)^{1}$ , $(36p+1)^{1}$ , $(60p+1)^{1}$ , $(208p+1)^{1}$ , $(2752p+1)^{1}$ , $(25198327236p+1)^{1}$ , $(5723305248671086p+1)^{1}$ $\bigr]$
$b=-37, p=37,$ $\bigl[$ $(16p+1)^{1}$ , $(3625276p+1)^{1}$ , $(117730600p+1)^{1}$ , $(167297460p+1)^{1}$ , $(3500248032963047748708304p+1)^{1}$ $\bigr]$
$b=-37, p=41,$ $\bigl[$ $(20p+1)^{1}$ , $(1422728318p+1)^{1}$ , $(12230546480557554876p+1)^{1}$ , $(528718521727591672579066446p+1)^{1}$ $\bigr]$
$b=-37, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(24p+1)^{1}$ , $(24539292p+1)^{1}$ , $(14730531174640852743952p+1)^{1}$ , $(138758089143705398905733844p+1)^{1}$ $\bigr]$
$b=-37, p=47,$ $\bigl[$ $(20p+1)^{1}$ , $(908p+1)^{1}$ , $(52034530902146322943010295906p+1)^{1}$ , $(289352053365322884145866947742366p+1)^{1}$ $\bigr]$
$b=-36, p=2,$ $\bigl[$ $(2p+1)^{1}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=-36, p=3,$ $\bigl[$ $(4p+1)^{1}$ , $(32p+1)^{1}$ $\bigr]$
$b=-36, p=5,$ $\bigl[$ $(48p+1)^{1}$ , $(1356p+1)^{1}$ $\bigr]$
$b=-36, p=7,$ $\bigl[$ $(60p+1)^{1}$ , $(718680p+1)^{1}$ $\bigr]$
$b=-36, p=11,$ $\bigl[$ $(5316p+1)^{1}$ , $(6408p+1)^{1}$ , $(78456p+1)^{1}$ $\bigr]$
$b=-36, p=13,$ $\bigl[$ $(24p+1)^{1}$ , $(180p+1)^{1}$ , $(483995899632p+1)^{1}$ $\bigr]$
$b=-36, p=17,$ $\bigl[$ $(54948p+1)^{1}$ , $(487630196785963176p+1)^{1}$ $\bigr]$
$b=-36, p=19,$ $\bigl[$ $(54250672692p+1)^{1}$ , $(512428718054832p+1)^{1}$ $\bigr]$
$b=-36, p=23,$ $\bigl[$ $(264p+1)^{1}$ , $(98256p+1)^{1}$ , $(415860p+1)^{1}$ , $(5582934562951464p+1)^{1}$ $\bigr]$
$b=-36, p=29,$ $\bigl[$ $(12p+1)^{1}$ , $(3625328567923416264500056246873387852752p+1)^{1}$ $\bigr]$
$b=-36, p=31,$ $\bigl[$ $(1533960250483708168801760315480283992296242900p+1)^{1}$ $\bigr]$
$b=-36, p=37,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(120p+1)^{1}$ , $(89190362184744p+1)^{1}$ , $(5159254259946567401109982350686568p+1)^{1}$ $\bigr]$
$b=-36, p=41,$ $\bigl[$ $(98700p+1)^{1}$ , $(4256613000p+1)^{1}$ , $(6004375029423458255279070779470584135051000p+1)^{1}$ $\bigr]$
$b=-36, p=43,$ $\bigl[$ $(24p+1)^{1}$ , $(151200p+1)^{1}$ , $(67785232311070767924p+1)^{1}$ , $(267678305210577060297251647581336p+1)^{1}$ $\bigr]$
$b=-36, p=47,$ $\bigl[$ $(36p+1)^{1}$ , $(21905075407409014836p+1)^{1}$ , $(650760901394333771340p+1)^{1}$ , $(151042468762359802202784p+1)^{1}$ $\bigr]$
$b=-35, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(8p+1)^{1}$ $\bigr]$
$b=-35, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(132p+1)^{1}$ $\bigr]$
$b=-35, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(26526p+1)^{1}$ $\bigr]$
$b=-35, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(744p+1)^{1}$ , $(1690p+1)^{1}$ $\bigr]$
$b=-35, p=11,$ $\bigl[$ $(243811003467290p+1)^{1}$ $\bigr]$
$b=-35, p=13,$ $\bigl[$ $(252719482440133380p+1)^{1}$ $\bigr]$
$b=-35, p=17,$ $\bigl[$ $(18p+1)^{1}$ , $(3048p+1)^{1}$ , $(18230336745564914p+1)^{1}$ $\bigr]$
$b=-35, p=19,$ $\bigl[$ $(697194p+1)^{1}$ , $(23995481346381961368p+1)^{1}$ $\bigr]$
$b=-35, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(352514p+1)^{1}$ , $(1034028636192284401022270p+1)^{1}$ $\bigr]$
$b=-35, p=29,$ $\bigl[$ $(539189813108p+1)^{1}$ , $(36739488963949239373520521344p+1)^{1}$ $\bigr]$
$b=-35, p=31,$ $\bigl[$ $(762p+1)^{1}$ , $(57265787608p+1)^{1}$ , $(15698320745823019722845532172p+1)^{1}$ $\bigr]$
$b=-35, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(50056p+1)^{1}$ , $(67800474532354p+1)^{1}$ , $(1464652474396410553292031961018p+1)^{1}$ $\bigr]$
$b=-35, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(61750694756274021102p+1)^{1}$ , $(6534308934749646625159531400576390748p+1)^{1}$ $\bigr]$
$b=-35, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(132402p+1)^{1}$ , $(336365095268506p+1)^{1}$ , $(21876698151520074p+1)^{1}$ , $(119678506819175554164p+1)^{1}$ $\bigr]$
$b=-35, p=47,$ $\bigl[$ $(145853688p+1)^{1}$ , $(24893589667987792680079503428p+1)^{1}$ , $(274534588124064869392786269474p+1)^{1}$ $\bigr]$
$b=-34, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ , $\color{magenta}\bm{(5p+1)^{1}}$ $\bigr]$
$b=-34, p=3,$ $\bigl[$ $(374p+1)^{1}$ $\bigr]$
$b=-34, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(51926p+1)^{1}$ $\bigr]$
$b=-34, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(4p+1)^{1}$ , $(10p+1)^{1}$ , $(14874p+1)^{1}$ $\bigr]$
$b=-34, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(7926464555396p+1)^{1}$ $\bigr]$
$b=-34, p=13,$ $\bigl[$ $(154614p+1)^{1}$ , $(88720124100p+1)^{1}$ $\bigr]$
$b=-34, p=17,$ $\bigl[$ $(18p+1)^{1}$ , $(26p+1)^{1}$ , $(90p+1)^{1}$ , $(1650p+1)^{1}$ , $(6626p+1)^{1}$ , $(276984p+1)^{1}$ $\bigr]$
$b=-34, p=19,$ $\bigl[$ $(22182200670p+1)^{1}$ , $(447218280791952p+1)^{1}$ $\bigr]$
$b=-34, p=23,$ $\bigl[$ $(173294506812p+1)^{1}$ , $(52204336352758975746p+1)^{1}$ $\bigr]$
$b=-34, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(15778974p+1)^{1}$ , $(56861883754280p+1)^{1}$ , $(5726305840646598p+1)^{1}$ $\bigr]$
$b=-34, p=31,$ $\bigl[$ $(348p+1)^{1}$ , $(25552623561615814423045380275200072941138p+1)^{1}$ $\bigr]$
$b=-34, p=37,$ $\bigl[$ $(100937399794936445596p+1)^{1}$ , $(95542439327014103841871518361534p+1)^{1}$ $\bigr]$
$b=-34, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(86660p+1)^{1}$ , $(197006p+1)^{1}$ , $(18132692029421887596p+1)^{1}$ , $(242992816990224440245382p+1)^{1}$ $\bigr]$
$b=-34, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(126p+1)^{1}$ , $(2452p+1)^{1}$ , $(106957118338719189401674p+1)^{1}$ , $(1043327102439829669834667026p+1)^{1}$ $\bigr]$
$b=-34, p=47,$ $\bigl[$ $(174p+1)^{1}$ , $(54724256424p+1)^{1}$ , $(65338280298778902973724p+1)^{1}$ , $(8976348507087716801393169956p+1)^{1}$ $\bigr]$
$b=-33, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{5}}$ $\bigr]$
$b=-33, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(50p+1)^{1}$ $\bigr]$
$b=-33, p=5,$ $\bigl[$ $(230208p+1)^{1}$ $\bigr]$
$b=-33, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(28p+1)^{1}$ , $(31344p+1)^{1}$ $\bigr]$
$b=-33, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(170p+1)^{1}$ , $(3140364888p+1)^{1}$ $\bigr]$
$b=-33, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(24p+1)^{1}$ , $(1516p+1)^{1}$ , $(255518842p+1)^{1}$ $\bigr]$
$b=-33, p=17,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(7785004916p+1)^{1}$ , $(50194069260p+1)^{1}$ $\bigr]$
$b=-33, p=19,$ $\bigl[$ $(142p+1)^{1}$ , $(7540p+1)^{1}$ , $(2590828p+1)^{1}$ , $(5781084070p+1)^{1}$ $\bigr]$
$b=-33, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(1160p+1)^{1}$ , $(321306p+1)^{1}$ , $(3934922p+1)^{1}$ , $(924673484p+1)^{1}$ $\bigr]$
$b=-33, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(18p+1)^{1}$ , $(26163480p+1)^{1}$ , $(2269082172p+1)^{1}$ , $(71669093619759764p+1)^{1}$ $\bigr]$
$b=-33, p=31,$ $\bigl[$ $(129126p+1)^{1}$ , $(28100627960666268782546190445822367310p+1)^{1}$ $\bigr]$
$b=-33, p=37,$ $\bigl[$ $(186p+1)^{1}$ , $(54867166p+1)^{1}$ , $(621406080p+1)^{1}$ , $(378848777065970268355524794044p+1)^{1}$ $\bigr]$
$b=-33, p=41,$ $\bigl[$ $(16239131408993664350p+1)^{1}$ , $(195642006516822005850451400179699663550p+1)^{1}$ $\bigr]$
$b=-33, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(22p+1)^{1}$ , $(12694p+1)^{1}$ , $(557309385432p+1)^{1}$ , $(63113665290498526644677490895215047932p+1)^{1}$ $\bigr]$
$b=-33, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(174p+1)^{1}$ , $(63400364622957923369914011982855316174682683833304096826152640p+1)^{1}$ $\bigr]$
$b=-32, p=2,$ $\bigl[$ $\color{magenta}\bm{(15p+1)^{1}}$ $\bigr]$
$b=-32, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(110p+1)^{1}$ $\bigr]$
$b=-32, p=5,$ $\bigl[$ $(50p+1)^{1}$ , $(810p+1)^{1}$ $\bigr]$
$b=-32, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(40p+1)^{1}$ , $(12310p+1)^{1}$ $\bigr]$
$b=-32, p=11,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(62p+1)^{1}$ , $(270p+1)^{1}$ , $(4446590p+1)^{1}$ $\bigr]$
$b=-32, p=13,$ $\bigl[$ $(10p+1)^{1}$ , $(210p+1)^{1}$ , $(31530p+1)^{1}$ , $(586450p+1)^{1}$ $\bigr]$
$b=-32, p=17,$ $\bigl[$ $(2570p+1)^{1}$ , $(1578319002121491330p+1)^{1}$ $\bigr]$
$b=-32, p=19,$ $\bigl[$ $(120p+1)^{1}$ , $(9198p+1)^{1}$ , $(158491972611276270p+1)^{1}$ $\bigr]$
$b=-32, p=23,$ $\bigl[$ $(30p+1)^{1}$ , $(121574p+1)^{1}$ , $(81917550p+1)^{1}$ , $(15033364572630p+1)^{1}$ $\bigr]$
$b=-32, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(104592p+1)^{1}$ , $(260480p+1)^{1}$ , $(34475960507748803478753290p+1)^{1}$ $\bigr]$
$b=-32, p=31,$ $\bigl[$ $(360p+1)^{1}$ , $(23091222p+1)^{1}$ , $(191858168432190p+1)^{1}$ , $(939550194940920p+1)^{1}$ $\bigr]$
$b=-32, p=37,$ $\bigl[$ $(40p+1)^{1}$ , $(48p+1)^{1}$ , $(696786p+1)^{1}$ , $(760450p+1)^{1}$ , $(21038631497240205636232927861440p+1)^{1}$ $\bigr]$
$b=-32, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(215400456p+1)^{1}$ , $(51849282033888720326591314483770679189202557650p+1)^{1}$ $\bigr]$
$b=-32, p=43,$ $\bigl[$ $(211270p+1)^{1}$ , $(68186767614p+1)^{1}$ , $(1393130427411759566916980990900272068003040p+1)^{1}$ $\bigr]$
$b=-32, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(3526990160p+1)^{1}$ , $(6978858350p+1)^{1}$ , $(9825487403191430p+1)^{1}$ , $(5009731372555151384826270p+1)^{1}$ $\bigr]$
$b=-31, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ , $(2p+1)^{1}$ $\bigr]$
$b=-31, p=3,$ $\bigl[$ $(2p+1)^{2}$ , $(6p+1)^{1}$ $\bigr]$
$b=-31, p=5,$ $\bigl[$ $(8p+1)^{1}$ , $(4364p+1)^{1}$ $\bigr]$
$b=-31, p=7,$ $\bigl[$ $(1710p+1)^{1}$ , $(10260p+1)^{1}$ $\bigr]$
$b=-31, p=11,$ $\bigl[$ $(68840p+1)^{1}$ , $(95323910p+1)^{1}$ $\bigr]$
$b=-31, p=13,$ $\bigl[$ $(1374p+1)^{1}$ , $(3285899611122p+1)^{1}$ $\bigr]$
$b=-31, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(402450684861556667238p+1)^{1}$ $\bigr]$
$b=-31, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(186610138984313827799620p+1)^{1}$ $\bigr]$
$b=-31, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(1974541244p+1)^{1}$ , $(12739407806743186140p+1)^{1}$ $\bigr]$
$b=-31, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(63402p+1)^{1}$ , $(57639375374p+1)^{1}$ , $(105553023452297189538p+1)^{1}$ $\bigr]$
$b=-31, p=31,$ $\bigl[$ $(12p+1)^{1}$ , $(52p+1)^{1}$ , $(2028p+1)^{1}$ , $(4696p+1)^{1}$ , $(1154488918846p+1)^{1}$ , $(87312587176408p+1)^{1}$ $\bigr]$
$b=-31, p=37,$ $\bigl[$ $(26215232082463718491954p+1)^{1}$ , $(13190933731948595215031244934p+1)^{1}$ $\bigr]$
$b=-31, p=41,$ $\bigl[$ $(172364231373894192p+1)^{1}$ , $(1508914418200399601824613067810632026296p+1)^{1}$ $\bigr]$
$b=-31, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(56479168960785064437315677401185635608953657666185937768322p+1)^{1}$ $\bigr]$
$b=-31, p=47,$ $\bigl[$ $(14p+1)^{1}$ , $(440p+1)^{1}$ , $(6868620p+1)^{1}$ , $(1876408861887289142548612032748194249375830389378344p+1)^{1}$ $\bigr]$

Mizar/みざー

$b=-30, p=2,$ $\bigl[$ $(14p+1)^{1}$ $\bigr]$
$b=-30, p=3,$ $\bigl[$ $(4p+1)^{1}$ , $(22p+1)^{1}$ $\bigr]$
$b=-30, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(14252p+1)^{1}$ $\bigr]$
$b=-30, p=7,$ $\bigl[$ $(90p+1)^{1}$ , $(159720p+1)^{1}$ $\bigr]$
$b=-30, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(8072p+1)^{1}$ , $(25437408p+1)^{1}$ $\bigr]$
$b=-30, p=13,$ $\bigl[$ $(42p+1)^{1}$ , $(15936p+1)^{1}$ , $(349107492p+1)^{1}$ $\bigr]$
$b=-30, p=17,$ $\bigl[$ $(36p+1)^{1}$ , $(426p+1)^{1}$ , $(33278p+1)^{1}$ , $(9755844038p+1)^{1}$ $\bigr]$
$b=-30, p=19,$ $\bigl[$ $(11934684p+1)^{1}$ , $(87020989553055318p+1)^{1}$ $\bigr]$
$b=-30, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(6452814p+1)^{1}$ , $(86210964p+1)^{1}$ , $(954627953642p+1)^{1}$ $\bigr]$
$b=-30, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(75319776895532918p+1)^{1}$ , $(59237628074273149338p+1)^{1}$ $\bigr]$
$b=-30, p=31,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(132p+1)^{1}$ , $(628p+1)^{1}$ , $(1572p+1)^{1}$ , $(3748p+1)^{1}$ , $(4486649436p+1)^{1}$ , $(3303820416756p+1)^{1}$ $\bigr]$
$b=-30, p=37,$ $\bigl[$ $(34p+1)^{1}$ , $(256p+1)^{1}$ , $(5140p+1)^{1}$ , $(5341714p+1)^{1}$ , $(6050148p+1)^{1}$ , $(39119431066399340767350p+1)^{1}$ $\bigr]$
$b=-30, p=41,$ $\bigl[$ $(68p+1)^{1}$ , $(1028909977552331625479326306928506081692746512586397218p+1)^{1}$ $\bigr]$
$b=-30, p=43,$ $\bigl[$ $(771804124120876869600580p+1)^{1}$ , $(74200742831014849834494068234576110p+1)^{1}$ $\bigr]$
$b=-30, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(49965675628842341520006p+1)^{1}$ , $(2745891434422000637438866279931616741354p+1)^{1}$ $\bigr]$
$b=-29, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=-29, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(90p+1)^{1}$ $\bigr]$
$b=-29, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(80p+1)^{1}$ $\bigr]$
$b=-29, p=7,$ $\bigl[$ $(82142268p+1)^{1}$ $\bigr]$
$b=-29, p=11,$ $\bigl[$ $(510762p+1)^{1}$ , $(6580406p+1)^{1}$ $\bigr]$
$b=-29, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(262p+1)^{1}$ , $(576p+1)^{1}$ , $(19455282p+1)^{1}$ $\bigr]$
$b=-29, p=17,$ $\bigl[$ $(116p+1)^{1}$ , $(228098p+1)^{1}$ , $(1859936821118p+1)^{1}$ $\bigr]$
$b=-29, p=19,$ $\bigl[$ $(882p+1)^{1}$ , $(638908996432395213630p+1)^{1}$ $\bigr]$
$b=-29, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(133108871962670853245168620806p+1)^{1}$ $\bigr]$
$b=-29, p=29,$ $\bigl[$ $(8p+1)^{1}$ , $(236724p+1)^{1}$ , $(327169788p+1)^{1}$ , $(194471168231605003008p+1)^{1}$ $\bigr]$
$b=-29, p=31,$ $\bigl[$ $(119272p+1)^{1}$ , $(6211422136p+1)^{1}$ , $(3261383983005765690347820p+1)^{1}$ $\bigr]$
$b=-29, p=37,$ $\bigl[$ $(34p+1)^{1}$ , $(264p+1)^{1}$ , $(515819879040p+1)^{1}$ , $(4929777342146324878530025297738p+1)^{1}$ $\bigr]$
$b=-29, p=41,$ $\bigl[$ $(506p+1)^{1}$ , $(19808p+1)^{1}$ , $(35448p+1)^{1}$ , $(123308p+1)^{1}$ , $(90525476p+1)^{1}$ , $(8538269718p+1)^{1}$ , $(4591694520668p+1)^{1}$ $\bigr]$
$b=-29, p=43,$ $\bigl[$ $(26452690596p+1)^{1}$ , $(47140692469962417856p+1)^{1}$ , $(256874786458246606390152304p+1)^{1}$ $\bigr]$
$b=-29, p=47,$ $\bigl[$ $(79584196146p+1)^{1}$ , $(29003685959834p+1)^{1}$ , $(3155221893563850p+1)^{1}$ , $(506854468833813272070p+1)^{1}$ $\bigr]$
$b=-28, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{3}}$ $\bigr]$
$b=-28, p=3,$ $\bigl[$ $(252p+1)^{1}$ $\bigr]$
$b=-28, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(10790p+1)^{1}$ $\bigr]$
$b=-28, p=7,$ $\bigl[$ $(1858p+1)^{1}$ , $(5110p+1)^{1}$ $\bigr]$
$b=-28, p=11,$ $\bigl[$ $(2p+1)^{2}$ , $(49146431532p+1)^{1}$ $\bigr]$
$b=-28, p=13,$ $\bigl[$ $(42p+1)^{1}$ , $(172p+1)^{1}$ , $(8820p+1)^{1}$ , $(122926p+1)^{1}$ $\bigr]$
$b=-28, p=17,$ $\bigl[$ $(14p+1)^{1}$ , $(36p+1)^{1}$ , $(138p+1)^{1}$ , $(518p+1)^{1}$ , $(2676949338p+1)^{1}$ $\bigr]$
$b=-28, p=19,$ $\bigl[$ $(5686577949236675919184764p+1)^{1}$ $\bigr]$
$b=-28, p=23,$ $\bigl[$ $(5006610p+1)^{1}$ , $(6116026980p+1)^{1}$ , $(178254316842p+1)^{1}$ $\bigr]$
$b=-28, p=29,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(1394p+1)^{1}$ , $(37052p+1)^{1}$ , $(876006529511845602406161998p+1)^{1}$ $\bigr]$
$b=-28, p=31,$ $\bigl[$ $(42p+1)^{1}$ , $(2215837786p+1)^{1}$ , $(9042639271516565395869497356p+1)^{1}$ $\bigr]$
$b=-28, p=37,$ $\bigl[$ $(27153800266p+1)^{1}$ , $(325248344329596037293522270894850649278p+1)^{1}$ $\bigr]$
$b=-28, p=41,$ $\bigl[$ $(220704362p+1)^{1}$ , $(4004291620559832p+1)^{1}$ , $(122009346773643642938388131318p+1)^{1}$ $\bigr]$
$b=-28, p=43,$ $\bigl[$ $(136p+1)^{1}$ , $(567112p+1)^{1}$ , $(949970157468576922959203695884683981860136539596p+1)^{1}$ $\bigr]$
$b=-28, p=47,$ $\bigl[$ $(3730291904p+1)^{1}$ , $(40261539015656p+1)^{1}$ , $(229669175712889246422305069051893531140p+1)^{1}$ $\bigr]$
$b=-27, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(6p+1)^{1}$ $\bigr]$
$b=-27, p=3,$ $\bigl[$ $(6p+1)^{1}$ , $(12p+1)^{1}$ $\bigr]$
$b=-27, p=5,$ $\bigl[$ $(6p+1)^{1}$ , $(12p+1)^{1}$ , $(54p+1)^{1}$ $\bigr]$
$b=-27, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(6p+1)^{1}$ , $(78p+1)^{1}$ , $(324p+1)^{1}$ $\bigr]$
$b=-27, p=11,$ $\bigl[$ $(6p+1)^{1}$ , $(60p+1)^{1}$ , $(2310p+1)^{1}$ , $(16038p+1)^{1}$ $\bigr]$
$b=-27, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(12p+1)^{1}$ , $(222p+1)^{1}$ , $(780p+1)^{1}$ , $(30660p+1)^{1}$ $\bigr]$
$b=-27, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(18p+1)^{1}$ , $(36p+1)^{1}$ , $(60p+1)^{1}$ , $(1770p+1)^{1}$ , $(7597638p+1)^{1}$ $\bigr]$
$b=-27, p=19,$ $\bigl[$ $(150p+1)^{1}$ , $(162p+1)^{1}$ , $(2838p+1)^{1}$ , $(5364p+1)^{1}$ , $(61174764p+1)^{1}$ $\bigr]$
$b=-27, p=23,$ $\bigl[$ $(6p+1)^{1}$ , $(222p+1)^{1}$ , $(396p+1)^{1}$ , $(5766p+1)^{1}$ , $(64194p+1)^{1}$ , $(1023295422p+1)^{1}$ $\bigr]$
$b=-27, p=29,$ $\bigl[$ $(12p+1)^{1}$ , $(18p+1)^{1}$ , $(210p+1)^{1}$ , $(4902p+1)^{1}$ , $(9024p+1)^{1}$ , $(47700p+1)^{1}$ , $(185724p+1)^{1}$ , $(1291878p+1)^{1}$ $\bigr]$
$b=-27, p=31,$ $\bigl[$ $(12p+1)^{1}$ , $(222p+1)^{1}$ , $(17466p+1)^{1}$ , $(98658p+1)^{1}$ , $(723701448p+1)^{1}$ , $(2846420982660p+1)^{1}$ $\bigr]$
$b=-27, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(498p+1)^{1}$ , $(2910p+1)^{1}$ , $(694854p+1)^{1}$ , $(1533456p+1)^{1}$ , $(2122680p+1)^{1}$ , $(1738547903680536p+1)^{1}$ $\bigr]$
$b=-27, p=41,$ $\bigl[$ $(822p+1)^{1}$ , $(57000p+1)^{1}$ , $(976818p+1)^{1}$ , $(3173160396p+1)^{1}$ , $(380652501966p+1)^{1}$ , $(6598709888526p+1)^{1}$ $\bigr]$
$b=-27, p=43,$ $\bigl[$ $(36p+1)^{1}$ , $(630p+1)^{1}$ , $(38405580p+1)^{1}$ , $(660365952p+1)^{1}$ , $(181915223094p+1)^{1}$ , $(1908470740665913242p+1)^{1}$ $\bigr]$
$b=-27, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(360p+1)^{1}$ , $(5448p+1)^{1}$ , $(32642126550p+1)^{1}$ , $(1999008672932491824p+1)^{1}$ , $(80817064921701923478p+1)^{1}$ $\bigr]$
$b=-26, p=2,$ $\bigl[$ $(2p+1)^{2}$ $\bigr]$
$b=-26, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(10p+1)^{1}$ $\bigr]$
$b=-26, p=5,$ $\bigl[$ $(86p+1)^{1}$ , $(204p+1)^{1}$ $\bigr]$
$b=-26, p=7,$ $\bigl[$ $(10p+1)^{2}$ , $(8430p+1)^{1}$ $\bigr]$
$b=-26, p=11,$ $\bigl[$ $(12358062245750p+1)^{1}$ $\bigr]$
$b=-26, p=13,$ $\bigl[$ $(72p+1)^{1}$ , $(496p+1)^{1}$ , $(2946p+1)^{1}$ , $(30544p+1)^{1}$ $\bigr]$
$b=-26, p=17,$ $\bigl[$ $(194p+1)^{1}$ , $(294p+1)^{1}$ , $(113840p+1)^{1}$ , $(77397110p+1)^{1}$ $\bigr]$
$b=-26, p=19,$ $\bigl[$ $(12p+1)^{1}$ , $(6524402778419281139922p+1)^{1}$ $\bigr]$
$b=-26, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(50336p+1)^{1}$ , $(16464060p+1)^{1}$ , $(27373217981192p+1)^{1}$ $\bigr]$
$b=-26, p=29,$ $\bigl[$ $(3237188p+1)^{1}$ , $(89414443094p+1)^{1}$ , $(567667108012607480p+1)^{1}$ $\bigr]$
$b=-26, p=31,$ $\bigl[$ $(166p+1)^{1}$ , $(491638471981096p+1)^{1}$ , $(1114003632082214543088p+1)^{1}$ $\bigr]$
$b=-26, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(1740526p+1)^{1}$ , $(10570000534233326004731979787465544550p+1)^{1}$ $\bigr]$
$b=-26, p=41,$ $\bigl[$ $(236p+1)^{1}$ , $(37380p+1)^{1}$ , $(628920089766421743768350638842232354211071842p+1)^{1}$ $\bigr]$
$b=-26, p=43,$ $\bigl[$ $(15844p+1)^{1}$ , $(8824453444755052646996782225902119837723617708562842p+1)^{1}$ $\bigr]$
$b=-26, p=47,$ $\bigl[$ $(56979674p+1)^{1}$ , $(938572692246250128959125042360958843127715368970403244p+1)^{1}$ $\bigr]$
$b=-25, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{3}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=-25, p=3,$ $\bigl[$ $(200p+1)^{1}$ $\bigr]$
$b=-25, p=5,$ $\bigl[$ $(8p+1)^{1}$ , $(1832p+1)^{1}$ $\bigr]$
$b=-25, p=7,$ $\bigl[$ $(33535800p+1)^{1}$ $\bigr]$
$b=-25, p=11,$ $\bigl[$ $(8p+1)^{1}$ , $(93666448928p+1)^{1}$ $\bigr]$
$b=-25, p=13,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(4p+1)^{1}$ , $(6398588638816p+1)^{1}$ $\bigr]$
$b=-25, p=17,$ $\bigl[$ $(116p+1)^{1}$ , $(1184p+1)^{1}$ , $(2664p+1)^{1}$ , $(732176628p+1)^{1}$ $\bigr]$
$b=-25, p=19,$ $\bigl[$ $(257114112p+1)^{1}$ , $(150748743432072p+1)^{1}$ $\bigr]$
$b=-25, p=23,$ $\bigl[$ $(237639710956555246110743902200p+1)^{1}$ $\bigr]$
$b=-25, p=29,$ $\bigl[$ $(46013885304424591363711524705355616400p+1)^{1}$ $\bigr]$
$b=-25, p=31,$ $\bigl[$ $(262084023160164888p+1)^{1}$ , $(3311333984629679608128p+1)^{1}$ $\bigr]$
$b=-25, p=37,$ $\bigl[$ $(264p+1)^{1}$ , $(1104p+1)^{1}$ , $(13790299867464425890019820646454619404760p+1)^{1}$ $\bigr]$
$b=-25, p=41,$ $\bigl[$ $(4716p+1)^{1}$ , $(155000p+1)^{1}$ , $(28005019080p+1)^{1}$ , $(1374953145188356793429243445572p+1)^{1}$ $\bigr]$
$b=-25, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(50497403884p+1)^{1}$ , $(3077478017282873067820566625080476858909736p+1)^{1}$ $\bigr]$
$b=-25, p=47,$ $\bigl[$ $(108p+1)^{1}$ , $(264p+1)^{1}$ , $(7012200366396p+1)^{1}$ , $(19898167329792153375587304604893052579704p+1)^{1}$ $\bigr]$
$b=-24, p=2,$ $\bigl[$ $\color{magenta}\bm{(11p+1)^{1}}$ $\bigr]$
$b=-24, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(26p+1)^{1}$ $\bigr]$
$b=-24, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(1158p+1)^{1}$ $\bigr]$
$b=-24, p=7,$ $\bigl[$ $(26208408p+1)^{1}$ $\bigr]$
$b=-24, p=11,$ $\bigl[$ $(5533385975160p+1)^{1}$ $\bigr]$
$b=-24, p=13,$ $\bigl[$ $(10p+1)^{1}$ , $(2554p+1)^{1}$ , $(5910p+1)^{1}$ , $(8070p+1)^{1}$ $\bigr]$
$b=-24, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(596p+1)^{1}$ , $(655581835224146p+1)^{1}$ $\bigr]$
$b=-24, p=19,$ $\bigl[$ $(352630589284263480150072p+1)^{1}$ $\bigr]$
$b=-24, p=23,$ $\bigl[$ $(4296p+1)^{1}$ , $(978124665380833644979152p+1)^{1}$ $\bigr]$
$b=-24, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(50p+1)^{1}$ , $(171107316003380514313589215984320p+1)^{1}$ $\bigr]$
$b=-24, p=31,$ $\bigl[$ $(299665483321026p+1)^{1}$ , $(849666263511568943513322p+1)^{1}$ $\bigr]$
$b=-24, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(19584p+1)^{1}$ , $(94259574330648p+1)^{1}$ , $(3356270997170151562985020p+1)^{1}$ $\bigr]$
$b=-24, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(4558888310285956811927109239866270908971226364853186p+1)^{1}$ $\bigr]$
$b=-24, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(70p+1)^{1}$ , $(480p+1)^{1}$ , $(19328018688284471976887528223897403419732225930p+1)^{1}$ $\bigr]$
$b=-24, p=47,$ $\bigl[$ $(14p+1)^{1}$ , $(470p+1)^{1}$ , $(1025510p+1)^{1}$ , $(4300268p+1)^{1}$ , $(273290483534p+1)^{1}$ , $(34628699967595250660662700p+1)^{1}$ $\bigr]$
$b=-23, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(5p+1)^{1}}$ $\bigr]$
$b=-23, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(4p+1)^{2}$ $\bigr]$
$b=-23, p=5,$ $\bigl[$ $(6p+1)^{1}$ , $(8p+1)^{1}$ , $(42p+1)^{1}$ $\bigr]$
$b=-23, p=7,$ $\bigl[$ $(10p+1)^{1}$ , $(96p+1)^{1}$ , $(424p+1)^{1}$ $\bigr]$
$b=-23, p=11,$ $\bigl[$ $(3609127870886p+1)^{1}$ $\bigr]$
$b=-23, p=13,$ $\bigl[$ $(1615501160052780p+1)^{1}$ $\bigr]$
$b=-23, p=17,$ $\bigl[$ $(14p+1)^{1}$ , $(6914p+1)^{1}$ , $(12306460349300p+1)^{1}$ $\bigr]$
$b=-23, p=19,$ $\bigl[$ $(25990p+1)^{1}$ , $(168178p+1)^{1}$ , $(103700383242p+1)^{1}$ $\bigr]$
$b=-23, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(44p+1)^{1}$ , $(71360p+1)^{1}$ , $(2288090p+1)^{1}$ , $(66175184p+1)^{1}$ $\bigr]$
$b=-23, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(37102885418p+1)^{1}$ , $(69958471186897277401868p+1)^{1}$ $\bigr]$
$b=-23, p=31,$ $\bigl[$ $(260866p+1)^{1}$ , $(74634699088078p+1)^{1}$ , $(117464943597139038p+1)^{1}$ $\bigr]$
$b=-23, p=37,$ $\bigl[$ $(16p+1)^{1}$ , $(282317418052786181316p+1)^{1}$ , $(44007112743484642811344p+1)^{1}$ $\bigr]$
$b=-23, p=41,$ $\bigl[$ $(27668p+1)^{1}$ , $(1076279180p+1)^{1}$ , $(1375230120631910804961331130870498168p+1)^{1}$ $\bigr]$
$b=-23, p=43,$ $\bigl[$ $(1524251314p+1)^{1}$ , $(529775924209940699437657936387022538752217676p+1)^{1}$ $\bigr]$
$b=-23, p=47,$ $\bigl[$ $(19321554207758556p+1)^{1}$ , $(9789472202178766040319656173297038243758294p+1)^{1}$ $\bigr]$
$b=-22, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=-22, p=3,$ $\bigl[$ $(154p+1)^{1}$ $\bigr]$
$b=-22, p=5,$ $\bigl[$ $(44814p+1)^{1}$ $\bigr]$
$b=-22, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(12424p+1)^{1}$ $\bigr]$
$b=-22, p=11,$ $\bigl[$ $(8p+1)^{1}$ , $(25950095546p+1)^{1}$ $\bigr]$
$b=-22, p=13,$ $\bigl[$ $(945853036398270p+1)^{1}$ $\bigr]$
$b=-22, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(8p+1)^{1}$ , $(7529466p+1)^{1}$ , $(93807578p+1)^{1}$ $\bigr]$
$b=-22, p=19,$ $\bigl[$ $(1261458p+1)^{1}$ , $(3061421192388240p+1)^{1}$ $\bigr]$
$b=-22, p=23,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(20p+1)^{1}$ , $(60p+1)^{1}$ , $(84p+1)^{1}$ , $(10673671558676630p+1)^{1}$ $\bigr]$
$b=-22, p=29,$ $\bigl[$ $(14760p+1)^{1}$ , $(78747362p+1)^{1}$ , $(522125592p+1)^{1}$ , $(86265977780p+1)^{1}$ $\bigr]$
$b=-22, p=31,$ $\bigl[$ $(12p+1)^{1}$ , $(786089320589790p+1)^{1}$ , $(63602055839444208360p+1)^{1}$ $\bigr]$
$b=-22, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(60p+1)^{1}$ , $(1308p+1)^{1}$ , $(263465498431410496p+1)^{1}$ , $(351747392278443594p+1)^{1}$ $\bigr]$
$b=-22, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(4477918088p+1)^{1}$ , $(761868691448917044938731529875599341652p+1)^{1}$ $\bigr]$
$b=-22, p=43,$ $\bigl[$ $(5357707300369360677465270773728795817256204058549595634p+1)^{1}$ $\bigr]$
$b=-22, p=47,$ $\bigl[$ $(4164p+1)^{1}$ , $(1824168036p+1)^{1}$ , $(68433193519583829801019595356508881417465554p+1)^{1}$ $\bigr]$
$b=-21, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $(2p+1)^{1}$ $\bigr]$
$b=-21, p=3,$ $\bigl[$ $(140p+1)^{1}$ $\bigr]$
$b=-21, p=5,$ $\bigl[$ $(37128p+1)^{1}$ $\bigr]$
$b=-21, p=7,$ $\bigl[$ $(11695380p+1)^{1}$ $\bigr]$
$b=-21, p=11,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(552p+1)^{1}$ , $(942048p+1)^{1}$ $\bigr]$
$b=-21, p=13,$ $\bigl[$ $(540113208878040p+1)^{1}$ $\bigr]$
$b=-21, p=17,$ $\bigl[$ $(704p+1)^{1}$ , $(6711174655534304p+1)^{1}$ $\bigr]$
$b=-21, p=19,$ $\bigl[$ $(32088p+1)^{1}$ , $(51986832349586484p+1)^{1}$ $\bigr]$
$b=-21, p=23,$ $\bigl[$ $(12p+1)^{1}$ , $(20p+1)^{1}$ , $(26p+1)^{1}$ , $(30p+1)^{1}$ , $(96340234219337112p+1)^{1}$ $\bigr]$
$b=-21, p=29,$ $\bigl[$ $(44p+1)^{1}$ , $(271236399845859022689839828918588p+1)^{1}$ $\bigr]$
$b=-21, p=31,$ $\bigl[$ $(2518p+1)^{1}$ , $(1830588706727557385082715236281098p+1)^{1}$ $\bigr]$
$b=-21, p=37,$ $\bigl[$ $(10268086066974522442092428252601421726520683080p+1)^{1}$ $\bigr]$
$b=-21, p=41,$ $\bigl[$ $(30p+1)^{1}$ , $(43076p+1)^{1}$ , $(828909319939460518802524214262117937622882p+1)^{1}$ $\bigr]$
$b=-21, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(366p+1)^{1}$ , $(2950p+1)^{1}$ , $(3938780196p+1)^{1}$ , $(27053686662p+1)^{1}$ , $(11135155620391714650p+1)^{1}$ $\bigr]$
$b=-21, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(24p+1)^{1}$ , $(216284p+1)^{1}$ , $(681630p+1)^{1}$ , $(4897851666p+1)^{1}$ , $(5629030330272122580523664594p+1)^{1}$ $\bigr]$

Mizar/みざー

$b=-20, p=2,$ $\bigl[$ $\color{magenta}\bm{(9p+1)^{1}}$ $\bigr]$
$b=-20, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(42p+1)^{1}$ $\bigr]$
$b=-20, p=5,$ $\bigl[$ $(30476p+1)^{1}$ $\bigr]$
$b=-20, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(118p+1)^{1}$ , $(1504p+1)^{1}$ $\bigr]$
$b=-20, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(38546960286p+1)^{1}$ $\bigr]$
$b=-20, p=13,$ $\bigl[$ $(160p+1)^{1}$ , $(196p+1)^{1}$ , $(56569896p+1)^{1}$ $\bigr]$
$b=-20, p=17,$ $\bigl[$ $(151046p+1)^{1}$ , $(155324p+1)^{1}$ , $(5414966p+1)^{1}$ $\bigr]$
$b=-20, p=19,$ $\bigl[$ $(5781622000p+1)^{1}$ , $(119617226020p+1)^{1}$ $\bigr]$
$b=-20, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(20p+1)^{1}$ , $(24480p+1)^{1}$ , $(142365240254619314p+1)^{1}$ $\bigr]$
$b=-20, p=29,$ $\bigl[$ $(60p+1)^{1}$ , $(377246221905938p+1)^{1}$ , $(4628400305347674p+1)^{1}$ $\bigr]$
$b=-20, p=31,$ $\bigl[$ $(1306p+1)^{1}$ , $(2428p+1)^{1}$ , $(10824731509661881304308807746p+1)^{1}$ $\bigr]$
$b=-20, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(9958p+1)^{1}$ , $(259703755141404p+1)^{1}$ , $(3353108250697943081706p+1)^{1}$ $\bigr]$
$b=-20, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(42p+1)^{1}$ , $(20115966p+1)^{1}$ , $(869307746p+1)^{1}$ , $(60754876812770996558033600p+1)^{1}$ $\bigr]$
$b=-20, p=43,$ $\bigl[$ $(22p+1)^{1}$ , $(102861317866971645611659363777435534023044152952554p+1)^{1}$ $\bigr]$
$b=-20, p=47,$ $\bigl[$ $(146p+1)^{1}$ , $(1364p+1)^{1}$ , $(32408553092994492550083220038478174529432641483586p+1)^{1}$ $\bigr]$
$b=-19, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(1p+1)^{2}}$ $\bigr]$
$b=-19, p=3,$ $\bigl[$ $(2p+1)^{3}$ $\bigr]$
$b=-19, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(450p+1)^{1}$ $\bigr]$
$b=-19, p=7,$ $\bigl[$ $(28p+1)^{1}$ , $(32410p+1)^{1}$ $\bigr]$
$b=-19, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(23021790296p+1)^{1}$ $\bigr]$
$b=-19, p=13,$ $\bigl[$ $(10p+1)^{1}$ , $(24p+1)^{1}$ , $(13540p+1)^{1}$ , $(22410p+1)^{1}$ $\bigr]$
$b=-19, p=17,$ $\bigl[$ $(16118784875837653488p+1)^{1}$ $\bigr]$
$b=-19, p=19,$ $\bigl[$ $(5700p+1)^{1}$ , $(55222p+1)^{1}$ , $(45818008480p+1)^{1}$ $\bigr]$
$b=-19, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(30p+1)^{1}$ , $(110p+1)^{1}$ , $(6818784099495310476p+1)^{1}$ $\bigr]$
$b=-19, p=29,$ $\bigl[$ $(3668p+1)^{1}$ , $(23125862344244p+1)^{1}$ , $(293156205898332p+1)^{1}$ $\bigr]$
$b=-19, p=31,$ $\bigl[$ $(48486292p+1)^{1}$ , $(462755205436p+1)^{1}$ , $(327548991587430p+1)^{1}$ $\bigr]$
$b=-19, p=37,$ $\bigl[$ $(278388643947587040669200754395183567419390668p+1)^{1}$ $\bigr]$
$b=-19, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(89052p+1)^{1}$ , $(108038374412883975529868065020723754385198p+1)^{1}$ $\bigr]$
$b=-19, p=43,$ $\bigl[$ $(64p+1)^{1}$ , $(1060414p+1)^{1}$ , $(1292529947624420730p+1)^{1}$ , $(1615277674168136971542p+1)^{1}$ $\bigr]$
$b=-19, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(236p+1)^{1}$ , $(296783214p+1)^{1}$ , $(30684478811472253320271282010182466319938p+1)^{1}$ $\bigr]$
$b=-18, p=2,$ $\bigl[$ $(8p+1)^{1}$ $\bigr]$
$b=-18, p=3,$ $\bigl[$ $(102p+1)^{1}$ $\bigr]$
$b=-18, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(1808p+1)^{1}$ $\bigr]$
$b=-18, p=7,$ $\bigl[$ $(4603158p+1)^{1}$ $\bigr]$
$b=-18, p=11,$ $\bigl[$ $(48800p+1)^{1}$ , $(572846p+1)^{1}$ $\bigr]$
$b=-18, p=13,$ $\bigl[$ $(10p+1)^{1}$ , $(160p+1)^{1}$ , $(309244680p+1)^{1}$ $\bigr]$
$b=-18, p=17,$ $\bigl[$ $(8p+1)^{1}$ , $(26p+1)^{1}$ , $(111507934433880p+1)^{1}$ $\bigr]$
$b=-18, p=19,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(103256355934587793608p+1)^{1}$ $\bigr]$
$b=-18, p=23,$ $\bigl[$ $(170132067766640567307365622p+1)^{1}$ $\bigr]$
$b=-18, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(77785569821525219265423446461472p+1)^{1}$ $\bigr]$
$b=-18, p=31,$ $\bigl[$ $(46p+1)^{1}$ , $(2278p+1)^{1}$ , $(13803423950257226896408384998p+1)^{1}$ $\bigr]$
$b=-18, p=37,$ $\bigl[$ $(34p+1)^{1}$ , $(31484850370871337166744723280530722412624p+1)^{1}$ $\bigr]$
$b=-18, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(4106p+1)^{1}$ , $(106203890p+1)^{1}$ , $(609700272p+1)^{1}$ , $(2469035027073357001496p+1)^{1}$ $\bigr]$
$b=-18, p=43,$ $\bigl[$ $(119296800p+1)^{1}$ , $(13894312446p+1)^{1}$ , $(378523543053832265250358447824p+1)^{1}$ $\bigr]$
$b=-18, p=47,$ $\bigl[$ $(9960p+1)^{1}$ , $(27374664p+1)^{1}$ , $(184991383893360584211679525776490424069046p+1)^{1}$ $\bigr]$
$b=-17, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{4}}$ $\bigr]$
$b=-17, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(4p+1)^{1}$ $\bigr]$
$b=-17, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(14p+1)^{1}$ , $(20p+1)^{1}$ $\bigr]$
$b=-17, p=7,$ $\bigl[$ $(3256656p+1)^{1}$ $\bigr]$
$b=-17, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(86p+1)^{1}$ , $(7946852p+1)^{1}$ $\bigr]$
$b=-17, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(5050p+1)^{1}$ , $(153984p+1)^{1}$ $\bigr]$
$b=-17, p=17,$ $\bigl[$ $(2703399548648159360p+1)^{1}$ $\bigr]$
$b=-17, p=19,$ $\bigl[$ $(24p+1)^{1}$ , $(82p+1)^{1}$ , $(154p+1)^{1}$ , $(16470p+1)^{1}$ , $(1071198p+1)^{1}$ $\bigr]$
$b=-17, p=23,$ $\bigl[$ $(48230842755699332856422864p+1)^{1}$ $\bigr]$
$b=-17, p=29,$ $\bigl[$ $(12p+1)^{1}$ , $(812p+1)^{1}$ , $(100682p+1)^{1}$ , $(621811542p+1)^{1}$ , $(2133750140p+1)^{1}$ $\bigr]$
$b=-17, p=31,$ $\bigl[$ $(12p+1)^{1}$ , $(1188562p+1)^{1}$ , $(18163100467991559756144766p+1)^{1}$ $\bigr]$
$b=-17, p=37,$ $\bigl[$ $(40p+1)^{1}$ , $(70p+1)^{1}$ , $(4667115886p+1)^{1}$ , $(7618387900150046780946208p+1)^{1}$ $\bigr]$
$b=-17, p=41,$ $\bigl[$ $(30p+1)^{1}$ , $(1534616p+1)^{1}$ , $(458488622p+1)^{1}$ , $(1858615832346p+1)^{1}$ , $(3429429410042p+1)^{1}$ $\bigr]$
$b=-17, p=43,$ $\bigl[$ $(190p+1)^{1}$ , $(6491145746620p+1)^{1}$ , $(45972448185374297570366981026674p+1)^{1}$ $\bigr]$
$b=-17, p=47,$ $\bigl[$ $(8011778643947672571479144293068900002409342617137928336p+1)^{1}$ $\bigr]$
$b=-16, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ , $(2p+1)^{1}$ $\bigr]$
$b=-16, p=3,$ $\bigl[$ $(80p+1)^{1}$ $\bigr]$
$b=-16, p=5,$ $\bigl[$ $(12336p+1)^{1}$ $\bigr]$
$b=-16, p=7,$ $\bigl[$ $(2255760p+1)^{1}$ $\bigr]$
$b=-16, p=11,$ $\bigl[$ $(32p+1)^{1}$ , $(266503856p+1)^{1}$ $\bigr]$
$b=-16, p=13,$ $\bigl[$ $(66000p+1)^{1}$ , $(23750880p+1)^{1}$ $\bigr]$
$b=-16, p=17,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(20864p+1)^{1}$ , $(169373406048p+1)^{1}$ $\bigr]$
$b=-16, p=19,$ $\bigl[$ $(64p+1)^{1}$ , $(7840p+1)^{1}$ , $(1290369207408p+1)^{1}$ $\bigr]$
$b=-16, p=23,$ $\bigl[$ $(12664348227983429922241680p+1)^{1}$ $\bigr]$
$b=-16, p=29,$ $\bigl[$ $(2048p+1)^{1}$ , $(2837248109211866201116916144p+1)^{1}$ $\bigr]$
$b=-16, p=31,$ $\bigl[$ $(9376p+1)^{1}$ , $(121619440p+1)^{1}$ , $(36826747754902480512p+1)^{1}$ $\bigr]$
$b=-16, p=37,$ $\bigl[$ $(567268558309205040166250385313789799834160p+1)^{1}$ $\bigr]$
$b=-16, p=41,$ $\bigl[$ $(320p+1)^{1}$ , $(208833936p+1)^{1}$ , $(298630832255258833051375416013472p+1)^{1}$ $\bigr]$
$b=-16, p=43,$ $\bigl[$ $(89657232p+1)^{1}$ , $(1490282575986592p+1)^{1}$ , $(33147518025654100636576p+1)^{1}$ $\bigr]$
$b=-16, p=47,$ $\bigl[$ $(25491648p+1)^{1}$ , $(501964736p+1)^{1}$ , $(95786098423856p+1)^{1}$ , $(3858559720265448288p+1)^{1}$ $\bigr]$
$b=-15, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=-15, p=3,$ $\bigl[$ $(70p+1)^{1}$ $\bigr]$
$b=-15, p=5,$ $\bigl[$ $(6p+1)^{1}$ , $(306p+1)^{1}$ $\bigr]$
$b=-15, p=7,$ $\bigl[$ $(1525530p+1)^{1}$ $\bigr]$
$b=-15, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(2136797396p+1)^{1}$ $\bigr]$
$b=-15, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(118439329866p+1)^{1}$ $\bigr]$
$b=-15, p=17,$ $\bigl[$ $(8p+1)^{1}$ , $(26p+1)^{1}$ , $(5968403914410p+1)^{1}$ $\bigr]$
$b=-15, p=19,$ $\bigl[$ $(12p+1)^{1}$ , $(724p+1)^{1}$ , $(23147341492294p+1)^{1}$ $\bigr]$
$b=-15, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(272p+1)^{1}$ , $(3540p+1)^{1}$ , $(35882p+1)^{1}$ , $(154328342p+1)^{1}$ $\bigr]$
$b=-15, p=29,$ $\bigl[$ $(27550439544954610153518874069740p+1)^{1}$ $\bigr]$
$b=-15, p=31,$ $\bigl[$ $(30918p+1)^{1}$ , $(415193590200p+1)^{1}$ , $(470068858222188p+1)^{1}$ $\bigr]$
$b=-15, p=37,$ $\bigl[$ $(16p+1)^{1}$ , $(160217566p+1)^{1}$ , $(15743030292569394088548176874p+1)^{1}$ $\bigr]$
$b=-15, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(30462089482460362572380592397247478606733826p+1)^{1}$ $\bigr]$
$b=-15, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(911752p+1)^{1}$ , $(128371744p+1)^{1}$ , $(374708639704p+1)^{1}$ , $(899175256191186p+1)^{1}$ $\bigr]$
$b=-15, p=47,$ $\bigl[$ $(62721711961849734p+1)^{1}$ , $(8522275575020394177485626992018804p+1)^{1}$ $\bigr]$
$b=-14, p=2,$ $\bigl[$ $(6p+1)^{1}$ $\bigr]$
$b=-14, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(20p+1)^{1}$ $\bigr]$
$b=-14, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(14p+1)^{1}$ , $(20p+1)^{1}$ $\bigr]$
$b=-14, p=7,$ $\bigl[$ $(1003938p+1)^{1}$ $\bigr]$
$b=-14, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(1067079096p+1)^{1}$ $\bigr]$
$b=-14, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(70p+1)^{1}$ , $(562p+1)^{1}$ , $(7740p+1)^{1}$ $\bigr]$
$b=-14, p=17,$ $\bigl[$ $(8p+1)^{1}$ , $(872802253594710p+1)^{1}$ $\bigr]$
$b=-14, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(1420p+1)^{1}$ , $(4069081689492p+1)^{1}$ $\bigr]$
$b=-14, p=23,$ $\bigl[$ $(6p+1)^{1}$ , $(42p+1)^{1}$ , $(866196p+1)^{1}$ , $(248508025946p+1)^{1}$ $\bigr]$
$b=-14, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(3938656020p+1)^{1}$ , $(589692649757531160p+1)^{1}$ $\bigr]$
$b=-14, p=31,$ $\bigl[$ $(52p+1)^{1}$ , $(102p+1)^{1}$ , $(5428p+1)^{1}$ , $(241188522p+1)^{1}$ , $(113516802606p+1)^{1}$ $\bigr]$
$b=-14, p=37,$ $\bigl[$ $(7650p+1)^{1}$ , $(3214020232864326p+1)^{1}$ , $(136561825292153514p+1)^{1}$ $\bigr]$
$b=-14, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(126p+1)^{1}$ , $(2109792p+1)^{1}$ , $(2323488p+1)^{1}$ , $(45093089866345667845002p+1)^{1}$ $\bigr]$
$b=-14, p=43,$ $\bigl[$ $(1584617402655272202p+1)^{1}$ , $(437071957216669122194661696p+1)^{1}$ $\bigr]$
$b=-14, p=47,$ $\bigl[$ $(24p+1)^{1}$ , $(36p+1)^{1}$ , $(5809908p+1)^{1}$ , $(2005444026275811202920170835141362066p+1)^{1}$ $\bigr]$
$b=-13, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=-13, p=3,$ $\bigl[$ $(52p+1)^{1}$ $\bigr]$
$b=-13, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(482p+1)^{1}$ $\bigr]$
$b=-13, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(4p+1)^{1}$ , $(3154p+1)^{1}$ $\bigr]$
$b=-13, p=11,$ $\bigl[$ $(11637405156p+1)^{1}$ $\bigr]$
$b=-13, p=13,$ $\bigl[$ $(1032p+1)^{1}$ , $(1564p+1)^{1}$ , $(6100p+1)^{1}$ $\bigr]$
$b=-13, p=17,$ $\bigl[$ $(36346285375551840p+1)^{1}$ $\bigr]$
$b=-13, p=19,$ $\bigl[$ $(5495940941261075604p+1)^{1}$ $\bigr]$
$b=-13, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(12p+1)^{1}$ , $(50p+1)^{1}$ , $(102p+1)^{1}$ , $(3687017433726p+1)^{1}$ $\bigr]$
$b=-13, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(60p+1)^{1}$ , $(294716893730p+1)^{1}$ , $(565428078852p+1)^{1}$ $\bigr]$
$b=-13, p=31,$ $\bigl[$ $(12p+1)^{1}$ , $(88p+1)^{1}$ , $(4704232p+1)^{1}$ , $(528678191727212976p+1)^{1}$ $\bigr]$
$b=-13, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(568p+1)^{1}$ , $(4114p+1)^{1}$ , $(41862742978p+1)^{1}$ , $(287210569722958p+1)^{1}$ $\bigr]$
$b=-13, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(15572p+1)^{1}$ , $(3421940126061548p+1)^{1}$ , $(1100277582863599370p+1)^{1}$ $\bigr]$
$b=-13, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(292252p+1)^{1}$ , $(186069844p+1)^{1}$ , $(8069349040p+1)^{1}$ , $(218395741969776p+1)^{1}$ $\bigr]$
$b=-13, p=47,$ $\bigl[$ $(10613854040p+1)^{1}$ , $(69046345308194145073786231732291307108p+1)^{1}$ $\bigr]$
$b=-12, p=2,$ $\bigl[$ $\color{magenta}\bm{(5p+1)^{1}}$ $\bigr]$
$b=-12, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ $\bigr]$
$b=-12, p=5,$ $\bigl[$ $(3828p+1)^{1}$ $\bigr]$
$b=-12, p=7,$ $\bigl[$ $(30p+1)^{1}$ , $(1866p+1)^{1}$ $\bigr]$
$b=-12, p=11,$ $\bigl[$ $(5195862732p+1)^{1}$ $\bigr]$
$b=-12, p=13,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(6p+1)^{1}$ , $(2772p+1)^{1}$ , $(17106p+1)^{1}$ $\bigr]$
$b=-12, p=17,$ $\bigl[$ $(150p+1)^{1}$ , $(3935305481730p+1)^{1}$ $\bigr]$
$b=-12, p=19,$ $\bigl[$ $(174p+1)^{1}$ , $(432p+1)^{1}$ , $(47645541930p+1)^{1}$ $\bigr]$
$b=-12, p=23,$ $\bigl[$ $(36p+1)^{1}$ , $(540p+1)^{1}$ , $(2151723080905932p+1)^{1}$ $\bigr]$
$b=-12, p=29,$ $\bigl[$ $(48365388p+1)^{1}$ , $(37409517846375187944p+1)^{1}$ $\bigr]$
$b=-12, p=31,$ $\bigl[$ $(40758p+1)^{1}$ , $(5594208886582563831651666p+1)^{1}$ $\bigr]$
$b=-12, p=37,$ $\bigl[$ $(141894p+1)^{1}$ , $(112183936374p+1)^{1}$ , $(811451916198021540p+1)^{1}$ $\bigr]$
$b=-12, p=41,$ $\bigl[$ $(300p+1)^{1}$ , $(41089086p+1)^{1}$ , $(333108218112p+1)^{1}$ , $(1169186840611590p+1)^{1}$ $\bigr]$
$b=-12, p=43,$ $\bigl[$ $(1656p+1)^{1}$ , $(8652564p+1)^{1}$ , $(238916760p+1)^{1}$ , $(166923904997564342856p+1)^{1}$ $\bigr]$
$b=-12, p=47,$ $\bigl[$ $(384p+1)^{1}$ , $(262758p+1)^{1}$ , $(460050960p+1)^{1}$ , $(178840785690164079611959410p+1)^{1}$ $\bigr]$
$b=-11, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ $\bigr]$
$b=-11, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(12p+1)^{1}$ $\bigr]$
$b=-11, p=5,$ $\bigl[$ $(2684p+1)^{1}$ $\bigr]$
$b=-11, p=7,$ $\bigl[$ $(231990p+1)^{1}$ $\bigr]$
$b=-11, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(18p+1)^{1}$ , $(5306p+1)^{1}$ $\bigr]$
$b=-11, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(70p+1)^{1}$ , $(4583382p+1)^{1}$ $\bigr]$
$b=-11, p=17,$ $\bigl[$ $(4218p+1)^{1}$ , $(15576p+1)^{1}$ , $(130490p+1)^{1}$ $\bigr]$
$b=-11, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(12p+1)^{1}$ , $(4410p+1)^{1}$ , $(73191382p+1)^{1}$ $\bigr]$
$b=-11, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(44p+1)^{1}$ , $(10494p+1)^{1}$ , $(282321971462p+1)^{1}$ $\bigr]$
$b=-11, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(378607144118p+1)^{1}$ , $(7036712566928p+1)^{1}$ $\bigr]$
$b=-11, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(42p+1)^{1}$ , $(348p+1)^{1}$ , $(118016927046939740362p+1)^{1}$ $\bigr]$
$b=-11, p=37,$ $\bigl[$ $(72746331730811800p+1)^{1}$ , $(284533599510493540p+1)^{1}$ $\bigr]$
$b=-11, p=41,$ $\bigl[$ $(17356782p+1)^{1}$ , $(29662199328p+1)^{1}$ , $(11692159114147813142p+1)^{1}$ $\bigr]$
$b=-11, p=43,$ $\bigl[$ $(124p+1)^{1}$ , $(218909281979986364895039707723185464862p+1)^{1}$ $\bigr]$
$b=-11, p=47,$ $\bigl[$ $(17964p+1)^{1}$ , $(11692010p+1)^{1}$ , $(555265028p+1)^{1}$ , $(1291488262697961688988p+1)^{1}$ $\bigr]$

Mizar/みざー

$b=-10, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{2}}$ $\bigr]$
$b=-10, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(4p+1)^{1}$ $\bigr]$
$b=-10, p=5,$ $\bigl[$ $(1818p+1)^{1}$ $\bigr]$
$b=-10, p=7,$ $\bigl[$ $(129870p+1)^{1}$ $\bigr]$
$b=-10, p=11,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(372p+1)^{1}$ , $(798p+1)^{1}$ $\bigr]$
$b=-10, p=13,$ $\bigl[$ $(66p+1)^{1}$ , $(81408696p+1)^{1}$ $\bigr]$
$b=-10, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(236p+1)^{1}$ , $(1293754904p+1)^{1}$ $\bigr]$
$b=-10, p=19,$ $\bigl[$ $(47846889952153110p+1)^{1}$ $\bigr]$
$b=-10, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(110p+1)^{1}$ , $(23904225412692p+1)^{1}$ $\bigr]$
$b=-10, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(5313213963126295095903512p+1)^{1}$ $\bigr]$
$b=-10, p=31,$ $\bigl[$ $(29325513196480938416422287390p+1)^{1}$ $\bigr]$
$b=-10, p=37,$ $\bigl[$ $(196p+1)^{1}$ , $(11422974965796p+1)^{1}$ , $(8015063440903954p+1)^{1}$ $\bigr]$
$b=-10, p=41,$ $\bigl[$ $(65134214180396756p+1)^{1}$ , $(83029117800147780422p+1)^{1}$ $\bigr]$
$b=-10, p=43,$ $\bigl[$ $(1325800p+1)^{1}$ , $(50758150p+1)^{1}$ , $(169909687362135296482680p+1)^{1}$ $\bigr]$
$b=-10, p=47,$ $\bigl[$ $(134p+1)^{1}$ , $(103299310597778p+1)^{1}$ , $(6324738404449766101523658p+1)^{1}$ $\bigr]$
$b=-9, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{3}}$ $\bigr]$
$b=-9, p=3,$ $\bigl[$ $(24p+1)^{1}$ $\bigr]$
$b=-9, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(236p+1)^{1}$ $\bigr]$
$b=-9, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(2356p+1)^{1}$ $\bigr]$
$b=-9, p=11,$ $\bigl[$ $(500p+1)^{1}$ , $(51860p+1)^{1}$ $\bigr]$
$b=-9, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(368921020p+1)^{1}$ $\bigr]$
$b=-9, p=17,$ $\bigl[$ $(56256p+1)^{1}$ , $(102578304p+1)^{1}$ $\bigr]$
$b=-9, p=19,$ $\bigl[$ $(279028p+1)^{1}$ , $(1341073588p+1)^{1}$ $\bigr]$
$b=-9, p=23,$ $\bigl[$ $(545804p+1)^{1}$ , $(3069624809900p+1)^{1}$ $\bigr]$
$b=-9, p=29,$ $\bigl[$ $(428p+1)^{1}$ , $(1308452678156172431828p+1)^{1}$ $\bigr]$
$b=-9, p=31,$ $\bigl[$ $(45284160p+1)^{1}$ , $(92279328p+1)^{1}$ , $(306465768p+1)^{1}$ $\bigr]$
$b=-9, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(25780p+1)^{1}$ , $(3855669183821754615443016p+1)^{1}$ $\bigr]$
$b=-9, p=41,$ $\bigl[$ $(50948p+1)^{1}$ , $(2701656p+1)^{1}$ , $(14022773366271139289396p+1)^{1}$ $\bigr]$
$b=-9, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(10944p+1)^{1}$ , $(61429900p+1)^{1}$ , $(1290079584p+1)^{1}$ , $(21005579256p+1)^{1}$ $\bigr]$
$b=-9, p=47,$ $\bigl[$ $(11996567016p+1)^{1}$ , $(2667750704940537569903784030624p+1)^{1}$ $\bigr]$
$b=-8, p=2,$ $\bigl[$ $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=-8, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(6p+1)^{1}$ $\bigr]$
$b=-8, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(66p+1)^{1}$ $\bigr]$
$b=-8, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(774p+1)^{1}$ $\bigr]$
$b=-8, p=11,$ $\bigl[$ $(6p+1)^{1}$ , $(62p+1)^{1}$ , $(1896p+1)^{1}$ $\bigr]$
$b=-8, p=13,$ $\bigl[$ $(210p+1)^{1}$ , $(1720530p+1)^{1}$ $\bigr]$
$b=-8, p=17,$ $\bigl[$ $(18p+1)^{1}$ , $(168p+1)^{1}$ , $(384p+1)^{1}$ , $(2570p+1)^{1}$ $\bigr]$
$b=-8, p=19,$ $\bigl[$ $(30p+1)^{1}$ , $(9198p+1)^{1}$ , $(8445552p+1)^{1}$ $\bigr]$
$b=-8, p=23,$ $\bigl[$ $(6p+1)^{1}$ , $(121574p+1)^{1}$ , $(7336955040p+1)^{1}$ $\bigr]$
$b=-8, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(104592p+1)^{1}$ , $(3312992823159090p+1)^{1}$ $\bigr]$
$b=-8, p=31,$ $\bigl[$ $(17080998p+1)^{1}$ , $(23091222p+1)^{1}$ , $(93648720p+1)^{1}$ $\bigr]$
$b=-8, p=37,$ $\bigl[$ $(48p+1)^{1}$ , $(90p+1)^{1}$ , $(474p+1)^{1}$ , $(696786p+1)^{1}$ , $(2912844089514p+1)^{1}$ $\bigr]$
$b=-8, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(18p+1)^{1}$ , $(4032p+1)^{1}$ , $(215400456p+1)^{1}$ , $(321812632025112p+1)^{1}$ $\bigr]$
$b=-8, p=43,$ $\bigl[$ $(24p+1)^{1}$ , $(37013544p+1)^{1}$ , $(68186767614p+1)^{1}$ , $(364804737150p+1)^{1}$ $\bigr]$
$b=-8, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(35766p+1)^{1}$ , $(750490200p+1)^{1}$ , $(2369131176p+1)^{1}$ , $(3526990160p+1)^{1}$ $\bigr]$
$b=-7, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=-7, p=3,$ $\bigl[$ $(14p+1)^{1}$ $\bigr]$
$b=-7, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(38p+1)^{1}$ $\bigr]$
$b=-7, p=7,$ $\bigl[$ $(16p+1)^{1}$ , $(130p+1)^{1}$ $\bigr]$
$b=-7, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(976940p+1)^{1}$ $\bigr]$
$b=-7, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(17577832p+1)^{1}$ $\bigr]$
$b=-7, p=17,$ $\bigl[$ $(1710518485200p+1)^{1}$ $\bigr]$
$b=-7, p=19,$ $\bigl[$ $(18480p+1)^{1}$ , $(213580878p+1)^{1}$ $\bigr]$
$b=-7, p=23,$ $\bigl[$ $(148743192065657154p+1)^{1}$ $\bigr]$
$b=-7, p=29,$ $\bigl[$ $(13878904119884395374300p+1)^{1}$ $\bigr]$
$b=-7, p=31,$ $\bigl[$ $(12p+1)^{1}$ , $(314658p+1)^{1}$ , $(174855062812668p+1)^{1}$ $\bigr]$
$b=-7, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(420871483788716993979075904p+1)^{1}$ $\bigr]$
$b=-7, p=41,$ $\bigl[$ $(118278p+1)^{1}$ , $(219512p+1)^{1}$ , $(39908750p+1)^{1}$ , $(1902671112p+1)^{1}$ $\bigr]$
$b=-7, p=43,$ $\bigl[$ $(22p+1)^{1}$ , $(462p+1)^{1}$ , $(486p+1)^{1}$ , $(3804p+1)^{1}$ , $(5470p+1)^{1}$ , $(88350p+1)^{1}$ , $(110460p+1)^{1}$ $\bigr]$
$b=-7, p=47,$ $\bigl[$ $(13945048714777403283142177443781785786p+1)^{1}$ $\bigr]$
$b=-6, p=2,$ $\bigl[$ $(2p+1)^{1}$ $\bigr]$
$b=-6, p=3,$ $\bigl[$ $(10p+1)^{1}$ $\bigr]$
$b=-6, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(20p+1)^{1}$ $\bigr]$
$b=-6, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(4p+1)^{1}$ , $(28p+1)^{1}$ $\bigr]$
$b=-6, p=11,$ $\bigl[$ $(4711650p+1)^{1}$ $\bigr]$
$b=-6, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(72p+1)^{1}$ , $(2890p+1)^{1}$ $\bigr]$
$b=-6, p=17,$ $\bigl[$ $(11208p+1)^{1}$ , $(746526p+1)^{1}$ $\bigr]$
$b=-6, p=19,$ $\bigl[$ $(94p+1)^{1}$ , $(2563879228p+1)^{1}$ $\bigr]$
$b=-6, p=23,$ $\bigl[$ $(4954700p+1)^{1}$ , $(43043510p+1)^{1}$ $\bigr]$
$b=-6, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(1128p+1)^{1}$ , $(94041129772028p+1)^{1}$ $\bigr]$
$b=-6, p=31,$ $\bigl[$ $(6112642941587097453450p+1)^{1}$ $\bigr]$
$b=-6, p=37,$ $\bigl[$ $(106p+1)^{1}$ , $(29642236066p+1)^{1}$ , $(55534837614p+1)^{1}$ $\bigr]$
$b=-6, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(696p+1)^{1}$ , $(117986674726269375000980p+1)^{1}$ $\bigr]$
$b=-6, p=43,$ $\bigl[$ $(9592620665748327437386015717410p+1)^{1}$ $\bigr]$
$b=-6, p=47,$ $\bigl[$ $(11373990733208995562354210295740970p+1)^{1}$ $\bigr]$
$b=-5, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ $\bigr]$
$b=-5, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ $\bigr]$
$b=-5, p=5,$ $\bigl[$ $(104p+1)^{1}$ $\bigr]$
$b=-5, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(64p+1)^{1}$ $\bigr]$
$b=-5, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(480p+1)^{1}$ $\bigr]$
$b=-5, p=13,$ $\bigl[$ $(402p+1)^{1}$ , $(2994p+1)^{1}$ $\bigr]$
$b=-5, p=17,$ $\bigl[$ $(180p+1)^{1}$ , $(2443580p+1)^{1}$ $\bigr]$
$b=-5, p=19,$ $\bigl[$ $(40p+1)^{1}$ , $(1032p+1)^{1}$ , $(11212p+1)^{1}$ $\bigr]$
$b=-5, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(1837947726654p+1)^{1}$ $\bigr]$
$b=-5, p=29,$ $\bigl[$ $(175754p+1)^{1}$ , $(210028183578p+1)^{1}$ $\bigr]$
$b=-5, p=31,$ $\bigl[$ $(42p+1)^{1}$ , $(684100p+1)^{1}$ , $(906006826p+1)^{1}$ $\bigr]$
$b=-5, p=37,$ $\bigl[$ $(246p+1)^{1}$ , $(784060p+1)^{1}$ , $(1241085226618p+1)^{1}$ $\bigr]$
$b=-5, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(1062p+1)^{1}$ , $(5400p+1)^{1}$ , $(231025039235988p+1)^{1}$ $\bigr]$
$b=-5, p=43,$ $\bigl[$ $(36p+1)^{1}$ , $(222p+1)^{1}$ , $(182944374p+1)^{1}$ , $(37877789496p+1)^{1}$ $\bigr]$
$b=-5, p=47,$ $\bigl[$ $(44p+1)^{1}$ , $(338058644p+1)^{1}$ , $(76646212998069380p+1)^{1}$ $\bigr]$
$b=-4, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=-4, p=3,$ $\bigl[$ $(4p+1)^{1}$ $\bigr]$
$b=-4, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(8p+1)^{1}$ $\bigr]$
$b=-4, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(16p+1)^{1}$ $\bigr]$
$b=-4, p=11,$ $\bigl[$ $(36p+1)^{1}$ , $(192p+1)^{1}$ $\bigr]$
$b=-4, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(12p+1)^{1}$ , $(124p+1)^{1}$ $\bigr]$
$b=-4, p=17,$ $\bigl[$ $(8p+1)^{1}$ , $(56p+1)^{1}$ , $(1548p+1)^{1}$ $\bigr]$
$b=-4, p=19,$ $\bigl[$ $(12p+1)^{1}$ , $(24p+1)^{1}$ , $(27648p+1)^{1}$ $\bigr]$
$b=-4, p=23,$ $\bigl[$ $(12p+1)^{1}$ , $(44p+1)^{1}$ , $(72p+1)^{1}$ , $(1316p+1)^{1}$ $\bigr]$
$b=-4, p=29,$ $\bigl[$ $(3702332p+1)^{1}$ , $(18513920p+1)^{1}$ $\bigr]$
$b=-4, p=31,$ $\bigl[$ $(180p+1)^{1}$ , $(280p+1)^{1}$ , $(1596p+1)^{1}$ , $(12412p+1)^{1}$ $\bigr]$
$b=-4, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(16p+1)^{1}$ , $(4985976p+1)^{1}$ , $(6264048p+1)^{1}$ $\bigr]$
$b=-4, p=41,$ $\bigl[$ $(248p+1)^{1}$ , $(4428p+1)^{1}$ , $(295428p+1)^{1}$ , $(1054868p+1)^{1}$ $\bigr]$
$b=-4, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(2364p+1)^{1}$ , $(11632p+1)^{1}$ , $(40912041060p+1)^{1}$ $\bigr]$
$b=-4, p=47,$ $\bigl[$ $(80p+1)^{1}$ , $(159235044p+1)^{1}$ , $(2994414288896p+1)^{1}$ $\bigr]$
$b=-3, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ $\bigr]$
$b=-3, p=3,$ $\bigl[$ $(2p+1)^{1}$ $\bigr]$
$b=-3, p=5,$ $\bigl[$ $(12p+1)^{1}$ $\bigr]$
$b=-3, p=7,$ $\bigl[$ $(78p+1)^{1}$ $\bigr]$
$b=-3, p=11,$ $\bigl[$ $(6p+1)^{1}$ , $(60p+1)^{1}$ $\bigr]$
$b=-3, p=13,$ $\bigl[$ $(30660p+1)^{1}$ $\bigr]$
$b=-3, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(18p+1)^{1}$ , $(60p+1)^{1}$ $\bigr]$
$b=-3, p=19,$ $\bigl[$ $(150p+1)^{1}$ , $(5364p+1)^{1}$ $\bigr]$
$b=-3, p=23,$ $\bigl[$ $(1023295422p+1)^{1}$ $\bigr]$
$b=-3, p=29,$ $\bigl[$ $(18p+1)^{1}$ , $(210p+1)^{1}$ , $(185724p+1)^{1}$ $\bigr]$
$b=-3, p=31,$ $\bigl[$ $(222p+1)^{1}$ , $(723701448p+1)^{1}$ $\bigr]$
$b=-3, p=37,$ $\bigl[$ $(498p+1)^{1}$ , $(2910p+1)^{1}$ , $(1533456p+1)^{1}$ $\bigr]$
$b=-3, p=41,$ $\bigl[$ $(822p+1)^{1}$ , $(6598709888526p+1)^{1}$ $\bigr]$
$b=-3, p=43,$ $\bigl[$ $(1908470740665913242p+1)^{1}$ $\bigr]$
$b=-3, p=47,$ $\bigl[$ $(360p+1)^{1}$ , $(5448p+1)^{1}$ , $(32642126550p+1)^{1}$ $\bigr]$
$b=-2, p=2,$ $\bigl[$ $\bigr]$
$b=-2, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ $\bigr]$
$b=-2, p=5,$ $\bigl[$ $(2p+1)^{1}$ $\bigr]$
$b=-2, p=7,$ $\bigl[$ $(6p+1)^{1}$ $\bigr]$
$b=-2, p=11,$ $\bigl[$ $(62p+1)^{1}$ $\bigr]$
$b=-2, p=13,$ $\bigl[$ $(210p+1)^{1}$ $\bigr]$
$b=-2, p=17,$ $\bigl[$ $(2570p+1)^{1}$ $\bigr]$
$b=-2, p=19,$ $\bigl[$ $(9198p+1)^{1}$ $\bigr]$
$b=-2, p=23,$ $\bigl[$ $(121574p+1)^{1}$ $\bigr]$
$b=-2, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(104592p+1)^{1}$ $\bigr]$
$b=-2, p=31,$ $\bigl[$ $(23091222p+1)^{1}$ $\bigr]$
$b=-2, p=37,$ $\bigl[$ $(48p+1)^{1}$ , $(696786p+1)^{1}$ $\bigr]$
$b=-2, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(215400456p+1)^{1}$ $\bigr]$
$b=-2, p=43,$ $\bigl[$ $(68186767614p+1)^{1}$ $\bigr]$
$b=-2, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(3526990160p+1)^{1}$ $\bigr]$

Mizar/みざー

$b=2, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=2, p=3,$ $\bigl[$ $(2p+1)^{1}$ $\bigr]$
$b=2, p=5,$ $\bigl[$ $(6p+1)^{1}$ $\bigr]$
$b=2, p=7,$ $\bigl[$ $(18p+1)^{1}$ $\bigr]$
$b=2, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ $\bigr]$
$b=2, p=13,$ $\bigl[$ $(630p+1)^{1}$ $\bigr]$
$b=2, p=17,$ $\bigl[$ $(7710p+1)^{1}$ $\bigr]$
$b=2, p=19,$ $\bigl[$ $(27594p+1)^{1}$ $\bigr]$
$b=2, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(7760p+1)^{1}$ $\bigr]$
$b=2, p=29,$ $\bigl[$ $(8p+1)^{1}$ , $(38p+1)^{1}$ , $(72p+1)^{1}$ $\bigr]$
$b=2, p=31,$ $\bigl[$ $(69273666p+1)^{1}$ $\bigr]$
$b=2, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(16657248p+1)^{1}$ $\bigr]$
$b=2, p=41,$ $\bigl[$ $(326p+1)^{1}$ , $(4012472p+1)^{1}$ $\bigr]$
$b=2, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(226p+1)^{1}$ , $(48834p+1)^{1}$ $\bigr]$
$b=2, p=47,$ $\bigl[$ $(50p+1)^{1}$ , $(96p+1)^{1}$ , $(282224p+1)^{1}$ $\bigr]$
$b=3, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ $\bigr]$
$b=3, p=3,$ $\bigl[$ $(4p+1)^{1}$ $\bigr]$
$b=3, p=5,$ $\bigl[$ $(2p+1)^{2}$ $\bigr]$
$b=3, p=7,$ $\bigl[$ $(156p+1)^{1}$ $\bigr]$
$b=3, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(350p+1)^{1}$ $\bigr]$
$b=3, p=13,$ $\bigl[$ $(61320p+1)^{1}$ $\bigr]$
$b=3, p=17,$ $\bigl[$ $(110p+1)^{1}$ , $(2030p+1)^{1}$ $\bigr]$
$b=3, p=19,$ $\bigl[$ $(84p+1)^{1}$ , $(19152p+1)^{1}$ $\bigr]$
$b=3, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(43544486p+1)^{1}$ $\bigr]$
$b=3, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(984p+1)^{1}$ , $(702794p+1)^{1}$ $\bigr]$
$b=3, p=31,$ $\bigl[$ $(22p+1)^{1}$ , $(3312p+1)^{1}$ , $(142066p+1)^{1}$ $\bigr]$
$b=3, p=37,$ $\bigl[$ $(353998p+1)^{1}$ , $(464571046p+1)^{1}$ $\bigr]$
$b=3, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(61632p+1)^{1}$ , $(2120748698p+1)^{1}$ $\bigr]$
$b=3, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(8856012717707254p+1)^{1}$ $\bigr]$
$b=3, p=47,$ $\bigl[$ $(26p+1)^{1}$ , $(468p+1)^{1}$ , $(108780p+1)^{1}$ , $(2056526p+1)^{1}$ $\bigr]$
$b=4, p=2,$ $\bigl[$ $(2p+1)^{1}$ $\bigr]$
$b=4, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ $\bigr]$
$b=4, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ $\bigr]$
$b=4, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(18p+1)^{1}$ $\bigr]$
$b=4, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(62p+1)^{1}$ $\bigr]$
$b=4, p=13,$ $\bigl[$ $(210p+1)^{1}$ , $(630p+1)^{1}$ $\bigr]$
$b=4, p=17,$ $\bigl[$ $(2570p+1)^{1}$ , $(7710p+1)^{1}$ $\bigr]$
$b=4, p=19,$ $\bigl[$ $(9198p+1)^{1}$ , $(27594p+1)^{1}$ $\bigr]$
$b=4, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(7760p+1)^{1}$ , $(121574p+1)^{1}$ $\bigr]$
$b=4, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(38p+1)^{1}$ , $(72p+1)^{1}$ , $(104592p+1)^{1}$ $\bigr]$
$b=4, p=31,$ $\bigl[$ $(23091222p+1)^{1}$ , $(69273666p+1)^{1}$ $\bigr]$
$b=4, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(48p+1)^{1}$ , $(696786p+1)^{1}$ , $(16657248p+1)^{1}$ $\bigr]$
$b=4, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(326p+1)^{1}$ , $(4012472p+1)^{1}$ , $(215400456p+1)^{1}$ $\bigr]$
$b=4, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(226p+1)^{1}$ , $(48834p+1)^{1}$ , $(68186767614p+1)^{1}$ $\bigr]$
$b=4, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(50p+1)^{1}$ , $(96p+1)^{1}$ , $(282224p+1)^{1}$ , $(3526990160p+1)^{1}$ $\bigr]$
$b=5, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=5, p=3,$ $\bigl[$ $(10p+1)^{1}$ $\bigr]$
$b=5, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(14p+1)^{1}$ $\bigr]$
$b=5, p=7,$ $\bigl[$ $(2790p+1)^{1}$ $\bigr]$
$b=5, p=11,$ $\bigl[$ $(1109730p+1)^{1}$ $\bigr]$
$b=5, p=13,$ $\bigl[$ $(23475060p+1)^{1}$ $\bigr]$
$b=5, p=17,$ $\bigl[$ $(24p+1)^{1}$ , $(27432024p+1)^{1}$ $\bigr]$
$b=5, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(330p+1)^{1}$ , $(209530p+1)^{1}$ $\bigr]$
$b=5, p=23,$ $\bigl[$ $(390p+1)^{1}$ , $(14443798320p+1)^{1}$ $\bigr]$
$b=5, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(1230p+1)^{1}$ , $(762965394632p+1)^{1}$ $\bigr]$
$b=5, p=31,$ $\bigl[$ $(60p+1)^{1}$ , $(20179113176567370p+1)^{1}$ $\bigr]$
$b=5, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(377620810p+1)^{1}$ , $(236148142074p+1)^{1}$ $\bigr]$
$b=5, p=41,$ $\bigl[$ $(54591128p+1)^{1}$ , $(123885479102846048p+1)^{1}$ $\bigr]$
$b=5, p=43,$ $\bigl[$ $(38244480p+1)^{1}$ , $(4019245399972462530p+1)^{1}$ $\bigr]$
$b=5, p=47,$ $\bigl[$ $(3779482637021809499314490784990p+1)^{1}$ $\bigr]$
$b=6, p=2,$ $\bigl[$ $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=6, p=3,$ $\bigl[$ $(14p+1)^{1}$ $\bigr]$
$b=6, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(62p+1)^{1}$ $\bigr]$
$b=6, p=7,$ $\bigl[$ $(7998p+1)^{1}$ $\bigr]$
$b=6, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(286796p+1)^{1}$ $\bigr]$
$b=6, p=13,$ $\bigl[$ $(264p+1)^{1}$ , $(58530p+1)^{1}$ $\bigr]$
$b=6, p=17,$ $\bigl[$ $(14p+1)^{1}$ , $(24p+1)^{1}$ , $(66p+1)^{1}$ , $(1814p+1)^{1}$ $\bigr]$
$b=6, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(33582790852p+1)^{1}$ $\bigr]$
$b=6, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(140p+1)^{1}$ , $(326345430p+1)^{1}$ $\bigr]$
$b=6, p=29,$ $\bigl[$ $(254107953701992365402p+1)^{1}$ $\bigr]$
$b=6, p=31,$ $\bigl[$ $(172p+1)^{1}$ , $(1604669063983112026p+1)^{1}$ $\bigr]$
$b=6, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(214p+1)^{1}$ , $(330p+1)^{1}$ , $(69454p+1)^{1}$ , $(9034779076p+1)^{1}$ $\bigr]$
$b=6, p=41,$ $\bigl[$ $(210930p+1)^{1}$ , $(45240265509426766516560p+1)^{1}$ $\bigr]$
$b=6, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(10p+1)^{1}$ , $(171706p+1)^{1}$ , $(24394276816975853386p+1)^{1}$ $\bigr]$
$b=6, p=47,$ $\bigl[$ $(19806624p+1)^{1}$ , $(959805024p+1)^{1}$ , $(379185492759918p+1)^{1}$ $\bigr]$
$b=7, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{3}}$ $\bigr]$
$b=7, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(6p+1)^{1}$ $\bigr]$
$b=7, p=5,$ $\bigl[$ $(560p+1)^{1}$ $\bigr]$
$b=7, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(676p+1)^{1}$ $\bigr]$
$b=7, p=11,$ $\bigl[$ $(102p+1)^{1}$ , $(26678p+1)^{1}$ $\bigr]$
$b=7, p=13,$ $\bigl[$ $(1242166800p+1)^{1}$ $\bigr]$
$b=7, p=17,$ $\bigl[$ $(824p+1)^{1}$ , $(162801864p+1)^{1}$ $\bigr]$
$b=7, p=19,$ $\bigl[$ $(22p+1)^{1}$ , $(238640354758p+1)^{1}$ $\bigr]$
$b=7, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(134p+1)^{1}$ , $(1368687973772p+1)^{1}$ $\bigr]$
$b=7, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(4397940p+1)^{1}$ , $(2459204240862p+1)^{1}$ $\bigr]$
$b=7, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(682p+1)^{1}$ , $(129002847722563368p+1)^{1}$ $\bigr]$
$b=7, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(78p+1)^{1}$ , $(129874192148440966702200p+1)^{1}$ $\bigr]$
$b=7, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(500388p+1)^{1}$ , $(106393642347050455026702p+1)^{1}$ $\bigr]$
$b=7, p=43,$ $\bigl[$ $(3860549019591832p+1)^{1}$ , $(50989234006306480p+1)^{1}$ $\bigr]$
$b=7, p=47,$ $\bigl[$ $(291974824457930p+1)^{1}$ , $(1354925787157841499138p+1)^{1}$ $\bigr]$
$b=8, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{2}}$ $\bigr]$
$b=8, p=3,$ $\bigl[$ $(24p+1)^{1}$ $\bigr]$
$b=8, p=5,$ $\bigl[$ $(6p+1)^{1}$ , $(30p+1)^{1}$ $\bigr]$
$b=8, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(18p+1)^{1}$ , $(48p+1)^{1}$ $\bigr]$
$b=8, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(54498p+1)^{1}$ $\bigr]$
$b=8, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(630p+1)^{1}$ , $(9336p+1)^{1}$ $\bigr]$
$b=8, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(126p+1)^{1}$ , $(654p+1)^{1}$ , $(7710p+1)^{1}$ $\bigr]$
$b=8, p=19,$ $\bigl[$ $(1704p+1)^{1}$ , $(27594p+1)^{1}$ , $(63834p+1)^{1}$ $\bigr]$
$b=8, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(7760p+1)^{1}$ , $(437072997306p+1)^{1}$ $\bigr]$
$b=8, p=29,$ $\bigl[$ $(8p+1)^{1}$ , $(38p+1)^{1}$ , $(72p+1)^{1}$ , $(144p+1)^{1}$ , $(339921970878p+1)^{1}$ $\bigr]$
$b=8, p=31,$ $\bigl[$ $(69273666p+1)^{1}$ , $(21252009311404938p+1)^{1}$ $\bigr]$
$b=8, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(8694p+1)^{1}$ , $(710688p+1)^{1}$ , $(8622168p+1)^{1}$ , $(16657248p+1)^{1}$ $\bigr]$
$b=8, p=41,$ $\bigl[$ $(326p+1)^{1}$ , $(94806p+1)^{1}$ , $(4012472p+1)^{1}$ , $(4334689120833552p+1)^{1}$ $\bigr]$
$b=8, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(226p+1)^{1}$ , $(48834p+1)^{1}$ , $(257047350349983598917666p+1)^{1}$ $\bigr]$
$b=8, p=47,$ $\bigl[$ $(50p+1)^{1}$ , $(96p+1)^{1}$ , $(282224p+1)^{1}$ , $(93097410p+1)^{1}$ , $(13759043303260824p+1)^{1}$ $\bigr]$
$b=9, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ $\bigr]$
$b=9, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(4p+1)^{1}$ $\bigr]$
$b=9, p=5,$ $\bigl[$ $(2p+1)^{2}$ , $(12p+1)^{1}$ $\bigr]$
$b=9, p=7,$ $\bigl[$ $(78p+1)^{1}$ , $(156p+1)^{1}$ $\bigr]$
$b=9, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(60p+1)^{1}$ , $(350p+1)^{1}$ $\bigr]$
$b=9, p=13,$ $\bigl[$ $(30660p+1)^{1}$ , $(61320p+1)^{1}$ $\bigr]$
$b=9, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(18p+1)^{1}$ , $(60p+1)^{1}$ , $(110p+1)^{1}$ , $(2030p+1)^{1}$ $\bigr]$
$b=9, p=19,$ $\bigl[$ $(84p+1)^{1}$ , $(150p+1)^{1}$ , $(5364p+1)^{1}$ , $(19152p+1)^{1}$ $\bigr]$
$b=9, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(43544486p+1)^{1}$ , $(1023295422p+1)^{1}$ $\bigr]$
$b=9, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(18p+1)^{1}$ , $(210p+1)^{1}$ , $(984p+1)^{1}$ , $(185724p+1)^{1}$ , $(702794p+1)^{1}$ $\bigr]$
$b=9, p=31,$ $\bigl[$ $(22p+1)^{1}$ , $(222p+1)^{1}$ , $(3312p+1)^{1}$ , $(142066p+1)^{1}$ , $(723701448p+1)^{1}$ $\bigr]$
$b=9, p=37,$ $\bigl[$ $(498p+1)^{1}$ , $(2910p+1)^{1}$ , $(353998p+1)^{1}$ , $(1533456p+1)^{1}$ , $(464571046p+1)^{1}$ $\bigr]$
$b=9, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(822p+1)^{1}$ , $(61632p+1)^{1}$ , $(2120748698p+1)^{1}$ , $(6598709888526p+1)^{1}$ $\bigr]$
$b=9, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(8856012717707254p+1)^{1}$ , $(1908470740665913242p+1)^{1}$ $\bigr]$
$b=9, p=47,$ $\bigl[$ $(26p+1)^{1}$ , $(360p+1)^{1}$ , $(468p+1)^{1}$ , $(5448p+1)^{1}$ , $(108780p+1)^{1}$ , $(2056526p+1)^{1}$ , $(32642126550p+1)^{1}$ $\bigr]$
$b=10, p=2,$ $\bigl[$ $\color{magenta}\bm{(5p+1)^{1}}$ $\bigr]$
$b=10, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(12p+1)^{1}$ $\bigr]$
$b=10, p=5,$ $\bigl[$ $(8p+1)^{1}$ , $(54p+1)^{1}$ $\bigr]$
$b=10, p=7,$ $\bigl[$ $(34p+1)^{1}$ , $(664p+1)^{1}$ $\bigr]$
$b=10, p=11,$ $\bigl[$ $(1968p+1)^{1}$ , $(46658p+1)^{1}$ $\bigr]$
$b=10, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(20413204p+1)^{1}$ $\bigr]$
$b=10, p=17,$ $\bigl[$ $(121866p+1)^{1}$ , $(315483668p+1)^{1}$ $\bigr]$
$b=10, p=19,$ $\bigl[$ $(58479532163742690p+1)^{1}$ $\bigr]$
$b=10, p=23,$ $\bigl[$ $(483091787439613526570p+1)^{1}$ $\bigr]$
$b=10, p=29,$ $\bigl[$ $(110p+1)^{1}$ , $(578p+1)^{1}$ , $(1484p+1)^{1}$ , $(2138p+1)^{1}$ , $(2684270324p+1)^{1}$ $\bigr]$
$b=10, p=31,$ $\bigl[$ $(90p+1)^{1}$ , $(223978p+1)^{1}$ , $(1849561776251309818p+1)^{1}$ $\bigr]$
$b=10, p=37,$ $\bigl[$ $(54814p+1)^{1}$ , $(6692676p+1)^{1}$ , $(59794440453248739676p+1)^{1}$ $\bigr]$
$b=10, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(30p+1)^{1}$ , $(13146p+1)^{1}$ , $(4921066095129824481674583960p+1)^{1}$ $\bigr]$
$b=10, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(35530p+1)^{1}$ , $(45662947029172p+1)^{1}$ , $(49790511985942480p+1)^{1}$ $\bigr]$
$b=10, p=47,$ $\bigl[$ $(747264p+1)^{1}$ , $(6731125718371457978753322426355880474p+1)^{1}$ $\bigr]$

Mizar/みざー

$b=11, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=11, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ $\bigr]$
$b=11, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(644p+1)^{1}$ $\bigr]$
$b=11, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(6474p+1)^{1}$ $\bigr]$
$b=11, p=11,$ $\bigl[$ $(1436p+1)^{1}$ , $(164192p+1)^{1}$ $\bigr]$
$b=11, p=13,$ $\bigl[$ $(84p+1)^{1}$ , $(242963700p+1)^{1}$ $\bigr]$
$b=11, p=17,$ $\bigl[$ $(2973217814701728p+1)^{1}$ $\bigr]$
$b=11, p=19,$ $\bigl[$ $(321889949728497612p+1)^{1}$ $\bigr]$
$b=11, p=23,$ $\bigl[$ $(36p+1)^{1}$ , $(1255602p+1)^{1}$ , $(162618347010p+1)^{1}$ $\bigr]$
$b=11, p=29,$ $\bigl[$ $(18p+1)^{1}$ , $(10458952312068909965150898p+1)^{1}$ $\bigr]$
$b=11, p=31,$ $\bigl[$ $(1618p+1)^{1}$ , $(78340p+1)^{1}$ , $(5082966373696847058p+1)^{1}$ $\bigr]$
$b=11, p=37,$ $\bigl[$ $(70p+1)^{1}$ , $(996084p+1)^{1}$ , $(3679776p+1)^{1}$ , $(70686976186262050p+1)^{1}$ $\bigr]$
$b=11, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(30p+1)^{1}$ , $(660p+1)^{1}$ , $(12420p+1)^{1}$ , $(343712p+1)^{1}$ , $(728450p+1)^{1}$ , $(20491216478p+1)^{1}$ $\bigr]$
$b=11, p=43,$ $\bigl[$ $(32936244692862p+1)^{1}$ , $(989178048641471349905015226p+1)^{1}$ $\bigr]$
$b=11, p=47,$ $\bigl[$ $(44p+1)^{1}$ , $(482274022688408p+1)^{1}$ , $(400134617911163629696747104p+1)^{1}$ $\bigr]$
$b=12, p=2,$ $\bigl[$ $(6p+1)^{1}$ $\bigr]$
$b=12, p=3,$ $\bigl[$ $(52p+1)^{1}$ $\bigr]$
$b=12, p=5,$ $\bigl[$ $(4524p+1)^{1}$ $\bigr]$
$b=12, p=7,$ $\bigl[$ $(94p+1)^{1}$ , $(706p+1)^{1}$ $\bigr]$
$b=12, p=11,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(24271008p+1)^{1}$ $\bigr]$
$b=12, p=13,$ $\bigl[$ $(36732p+1)^{1}$ , $(1566864p+1)^{1}$ $\bigr]$
$b=12, p=17,$ $\bigl[$ $(158450p+1)^{1}$ , $(4404516590p+1)^{1}$ $\bigr]$
$b=12, p=19,$ $\bigl[$ $(1528612437180014004p+1)^{1}$ $\bigr]$
$b=12, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(1734402192p+1)^{1}$ , $(13966019054p+1)^{1}$ $\bigr]$
$b=12, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(854p+1)^{1}$ , $(12722p+1)^{1}$ , $(115023206499068018p+1)^{1}$ $\bigr]$
$b=12, p=31,$ $\bigl[$ $(12p+1)^{1}$ , $(4093020p+1)^{1}$ , $(753678322p+1)^{1}$ , $(7554437542p+1)^{1}$ $\bigr]$
$b=12, p=37,$ $\bigl[$ $(106320p+1)^{1}$ , $(5312450447386111529431901441820p+1)^{1}$ $\bigr]$
$b=12, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(48241416p+1)^{1}$ , $(2382168896595609426618782956070p+1)^{1}$ $\bigr]$
$b=12, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(286356p+1)^{1}$ , $(312662014p+1)^{1}$ , $(752552519966570347985220p+1)^{1}$ $\bigr]$
$b=12, p=47,$ $\bigl[$ $(225898935978660p+1)^{1}$ , $(95943592893056341227702299506368p+1)^{1}$ $\bigr]$
$b=13, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=13, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(20p+1)^{1}$ $\bigr]$
$b=13, p=5,$ $\bigl[$ $(6188p+1)^{1}$ $\bigr]$
$b=13, p=7,$ $\bigl[$ $(747006p+1)^{1}$ $\bigr]$
$b=13, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(38p+1)^{1}$ , $(78p+1)^{1}$ , $(1640p+1)^{1}$ $\bigr]$
$b=13, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(20310p+1)^{1}$ , $(138742p+1)^{1}$ $\bigr]$
$b=13, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(26p+1)^{1}$ , $(929321256324p+1)^{1}$ $\bigr]$
$b=13, p=19,$ $\bigl[$ $(677154p+1)^{1}$ , $(498365263392p+1)^{1}$ $\bigr]$
$b=13, p=23,$ $\bigl[$ $(60p+1)^{1}$ , $(109545449667362225354p+1)^{1}$ $\bigr]$
$b=13, p=29,$ $\bigl[$ $(68p+1)^{1}$ , $(98p+1)^{1}$ , $(122p+1)^{1}$ , $(29173831171547340240p+1)^{1}$ $\bigr]$
$b=13, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(36p+1)^{1}$ , $(263564806820366561566714528p+1)^{1}$ $\bigr]$
$b=13, p=37,$ $\bigl[$ $(40p+1)^{1}$ , $(1824207516p+1)^{1}$ , $(115885291804p+1)^{1}$ , $(863893087836p+1)^{1}$ $\bigr]$
$b=13, p=41,$ $\bigl[$ $(164410904042p+1)^{1}$ , $(1415786828715838643232432856746p+1)^{1}$ $\bigr]$
$b=13, p=43,$ $\bigl[$ $(2782p+1)^{1}$ , $(12855389388348064631970644285244132616996p+1)^{1}$ $\bigr]$
$b=13, p=47,$ $\bigl[$ $(3914p+1)^{1}$ , $(408853968p+1)^{1}$ , $(11367666903870409252205767432476420p+1)^{1}$ $\bigr]$
$b=14, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ , $(2p+1)^{1}$ $\bigr]$
$b=14, p=3,$ $\bigl[$ $(70p+1)^{1}$ $\bigr]$
$b=14, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(752p+1)^{1}$ $\bigr]$
$b=14, p=7,$ $\bigl[$ $(1158390p+1)^{1}$ $\bigr]$
$b=14, p=11,$ $\bigl[$ $(6p+1)^{1}$ , $(366p+1)^{1}$ , $(104958p+1)^{1}$ $\bigr]$
$b=14, p=13,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(12p+1)^{1}$ , $(2301096090p+1)^{1}$ $\bigr]$
$b=14, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(1339513540804428p+1)^{1}$ $\bigr]$
$b=14, p=19,$ $\bigl[$ $(24195562586837710110p+1)^{1}$ $\bigr]$
$b=14, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(20p+1)^{1}$ , $(102p+1)^{1}$ , $(462p+1)^{1}$ , $(97820p+1)^{1}$ , $(631532p+1)^{1}$ $\bigr]$
$b=14, p=29,$ $\bigl[$ $(452p+1)^{1}$ , $(882115518p+1)^{1}$ , $(13673467443415928p+1)^{1}$ $\bigr]$
$b=14, p=31,$ $\bigl[$ $(840744548329489667263460350902150p+1)^{1}$ $\bigr]$
$b=14, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(3821783428p+1)^{1}$ , $(168197518322504961042705040p+1)^{1}$ $\bigr]$
$b=14, p=41,$ $\bigl[$ $(183874817115853273584973835186677469699745450p+1)^{1}$ $\bigr]$
$b=14, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(198631271722408510085878443280029593561924242p+1)^{1}$ $\bigr]$
$b=14, p=47,$ $\bigl[$ $(14p+1)^{1}$ , $(78524p+1)^{1}$ , $(450144p+1)^{1}$ , $(522810p+1)^{1}$ , $(955211530565735720426400174p+1)^{1}$ $\bigr]$
$b=15, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{4}}$ $\bigr]$
$b=15, p=3,$ $\bigl[$ $(80p+1)^{1}$ $\bigr]$
$b=15, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(986p+1)^{1}$ $\bigr]$
$b=15, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(249066p+1)^{1}$ $\bigr]$
$b=15, p=11,$ $\bigl[$ $(6p+1)^{1}$ , $(42p+1)^{1}$ , $(212p+1)^{1}$ , $(776p+1)^{1}$ $\bigr]$
$b=15, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(12114p+1)^{1}$ , $(1281166p+1)^{1}$ $\bigr]$
$b=15, p=17,$ $\bigl[$ $(61470744p+1)^{1}$ , $(396147624p+1)^{1}$ $\bigr]$
$b=15, p=19,$ $\bigl[$ $(224848p+1)^{1}$ , $(19507856573824p+1)^{1}$ $\bigr]$
$b=15, p=23,$ $\bigl[$ $(36p+1)^{1}$ , $(1380p+1)^{1}$ , $(132454876166589816p+1)^{1}$ $\bigr]$
$b=15, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(533664688522123199099639207162p+1)^{1}$ $\bigr]$
$b=15, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(21309777353366287581514739526730p+1)^{1}$ $\bigr]$
$b=15, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(120p+1)^{1}$ , $(870730p+1)^{1}$ , $(66866769078p+1)^{1}$ , $(801242321368570p+1)^{1}$ $\bigr]$
$b=15, p=41,$ $\bigl[$ $(205617859086p+1)^{1}$ , $(342755978945117678487281772983502p+1)^{1}$ $\bigr]$
$b=15, p=43,$ $\bigl[$ $(619908581115822939869967045415613639394310225680p+1)^{1}$ $\bigr]$
$b=15, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(14p+1)^{1}$ , $(50p+1)^{1}$ , $(134p+1)^{1}$ , $(3914p+1)^{1}$ , $(56512712660997277178892779441592006p+1)^{1}$ $\bigr]$
$b=16, p=2,$ $\bigl[$ $(8p+1)^{1}$ $\bigr]$
$b=16, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(4p+1)^{1}$ $\bigr]$
$b=16, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(8p+1)^{1}$ $\bigr]$
$b=16, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(16p+1)^{1}$ , $(18p+1)^{1}$ $\bigr]$
$b=16, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(36p+1)^{1}$ , $(62p+1)^{1}$ , $(192p+1)^{1}$ $\bigr]$
$b=16, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(12p+1)^{1}$ , $(124p+1)^{1}$ , $(210p+1)^{1}$ , $(630p+1)^{1}$ $\bigr]$
$b=16, p=17,$ $\bigl[$ $(8p+1)^{1}$ , $(56p+1)^{1}$ , $(1548p+1)^{1}$ , $(2570p+1)^{1}$ , $(7710p+1)^{1}$ $\bigr]$
$b=16, p=19,$ $\bigl[$ $(12p+1)^{1}$ , $(24p+1)^{1}$ , $(9198p+1)^{1}$ , $(27594p+1)^{1}$ , $(27648p+1)^{1}$ $\bigr]$
$b=16, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(12p+1)^{1}$ , $(44p+1)^{1}$ , $(72p+1)^{1}$ , $(1316p+1)^{1}$ , $(7760p+1)^{1}$ , $(121574p+1)^{1}$ $\bigr]$
$b=16, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(38p+1)^{1}$ , $(72p+1)^{1}$ , $(104592p+1)^{1}$ , $(3702332p+1)^{1}$ , $(18513920p+1)^{1}$ $\bigr]$
$b=16, p=31,$ $\bigl[$ $(180p+1)^{1}$ , $(280p+1)^{1}$ , $(1596p+1)^{1}$ , $(12412p+1)^{1}$ , $(23091222p+1)^{1}$ , $(69273666p+1)^{1}$ $\bigr]$
$b=16, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(16p+1)^{1}$ , $(48p+1)^{1}$ , $(696786p+1)^{1}$ , $(4985976p+1)^{1}$ , $(6264048p+1)^{1}$ , $(16657248p+1)^{1}$ $\bigr]$
$b=16, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(248p+1)^{1}$ , $(326p+1)^{1}$ , $(4428p+1)^{1}$ , $(295428p+1)^{1}$ , $(1054868p+1)^{1}$ , $(4012472p+1)^{1}$ , $(215400456p+1)^{1}$ $\bigr]$
$b=16, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(10p+1)^{1}$ , $(226p+1)^{1}$ , $(2364p+1)^{1}$ , $(11632p+1)^{1}$ , $(48834p+1)^{1}$ , $(40912041060p+1)^{1}$ , $(68186767614p+1)^{1}$ $\bigr]$
$b=16, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(50p+1)^{1}$ , $(80p+1)^{1}$ , $(96p+1)^{1}$ , $(282224p+1)^{1}$ , $(159235044p+1)^{1}$ , $(3526990160p+1)^{1}$ , $(2994414288896p+1)^{1}$ $\bigr]$
$b=17, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(1p+1)^{2}}$ $\bigr]$
$b=17, p=3,$ $\bigl[$ $(102p+1)^{1}$ $\bigr]$
$b=17, p=5,$ $\bigl[$ $(17748p+1)^{1}$ $\bigr]$
$b=17, p=7,$ $\bigl[$ $(3663738p+1)^{1}$ $\bigr]$
$b=17, p=11,$ $\bigl[$ $(194726683566p+1)^{1}$ $\bigr]$
$b=17, p=13,$ $\bigl[$ $(16312p+1)^{1}$ , $(224553604p+1)^{1}$ $\bigr]$
$b=17, p=17,$ $\bigl[$ $(644p+1)^{1}$ , $(102896p+1)^{1}$ , $(158796396p+1)^{1}$ $\bigr]$
$b=17, p=19,$ $\bigl[$ $(12p+1)^{1}$ , $(58p+1)^{1}$ , $(10663534p+1)^{1}$ , $(15367038p+1)^{1}$ $\bigr]$
$b=17, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(1154461661705569137520760p+1)^{1}$ $\bigr]$
$b=17, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(248p+1)^{1}$ , $(209934p+1)^{1}$ , $(402029403471929035512p+1)^{1}$ $\bigr]$
$b=17, p=31,$ $\bigl[$ $(132p+1)^{1}$ , $(197532p+1)^{1}$ , $(11204537020193835546420162p+1)^{1}$ $\bigr]$
$b=17, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(27484313636744340p+1)^{1}$ , $(168077907600266909146p+1)^{1}$ $\bigr]$
$b=17, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(21758p+1)^{1}$ , $(325992p+1)^{1}$ , $(23419929629772p+1)^{1}$ , $(450464171879256456p+1)^{1}$ $\bigr]$
$b=17, p=43,$ $\bigl[$ $(36p+1)^{1}$ , $(71532040096596890224p+1)^{1}$ , $(24756810727222807165642690p+1)^{1}$ $\bigr]$
$b=17, p=47,$ $\bigl[$ $(9013250974441131642914037329702512502710510444280169378p+1)^{1}$ $\bigr]$
$b=18, p=2,$ $\bigl[$ $\color{magenta}\bm{(9p+1)^{1}}$ $\bigr]$
$b=18, p=3,$ $\bigl[$ $(2p+1)^{3}$ $\bigr]$
$b=18, p=5,$ $\bigl[$ $(8p+1)^{1}$ , $(542p+1)^{1}$ $\bigr]$
$b=18, p=7,$ $\bigl[$ $(64p+1)^{1}$ , $(11458p+1)^{1}$ $\bigr]$
$b=18, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(18p+1)^{1}$ , $(1466p+1)^{1}$ , $(4656p+1)^{1}$ $\bigr]$
$b=18, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(40p+1)^{1}$ , $(2289209176p+1)^{1}$ $\bigr]$
$b=18, p=17,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(444923989362649406p+1)^{1}$ $\bigr]$
$b=18, p=19,$ $\bigl[$ $(360p+1)^{1}$ , $(320520258410674338p+1)^{1}$ $\bigr]$
$b=18, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(26p+1)^{1}$ , $(324696p+1)^{1}$ , $(904401652054146p+1)^{1}$ $\bigr]$
$b=18, p=29,$ $\bigl[$ $(51915450620958p+1)^{1}$ , $(3406913465907314424p+1)^{1}$ $\bigr]$
$b=18, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(418p+1)^{1}$ , $(41187985066p+1)^{1}$ , $(302115441836262880p+1)^{1}$ $\bigr]$
$b=18, p=37,$ $\bigl[$ $(4270p+1)^{1}$ , $(280414001885294752964595721794121337080p+1)^{1}$ $\bigr]$
$b=18, p=41,$ $\bigl[$ $(92958p+1)^{1}$ , $(2788806p+1)^{1}$ , $(9630903349870633232340773738166486p+1)^{1}$ $\bigr]$
$b=18, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(103836087284000652753784p+1)^{1}$ , $(673761672151378219550760p+1)^{1}$ $\bigr]$
$b=18, p=47,$ $\bigl[$ $(440p+1)^{1}$ , $(6021288357544943085064491605149793229808791352459466p+1)^{1}$ $\bigr]$
$b=19, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $(2p+1)^{1}$ $\bigr]$
$b=19, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(42p+1)^{1}$ $\bigr]$
$b=19, p=5,$ $\bigl[$ $(30p+1)^{1}$ , $(182p+1)^{1}$ $\bigr]$
$b=19, p=7,$ $\bigl[$ $(100p+1)^{1}$ , $(10120p+1)^{1}$ $\bigr]$
$b=19, p=11,$ $\bigl[$ $(9480p+1)^{1}$ , $(5641820p+1)^{1}$ $\bigr]$
$b=19, p=13,$ $\bigl[$ $(46p+1)^{1}$ , $(2250p+1)^{1}$ , $(10256836p+1)^{1}$ $\bigr]$
$b=19, p=17,$ $\bigl[$ $(179106p+1)^{1}$ , $(5882075448938p+1)^{1}$ $\bigr]$
$b=19, p=19,$ $\bigl[$ $(5784852794328402307380p+1)^{1}$ $\bigr]$
$b=19, p=23,$ $\bigl[$ $(12p+1)^{1}$ , $(102p+1)^{1}$ , $(717294044p+1)^{1}$ , $(58065017514p+1)^{1}$ $\bigr]$
$b=19, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(10241483498340p+1)^{1}$ , $(5691347776384478p+1)^{1}$ $\bigr]$
$b=19, p=31,$ $\bigl[$ $(7847429641660768971083657470811348700p+1)^{1}$ $\bigr]$
$b=19, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(96977691569850p+1)^{1}$ , $(578561021877730643548137934p+1)^{1}$ $\bigr]$
$b=19, p=41,$ $\bigl[$ $(259866p+1)^{1}$ , $(285694052p+1)^{1}$ , $(291489464736570326880542313147270p+1)^{1}$ $\bigr]$
$b=19, p=43,$ $\bigl[$ $(439945873212783462687384p+1)^{1}$ , $(661905784433527115671976652p+1)^{1}$ $\bigr]$
$b=19, p=47,$ $\bigl[$ $(1492962439576714348948446916507553571122192695040806434620p+1)^{1}$ $\bigr]$
$b=20, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=20, p=3,$ $\bigl[$ $(140p+1)^{1}$ $\bigr]$
$b=20, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(12p+1)^{1}$ , $(50p+1)^{1}$ $\bigr]$
$b=20, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(10p+1)^{1}$ , $(4674p+1)^{1}$ $\bigr]$
$b=20, p=11,$ $\bigl[$ $(979904306220p+1)^{1}$ $\bigr]$
$b=20, p=13,$ $\bigl[$ $(240p+1)^{1}$ , $(10966p+1)^{1}$ , $(745426p+1)^{1}$ $\bigr]$
$b=20, p=17,$ $\bigl[$ $(40579566563467492260p+1)^{1}$ $\bigr]$
$b=20, p=19,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(3966762322p+1)^{1}$ , $(10141900240p+1)^{1}$ $\bigr]$
$b=20, p=23,$ $\bigl[$ $(30p+1)^{1}$ , $(60p+1)^{1}$ , $(2011577352083542742550p+1)^{1}$ $\bigr]$
$b=20, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(32p+1)^{1}$ , $(372p+1)^{1}$ , $(4952p+1)^{1}$ , $(16079562p+1)^{1}$ , $(2460455332472p+1)^{1}$ $\bigr]$
$b=20, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(360p+1)^{1}$ , $(53100p+1)^{1}$ , $(10968963928p+1)^{1}$ , $(18765809044938p+1)^{1}$ $\bigr]$
$b=20, p=37,$ $\bigl[$ $(1764p+1)^{1}$ , $(78106950p+1)^{1}$ , $(10364686060546107925082690755734p+1)^{1}$ $\bigr]$
$b=20, p=41,$ $\bigl[$ $(18p+1)^{1}$ , $(19243556828524373918p+1)^{1}$ , $(484148647230439901779374200p+1)^{1}$ $\bigr]$
$b=20, p=43,$ $\bigl[$ $(8584240p+1)^{1}$ , $(291673819653099866856597948225215830727328700p+1)^{1}$ $\bigr]$
$b=20, p=47,$ $\bigl[$ $(24p+1)^{1}$ , $(104p+1)^{1}$ , $(16820251824p+1)^{1}$ , $(41083864740p+1)^{1}$ , $(1870444636489830943284557864p+1)^{1}$ $\bigr]$

Mizar/みざー

$b=21, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(5p+1)^{1}}$ $\bigr]$
$b=21, p=3,$ $\bigl[$ $(154p+1)^{1}$ $\bigr]$
$b=21, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(8168p+1)^{1}$ $\bigr]$
$b=21, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(90p+1)^{1}$ , $(474p+1)^{1}$ $\bigr]$
$b=21, p=11,$ $\bigl[$ $(1592170457010p+1)^{1}$ $\bigr]$
$b=21, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(14572p+1)^{1}$ , $(39699550p+1)^{1}$ $\bigr]$
$b=21, p=17,$ $\bigl[$ $(88358654397299093808p+1)^{1}$ $\bigr]$
$b=21, p=19,$ $\bigl[$ $(634809948p+1)^{1}$ , $(2890584559158p+1)^{1}$ $\bigr]$
$b=21, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(852p+1)^{1}$ , $(6081328961526229689032p+1)^{1}$ $\bigr]$
$b=21, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(38058762p+1)^{1}$ , $(8509079328p+1)^{1}$ , $(23710805947988p+1)^{1}$ $\bigr]$
$b=21, p=31,$ $\bigl[$ $(146474622p+1)^{1}$ , $(126994644852p+1)^{1}$ , $(8792963404891548p+1)^{1}$ $\bigr]$
$b=21, p=37,$ $\bigl[$ $(840p+1)^{1}$ , $(45453046p+1)^{1}$ , $(216083937658202929529732929120354p+1)^{1}$ $\bigr]$
$b=21, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(344460p+1)^{1}$ , $(2029730p+1)^{1}$ , $(420050862p+1)^{1}$ , $(22305640230p+1)^{1}$ , $(1290238613388p+1)^{1}$ $\bigr]$
$b=21, p=43,$ $\bigl[$ $(833549167925186640102525304049878755654656600734807314p+1)^{1}$ $\bigr]$
$b=21, p=47,$ $\bigl[$ $(1058p+1)^{1}$ , $(4830p+1)^{1}$ , $(1596650p+1)^{1}$ , $(3373314p+1)^{1}$ , $(112741986p+1)^{1}$ , $(208398256132949975172216p+1)^{1}$ $\bigr]$
$b=22, p=2,$ $\bigl[$ $\color{magenta}\bm{(11p+1)^{1}}$ $\bigr]$
$b=22, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(4p+1)^{2}$ $\bigr]$
$b=22, p=5,$ $\bigl[$ $(49082p+1)^{1}$ $\bigr]$
$b=22, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2424060p+1)^{1}$ $\bigr]$
$b=22, p=11,$ $\bigl[$ $(6p+1)^{1}$ , $(32p+1)^{1}$ , $(106951776p+1)^{1}$ $\bigr]$
$b=22, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(154p+1)^{1}$ , $(6546725974p+1)^{1}$ $\bigr]$
$b=22, p=17,$ $\bigl[$ $(14p+1)^{1}$ , $(4395854p+1)^{1}$ , $(10390280450p+1)^{1}$ $\bigr]$
$b=22, p=19,$ $\bigl[$ $(2418p+1)^{1}$ , $(17958p+1)^{1}$ , $(5126557684338p+1)^{1}$ $\bigr]$
$b=22, p=23,$ $\bigl[$ $(194p+1)^{1}$ , $(57524522550p+1)^{1}$ , $(2633702903706p+1)^{1}$ $\bigr]$
$b=22, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(3068538p+1)^{1}$ , $(4158380p+1)^{1}$ , $(2208700126495365878p+1)^{1}$ $\bigr]$
$b=22, p=31,$ $\bigl[$ $(115876110p+1)^{1}$ , $(176265174634636365824578310736p+1)^{1}$ $\bigr]$
$b=22, p=37,$ $\bigl[$ $(8398p+1)^{1}$ , $(50999706480240p+1)^{1}$ , $(102581673291225437954529316p+1)^{1}$ $\bigr]$
$b=22, p=41,$ $\bigl[$ $(31668510p+1)^{1}$ , $(2241518445102p+1)^{1}$ , $(106558746041916111943269206786p+1)^{1}$ $\bigr]$
$b=22, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(22p+1)^{1}$ , $(6041842p+1)^{1}$ , $(137864871952787324919893591638090114353190p+1)^{1}$ $\bigr]$
$b=22, p=47,$ $\bigl[$ $(524334p+1)^{1}$ , $(863778p+1)^{1}$ , $(229880280112040p+1)^{1}$ , $(116343832943805381253366911354p+1)^{1}$ $\bigr]$
$b=23, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{3}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=23, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(26p+1)^{1}$ $\bigr]$
$b=23, p=5,$ $\bigl[$ $(58512p+1)^{1}$ $\bigr]$
$b=23, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(762388p+1)^{1}$ $\bigr]$
$b=23, p=11,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(357930036782p+1)^{1}$ $\bigr]$
$b=23, p=13,$ $\bigl[$ $(3668586p+1)^{1}$ , $(36953346p+1)^{1}$ $\bigr]$
$b=23, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(3661545079711930038p+1)^{1}$ $\bigr]$
$b=23, p=19,$ $\bigl[$ $(112p+1)^{1}$ , $(3361972p+1)^{1}$ , $(1312590453348p+1)^{1}$ $\bigr]$
$b=23, p=23,$ $\bigl[$ $(20p+1)^{1}$ , $(56p+1)^{1}$ , $(36156653556p+1)^{1}$ , $(83506408344p+1)^{1}$ $\bigr]$
$b=23, p=29,$ $\bigl[$ $(8p+1)^{1}$ , $(60p+1)^{1}$ , $(2934p+1)^{1}$ , $(393452p+1)^{1}$ , $(12302089120147162182p+1)^{1}$ $\bigr]$
$b=23, p=31,$ $\bigl[$ $(1318999678342p+1)^{1}$ , $(58637056125461925661703110p+1)^{1}$ $\bigr]$
$b=23, p=37,$ $\bigl[$ $(52044819940p+1)^{1}$ , $(154428087625359665618636173637782780p+1)^{1}$ $\bigr]$
$b=23, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(2854121706p+1)^{1}$ , $(7732150553626619578222085879678992328000p+1)^{1}$ $\bigr]$
$b=23, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(2142p+1)^{1}$ , $(2377207391869483999786619463499426519942310158354p+1)^{1}$ $\bigr]$
$b=23, p=47,$ $\bigl[$ $(34314p+1)^{1}$ , $(3420899550958760433514194p+1)^{1}$ , $(37400731804750471711868941056p+1)^{1}$ $\bigr]$
$b=24, p=2,$ $\bigl[$ $(2p+1)^{2}$ $\bigr]$
$b=24, p=3,$ $\bigl[$ $(200p+1)^{1}$ $\bigr]$
$b=24, p=5,$ $\bigl[$ $(69240p+1)^{1}$ $\bigr]$
$b=24, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(34p+1)^{1}$ , $(4110p+1)^{1}$ $\bigr]$
$b=24, p=11,$ $\bigl[$ $(6p+1)^{1}$ , $(668p+1)^{1}$ , $(12215186p+1)^{1}$ $\bigr]$
$b=24, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(504p+1)^{1}$ , $(1224p+1)^{1}$ , $(530404p+1)^{1}$ $\bigr]$
$b=24, p=17,$ $\bigl[$ $(18p+1)^{1}$ , $(7092590p+1)^{1}$ , $(20091954956p+1)^{1}$ $\bigr]$
$b=24, p=19,$ $\bigl[$ $(383294118787242913206600p+1)^{1}$ $\bigr]$
$b=24, p=23,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(5426p+1)^{1}$ , $(13250p+1)^{1}$ , $(2555176758861936p+1)^{1}$ $\bigr]$
$b=24, p=29,$ $\bigl[$ $(68p+1)^{1}$ , $(350p+1)^{1}$ , $(38970p+1)^{1}$ , $(703453629457372200890544p+1)^{1}$ $\bigr]$
$b=24, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(52p+1)^{1}$ , $(318p+1)^{1}$ , $(1138p+1)^{1}$ , $(1278p+1)^{1}$ , $(130508862p+1)^{1}$ , $(306767867650p+1)^{1}$ $\bigr]$
$b=24, p=37,$ $\bigl[$ $(100p+1)^{1}$ , $(1320134470p+1)^{1}$ , $(7598841799511964908388171197048130p+1)^{1}$ $\bigr]$
$b=24, p=41,$ $\bigl[$ $(68p+1)^{1}$ , $(986891082p+1)^{1}$ , $(123887549761896p+1)^{1}$ , $(717523454028035991361718p+1)^{1}$ $\bigr]$
$b=24, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(1374p+1)^{1}$ , $(525792p+1)^{1}$ , $(392342038419374618566043976108571809671980p+1)^{1}$ $\bigr]$
$b=24, p=47,$ $\bigl[$ $(314p+1)^{1}$ , $(10580p+1)^{1}$ , $(9342461885647817213787994804104501584339459046438534p+1)^{1}$ $\bigr]$
$b=25, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(6p+1)^{1}$ $\bigr]$
$b=25, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(10p+1)^{1}$ $\bigr]$
$b=25, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(14p+1)^{1}$ , $(104p+1)^{1}$ $\bigr]$
$b=25, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(64p+1)^{1}$ , $(2790p+1)^{1}$ $\bigr]$
$b=25, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(480p+1)^{1}$ , $(1109730p+1)^{1}$ $\bigr]$
$b=25, p=13,$ $\bigl[$ $(402p+1)^{1}$ , $(2994p+1)^{1}$ , $(23475060p+1)^{1}$ $\bigr]$
$b=25, p=17,$ $\bigl[$ $(24p+1)^{1}$ , $(180p+1)^{1}$ , $(2443580p+1)^{1}$ , $(27432024p+1)^{1}$ $\bigr]$
$b=25, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(40p+1)^{1}$ , $(330p+1)^{1}$ , $(1032p+1)^{1}$ , $(11212p+1)^{1}$ , $(209530p+1)^{1}$ $\bigr]$
$b=25, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(390p+1)^{1}$ , $(14443798320p+1)^{1}$ , $(1837947726654p+1)^{1}$ $\bigr]$
$b=25, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(1230p+1)^{1}$ , $(175754p+1)^{1}$ , $(210028183578p+1)^{1}$ , $(762965394632p+1)^{1}$ $\bigr]$
$b=25, p=31,$ $\bigl[$ $(42p+1)^{1}$ , $(60p+1)^{1}$ , $(684100p+1)^{1}$ , $(906006826p+1)^{1}$ , $(20179113176567370p+1)^{1}$ $\bigr]$
$b=25, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(246p+1)^{1}$ , $(784060p+1)^{1}$ , $(377620810p+1)^{1}$ , $(236148142074p+1)^{1}$ , $(1241085226618p+1)^{1}$ $\bigr]$
$b=25, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(1062p+1)^{1}$ , $(5400p+1)^{1}$ , $(54591128p+1)^{1}$ , $(231025039235988p+1)^{1}$ , $(123885479102846048p+1)^{1}$ $\bigr]$
$b=25, p=43,$ $\bigl[$ $(36p+1)^{1}$ , $(222p+1)^{1}$ , $(38244480p+1)^{1}$ , $(182944374p+1)^{1}$ , $(37877789496p+1)^{1}$ , $(4019245399972462530p+1)^{1}$ $\bigr]$
$b=25, p=47,$ $\bigl[$ $(44p+1)^{1}$ , $(338058644p+1)^{1}$ , $(76646212998069380p+1)^{1}$ , $(3779482637021809499314490784990p+1)^{1}$ $\bigr]$
$b=26, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{3}}$ $\bigr]$
$b=26, p=3,$ $\bigl[$ $(6p+1)^{1}$ , $(12p+1)^{1}$ $\bigr]$
$b=26, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(1728p+1)^{1}$ $\bigr]$
$b=26, p=7,$ $\bigl[$ $(45896058p+1)^{1}$ $\bigr]$
$b=26, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(5958p+1)^{1}$ , $(8854142p+1)^{1}$ $\bigr]$
$b=26, p=13,$ $\bigl[$ $(2135752p+1)^{1}$ , $(274964086p+1)^{1}$ $\bigr]$
$b=26, p=17,$ $\bigl[$ $(66p+1)^{1}$ , $(2375626872107591484p+1)^{1}$ $\bigr]$
$b=26, p=19,$ $\bigl[$ $(1758p+1)^{1}$ , $(48307496187727348188p+1)^{1}$ $\bigr]$
$b=26, p=23,$ $\bigl[$ $(596p+1)^{1}$ , $(47226p+1)^{1}$ , $(66456864p+1)^{1}$ , $(26763093020p+1)^{1}$ $\bigr]$
$b=26, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(2529513915645143118516945582534704420p+1)^{1}$ $\bigr]$
$b=26, p=31,$ $\bigl[$ $(21792713068475842p+1)^{1}$ , $(139700863317388509431896p+1)^{1}$ $\bigr]$
$b=26, p=37,$ $\bigl[$ $(34p+1)^{1}$ , $(1662280p+1)^{1}$ , $(25248549692668p+1)^{1}$ , $(337677668437956045172624p+1)^{1}$ $\bigr]$
$b=26, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(64242p+1)^{1}$ , $(46078913936664394390832903021906039587529824478p+1)^{1}$ $\bigr]$
$b=26, p=43,$ $\bigl[$ $(6493001429596504409672809053274055565050415613881496676994p+1)^{1}$ $\bigr]$
$b=26, p=47,$ $\bigl[$ $(255029587211664258p+1)^{1}$ , $(226475413950631558338306629782655747882780280p+1)^{1}$ $\bigr]$
$b=27, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=27, p=3,$ $\bigl[$ $(252p+1)^{1}$ $\bigr]$
$b=27, p=5,$ $\bigl[$ $(2p+1)^{2}$ , $(912p+1)^{1}$ $\bigr]$
$b=27, p=7,$ $\bigl[$ $(156p+1)^{1}$ , $(52584p+1)^{1}$ $\bigr]$
$b=27, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(350p+1)^{1}$ , $(219449208p+1)^{1}$ $\bigr]$
$b=27, p=13,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(24p+1)^{1}$ , $(504p+1)^{1}$ , $(564p+1)^{1}$ , $(61320p+1)^{1}$ $\bigr]$
$b=27, p=17,$ $\bigl[$ $(110p+1)^{1}$ , $(756p+1)^{1}$ , $(2030p+1)^{1}$ , $(5871186588p+1)^{1}$ $\bigr]$
$b=27, p=19,$ $\bigl[$ $(12p+1)^{1}$ , $(84p+1)^{1}$ , $(13092p+1)^{1}$ , $(19152p+1)^{1}$ , $(96009432p+1)^{1}$ $\bigr]$
$b=27, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(12p+1)^{1}$ , $(43544486p+1)^{1}$ , $(107010590291907372p+1)^{1}$ $\bigr]$
$b=27, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(984p+1)^{1}$ , $(2580p+1)^{1}$ , $(702794p+1)^{1}$ , $(1111548p+1)^{1}$ , $(5180142206064p+1)^{1}$ $\bigr]$
$b=27, p=31,$ $\bigl[$ $(22p+1)^{1}$ , $(36p+1)^{1}$ , $(3312p+1)^{1}$ , $(142066p+1)^{1}$ , $(847538769161784488542836p+1)^{1}$ $\bigr]$
$b=27, p=37,$ $\bigl[$ $(353998p+1)^{1}$ , $(505464p+1)^{1}$ , $(3237276p+1)^{1}$ , $(464571046p+1)^{1}$ , $(188171713872161196p+1)^{1}$ $\bigr]$
$b=27, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(1248p+1)^{1}$ , $(61632p+1)^{1}$ , $(2120748698p+1)^{1}$ , $(48776288232131391330769970995008p+1)^{1}$ $\bigr]$
$b=27, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(96p+1)^{1}$ , $(51141216p+1)^{1}$ , $(8856012717707254p+1)^{1}$ , $(21229106178205979323121976p+1)^{1}$ $\bigr]$
$b=27, p=47,$ $\bigl[$ $(26p+1)^{1}$ , $(468p+1)^{1}$ , $(108780p+1)^{1}$ , $(2056526p+1)^{1}$ , $(3446161608p+1)^{1}$ , $(43216193316p+1)^{1}$ , $(3517052637072320844p+1)^{1}$ $\bigr]$
$b=28, p=2,$ $\bigl[$ $(14p+1)^{1}$ $\bigr]$
$b=28, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(90p+1)^{1}$ $\bigr]$
$b=28, p=5,$ $\bigl[$ $(127484p+1)^{1}$ $\bigr]$
$b=28, p=7,$ $\bigl[$ $(16p+1)^{1}$ , $(631780p+1)^{1}$ $\bigr]$
$b=28, p=11,$ $\bigl[$ $(552458p+1)^{1}$ , $(4595046p+1)^{1}$ $\bigr]$
$b=28, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(349519508815672p+1)^{1}$ $\bigr]$
$b=28, p=17,$ $\bigl[$ $(8707106314829844247340p+1)^{1}$ $\bigr]$
$b=28, p=19,$ $\bigl[$ $(1109694p+1)^{1}$ , $(289686576270473682p+1)^{1}$ $\bigr]$
$b=28, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(65985006339715492131912122286p+1)^{1}$ $\bigr]$
$b=28, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(20089500339223207051367759618464596462p+1)^{1}$ $\bigr]$
$b=28, p=31,$ $\bigl[$ $(348p+1)^{1}$ , $(54058p+1)^{1}$ , $(461536p+1)^{1}$ , $(3360493715578764100906338p+1)^{1}$ $\bigr]$
$b=28, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(40p+1)^{1}$ , $(544p+1)^{1}$ , $(976469424p+1)^{1}$ , $(9807377870748753776147591206p+1)^{1}$ $\bigr]$
$b=28, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(20p+1)^{1}$ , $(19548p+1)^{1}$ , $(792986p+1)^{1}$ , $(109641330133707621243232153884979319868p+1)^{1}$ $\bigr]$
$b=28, p=43,$ $\bigl[$ $(84p+1)^{1}$ , $(1396p+1)^{1}$ , $(15912p+1)^{1}$ , $(2463769170p+1)^{1}$ , $(542358266634p+1)^{1}$ , $(396932816373169568236p+1)^{1}$ $\bigr]$
$b=28, p=47,$ $\bigl[$ $(134p+1)^{1}$ , $(513380p+1)^{1}$ , $(452705881484p+1)^{1}$ , $(72875866227083786p+1)^{1}$ , $(7388594603711568907520p+1)^{1}$ $\bigr]$
$b=29, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ , $(2p+1)^{1}$ $\bigr]$
$b=29, p=3,$ $\bigl[$ $(4p+1)^{1}$ , $(22p+1)^{1}$ $\bigr]$
$b=29, p=5,$ $\bigl[$ $(146508p+1)^{1}$ $\bigr]$
$b=29, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(12572796p+1)^{1}$ $\bigr]$
$b=29, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(1722262812776p+1)^{1}$ $\bigr]$
$b=29, p=13,$ $\bigl[$ $(40p+1)^{1}$ , $(11394p+1)^{1}$ , $(365268622p+1)^{1}$ $\bigr]$
$b=29, p=17,$ $\bigl[$ $(230p+1)^{1}$ , $(116348p+1)^{1}$ , $(1970893387506p+1)^{1}$ $\bigr]$
$b=29, p=19,$ $\bigl[$ $(72982p+1)^{1}$ , $(8273335821061253332p+1)^{1}$ $\bigr]$
$b=29, p=23,$ $\bigl[$ $(5709902664p+1)^{1}$ , $(51040103143488493062p+1)^{1}$ $\bigr]$
$b=29, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(578p+1)^{1}$ , $(2912p+1)^{1}$ , $(83744p+1)^{1}$ , $(486602p+1)^{1}$ , $(2011068p+1)^{1}$ , $(18942578p+1)^{1}$ $\bigr]$
$b=29, p=31,$ $\bigl[$ $(1186p+1)^{1}$ , $(493374930264478p+1)^{1}$ , $(4424062387939988574906p+1)^{1}$ $\bigr]$
$b=29, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(376p+1)^{1}$ , $(664962138p+1)^{1}$ , $(24308629329392585340539408578622994p+1)^{1}$ $\bigr]$
$b=29, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(68p+1)^{1}$ , $(10902p+1)^{1}$ , $(6068476030170432p+1)^{1}$ , $(30739366680917316267465864096p+1)^{1}$ $\bigr]$
$b=29, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(324p+1)^{1}$ , $(4968222p+1)^{1}$ , $(1232330596272194297913941271797695062715646332p+1)^{1}$ $\bigr]$
$b=29, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(14036p+1)^{1}$ , $(94488p+1)^{1}$ , $(166466p+1)^{1}$ , $(344686453046p+1)^{1}$ , $(2134871332470p+1)^{1}$ , $(38943232242957446p+1)^{1}$ $\bigr]$
$b=30, p=2,$ $\bigl[$ $\color{magenta}\bm{(15p+1)^{1}}$ $\bigr]$
$b=30, p=3,$ $\bigl[$ $(2p+1)^{2}$ , $(6p+1)^{1}$ $\bigr]$
$b=30, p=5,$ $\bigl[$ $(167586p+1)^{1}$ $\bigr]$
$b=30, p=7,$ $\bigl[$ $(10p+1)^{1}$ , $(16p+1)^{1}$ , $(13428p+1)^{1}$ $\bigr]$
$b=30, p=11,$ $\bigl[$ $(55531974921630p+1)^{1}$ $\bigr]$
$b=30, p=13,$ $\bigl[$ $(70p+1)^{1}$ , $(1026p+1)^{1}$ , $(13762p+1)^{1}$ , $(19452p+1)^{1}$ $\bigr]$
$b=30, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(24p+1)^{1}$ , $(621804525107625156p+1)^{1}$ $\bigr]$
$b=30, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(110438086582225558480060p+1)^{1}$ $\bigr]$
$b=30, p=23,$ $\bigl[$ $(12p+1)^{1}$ , $(20p+1)^{1}$ , $(6475092p+1)^{1}$ , $(75373200p+1)^{1}$ , $(428118266p+1)^{1}$ $\bigr]$
$b=30, p=29,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(332p+1)^{1}$ , $(29224104116714698529176343274429210p+1)^{1}$ $\bigr]$
$b=30, p=31,$ $\bigl[$ $(12p+1)^{1}$ , $(35013662530p+1)^{1}$ , $(16970363205567234639344808256p+1)^{1}$ $\bigr]$
$b=30, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(126297737655721199741808241543085350001827357696p+1)^{1}$ $\bigr]$
$b=30, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(71862p+1)^{1}$ , $(73473930p+1)^{1}$ , $(4164003303859382830832088215239985860508p+1)^{1}$ $\bigr]$
$b=30, p=43,$ $\bigl[$ $(22p+1)^{1}$ , $(30p+1)^{1}$ , $(248952784p+1)^{1}$ , $(14838630262p+1)^{1}$ , $(2013967988790p+1)^{1}$ , $(3640009752697695574p+1)^{1}$ $\bigr]$
$b=30, p=47,$ $\bigl[$ $(24p+1)^{1}$ , $(50p+1)^{1}$ , $(4646p+1)^{1}$ , $(21170p+1)^{1}$ , $(3382659940230252196006729498962625642462548708056p+1)^{1}$ $\bigr]$

Mizar/みざー

$b=31, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{5}}$ $\bigr]$
$b=31, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(110p+1)^{1}$ $\bigr]$
$b=31, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(3470p+1)^{1}$ $\bigr]$
$b=31, p=7,$ $\bigl[$ $(131012448p+1)^{1}$ $\bigr]$
$b=31, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(36p+1)^{1}$ , $(56p+1)^{1}$ , $(13666622p+1)^{1}$ $\bigr]$
$b=31, p=13,$ $\bigl[$ $(3262p+1)^{1}$ , $(186676p+1)^{1}$ , $(608370p+1)^{1}$ $\bigr]$
$b=31, p=17,$ $\bigl[$ $(44215915243456359173888p+1)^{1}$ $\bigr]$
$b=31, p=19,$ $\bigl[$ $(30p+1)^{1}$ , $(750p+1)^{1}$ , $(4672140333295303272p+1)^{1}$ $\bigr]$
$b=31, p=23,$ $\bigl[$ $(65652p+1)^{1}$ , $(2676632p+1)^{1}$ , $(312016293970597092p+1)^{1}$ $\bigr]$
$b=31, p=29,$ $\bigl[$ $(12p+1)^{1}$ , $(372p+1)^{1}$ , $(1718p+1)^{1}$ , $(51123110p+1)^{1}$ , $(387675128p+1)^{1}$ , $(6529082760p+1)^{1}$ $\bigr]$
$b=31, p=31,$ $\bigl[$ $(18353950678197027912484562396837972855962080p+1)^{1}$ $\bigr]$
$b=31, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(114p+1)^{1}$ , $(4124265748p+1)^{1}$ , $(6967661010p+1)^{1}$ , $(10449370488p+1)^{1}$ , $(1427364676296p+1)^{1}$ $\bigr]$
$b=31, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(1036141394010565283238p+1)^{1}$ , $(3225844008645692105918617723816572p+1)^{1}$ $\bigr]$
$b=31, p=43,$ $\bigl[$ $(3418202352p+1)^{1}$ , $(70908271732710713102566303418571725135834785195056p+1)^{1}$ $\bigr]$
$b=31, p=47,$ $\bigl[$ $(66565386010544p+1)^{1}$ , $(3637084776656297227586p+1)^{1}$ , $(16465802530824261473310577490p+1)^{1}$ $\bigr]$
$b=32, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ , $\color{magenta}\bm{(5p+1)^{1}}$ $\bigr]$
$b=32, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(50p+1)^{1}$ $\bigr]$
$b=32, p=5,$ $\bigl[$ $(120p+1)^{1}$ , $(360p+1)^{1}$ $\bigr]$
$b=32, p=7,$ $\bigl[$ $(10p+1)^{1}$ , $(18p+1)^{1}$ , $(17560p+1)^{1}$ $\bigr]$
$b=32, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(80p+1)^{1}$ , $(290p+1)^{1}$ , $(18360p+1)^{1}$ $\bigr]$
$b=32, p=13,$ $\bigl[$ $(630p+1)^{1}$ , $(11176549504470p+1)^{1}$ $\bigr]$
$b=32, p=17,$ $\bigl[$ $(7710p+1)^{1}$ , $(560057223901985790p+1)^{1}$ $\bigr]$
$b=32, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(27594p+1)^{1}$ , $(22146250p+1)^{1}$ , $(1596165930p+1)^{1}$ $\bigr]$
$b=32, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(650p+1)^{1}$ , $(7760p+1)^{1}$ , $(175520p+1)^{1}$ , $(115065552651480p+1)^{1}$ $\bigr]$
$b=32, p=29,$ $\bigl[$ $(8p+1)^{1}$ , $(38p+1)^{1}$ , $(72p+1)^{1}$ , $(92410177854615959127242327384310p+1)^{1}$ $\bigr]$
$b=32, p=31,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(10p+1)^{1}$ , $(370p+1)^{1}$ , $(2370p+1)^{1}$ , $(69273666p+1)^{1}$ , $(149997400p+1)^{1}$ , $(585748703650p+1)^{1}$ $\bigr]$
$b=32, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(16657248p+1)^{1}$ , $(42915018864670p+1)^{1}$ , $(195913745926642162193317720p+1)^{1}$ $\bigr]$
$b=32, p=41,$ $\bigl[$ $(326p+1)^{1}$ , $(71720p+1)^{1}$ , $(4012472p+1)^{1}$ , $(1711496150p+1)^{1}$ , $(89164025988019443455465340480p+1)^{1}$ $\bigr]$
$b=32, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(40p+1)^{1}$ , $(226p+1)^{1}$ , $(48834p+1)^{1}$ , $(17012010p+1)^{1}$ , $(11973299970p+1)^{1}$ , $(6928541621954599173136330p+1)^{1}$ $\bigr]$
$b=32, p=47,$ $\bigl[$ $(50p+1)^{1}$ , $(96p+1)^{1}$ , $(282224p+1)^{1}$ , $(50879040p+1)^{1}$ , $(1538218880p+1)^{1}$ , $(1557495753088468209478160364829250p+1)^{1}$ $\bigr]$
$b=33, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(8p+1)^{1}$ $\bigr]$
$b=33, p=3,$ $\bigl[$ $(374p+1)^{1}$ $\bigr]$
$b=33, p=5,$ $\bigl[$ $(6p+1)^{1}$ , $(7890p+1)^{1}$ $\bigr]$
$b=33, p=7,$ $\bigl[$ $(60p+1)^{1}$ , $(451926p+1)^{1}$ $\bigr]$
$b=33, p=11,$ $\bigl[$ $(192p+1)^{1}$ , $(67953397950p+1)^{1}$ $\bigr]$
$b=33, p=13,$ $\bigl[$ $(429754p+1)^{1}$ , $(23682335542p+1)^{1}$ $\bigr]$
$b=33, p=17,$ $\bigl[$ $(4866p+1)^{1}$ , $(6668p+1)^{1}$ , $(11250p+1)^{1}$ , $(66905180p+1)^{1}$ $\bigr]$
$b=33, p=19,$ $\bigl[$ $(3999955410p+1)^{1}$ , $(1538340689685228p+1)^{1}$ $\bigr]$
$b=33, p=23,$ $\bigl[$ $(20p+1)^{1}$ , $(170p+1)^{1}$ , $(63526373182973380660535244p+1)^{1}$ $\bigr]$
$b=33, p=29,$ $\bigl[$ $(122p+1)^{1}$ , $(7101398p+1)^{1}$ , $(160965893298692291275866484848p+1)^{1}$ $\bigr]$
$b=33, p=31,$ $\bigl[$ $(2608p+1)^{1}$ , $(17383792620p+1)^{1}$ , $(2743087020532567371268091566p+1)^{1}$ $\bigr]$
$b=33, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(18340p+1)^{1}$ , $(5735499499875580396735149501302512279558986p+1)^{1}$ $\bigr]$
$b=33, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(62p+1)^{1}$ , $(655712174781490170201408510976779913462819629391726908p+1)^{1}$ $\bigr]$
$b=33, p=43,$ $\bigl[$ $(150p+1)^{1}$ , $(22276858124694180158241666377691324352658792382730362262104p+1)^{1}$ $\bigr]$
$b=33, p=47,$ $\bigl[$ $(1476870p+1)^{1}$ , $(5563266p+1)^{1}$ , $(23424300722488019868p+1)^{1}$ , $(7803241124662766994047354477466p+1)^{1}$ $\bigr]$
$b=34, p=2,$ $\bigl[$ $(2p+1)^{1}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=34, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(132p+1)^{1}$ $\bigr]$
$b=34, p=5,$ $\bigl[$ $(12p+1)^{1}$ , $(4514p+1)^{1}$ $\bigr]$
$b=34, p=7,$ $\bigl[$ $(66p+1)^{1}$ , $(491088p+1)^{1}$ $\bigr]$
$b=34, p=11,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(4122p+1)^{1}$ , $(387666726p+1)^{1}$ $\bigr]$
$b=34, p=13,$ $\bigl[$ $(189133573998987030p+1)^{1}$ $\bigr]$
$b=34, p=17,$ $\bigl[$ $(6p+1)^{1}$ , $(8p+1)^{1}$ , $(13696857473167092480p+1)^{1}$ $\bigr]$
$b=34, p=19,$ $\bigl[$ $(30304p+1)^{1}$ , $(347198284300809191818p+1)^{1}$ $\bigr]$
$b=34, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(2844p+1)^{1}$ , $(516412315066933403332986p+1)^{1}$ $\bigr]$
$b=34, p=29,$ $\bigl[$ $(735624p+1)^{1}$ , $(651131252930p+1)^{1}$ , $(671206586301110255988p+1)^{1}$ $\bigr]$
$b=34, p=31,$ $\bigl[$ $(344356p+1)^{1}$ , $(27390591164027377718913026697364496662p+1)^{1}$ $\bigr]$
$b=34, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(138p+1)^{1}$ , $(1050p+1)^{1}$ , $(31276p+1)^{1}$ , $(5313282538288p+1)^{1}$ , $(37597018456415258916060p+1)^{1}$ $\bigr]$
$b=34, p=41,$ $\bigl[$ $(1398866p+1)^{1}$ , $(7957521546735918477242950607755754781448083616261812p+1)^{1}$ $\bigr]$
$b=34, p=43,$ $\bigl[$ $(10882p+1)^{1}$ , $(60016p+1)^{1}$ , $(61814932p+1)^{1}$ , $(2002393242p+1)^{1}$ , $(1820193601552294415277998959654p+1)^{1}$ $\bigr]$
$b=34, p=47,$ $\bigl[$ $(20p+1)^{1}$ , $(653593432677838541099283438319733850234685109297716941550308468390p+1)^{1}$ $\bigr]$
$b=35, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $\color{magenta}\bm{(1p+1)^{2}}$ $\bigr]$
$b=35, p=3,$ $\bigl[$ $(4p+1)^{1}$ , $(32p+1)^{1}$ $\bigr]$
$b=35, p=5,$ $\bigl[$ $(6p+1)^{1}$ , $(9966p+1)^{1}$ $\bigr]$
$b=35, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(6286818p+1)^{1}$ $\bigr]$
$b=35, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(5082p+1)^{1}$ , $(200776988p+1)^{1}$ $\bigr]$
$b=35, p=13,$ $\bigl[$ $(34p+1)^{1}$ , $(604030100109202p+1)^{1}$ $\bigr]$
$b=35, p=17,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(104706p+1)^{1}$ , $(10147504670791130p+1)^{1}$ $\bigr]$
$b=35, p=19,$ $\bigl[$ $(6897808p+1)^{1}$ , $(2568003544002619444p+1)^{1}$ $\bigr]$
$b=35, p=23,$ $\bigl[$ $(2233843824p+1)^{1}$ , $(3617944464p+1)^{1}$ , $(97586084316p+1)^{1}$ $\bigr]$
$b=35, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(1576082p+1)^{1}$ , $(316925033504p+1)^{1}$ , $(24542172270603723488p+1)^{1}$ $\bigr]$
$b=35, p=31,$ $\bigl[$ $(1530p+1)^{1}$ , $(322681266201823002p+1)^{1}$ , $(1469166566393328446556p+1)^{1}$ $\bigr]$
$b=35, p=37,$ $\bigl[$ $(10492706444716p+1)^{1}$ , $(42672591219448p+1)^{1}$ , $(1751447055380668864512900p+1)^{1}$ $\bigr]$
$b=35, p=41,$ $\bigl[$ $(20p+1)^{1}$ , $(300p+1)^{1}$ , $(23048p+1)^{1}$ , $(398786679298200900p+1)^{1}$ , $(9317543040653798555714269668p+1)^{1}$ $\bigr]$
$b=35, p=43,$ $\bigl[$ $(22430082p+1)^{1}$ , $(146998742502p+1)^{1}$ , $(278546138345544307527712020741934440769416p+1)^{1}$ $\bigr]$
$b=35, p=47,$ $\bigl[$ $(266p+1)^{1}$ , $(366p+1)^{1}$ , $(10839341244273955820943040454371958831284927292883565845823424p+1)^{1}$ $\bigr]$
$b=36, p=2,$ $\bigl[$ $(18p+1)^{1}$ $\bigr]$
$b=36, p=3,$ $\bigl[$ $(10p+1)^{1}$ , $(14p+1)^{1}$ $\bigr]$
$b=36, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(20p+1)^{1}$ , $(62p+1)^{1}$ $\bigr]$
$b=36, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(4p+1)^{1}$ , $(28p+1)^{1}$ , $(7998p+1)^{1}$ $\bigr]$
$b=36, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(286796p+1)^{1}$ , $(4711650p+1)^{1}$ $\bigr]$
$b=36, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(72p+1)^{1}$ , $(264p+1)^{1}$ , $(2890p+1)^{1}$ , $(58530p+1)^{1}$ $\bigr]$
$b=36, p=17,$ $\bigl[$ $(14p+1)^{1}$ , $(24p+1)^{1}$ , $(66p+1)^{1}$ , $(1814p+1)^{1}$ , $(11208p+1)^{1}$ , $(746526p+1)^{1}$ $\bigr]$
$b=36, p=19,$ $\bigl[$ $(10p+1)^{1}$ , $(94p+1)^{1}$ , $(2563879228p+1)^{1}$ , $(33582790852p+1)^{1}$ $\bigr]$
$b=36, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(140p+1)^{1}$ , $(4954700p+1)^{1}$ , $(43043510p+1)^{1}$ , $(326345430p+1)^{1}$ $\bigr]$
$b=36, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(1128p+1)^{1}$ , $(94041129772028p+1)^{1}$ , $(254107953701992365402p+1)^{1}$ $\bigr]$
$b=36, p=31,$ $\bigl[$ $(172p+1)^{1}$ , $(1604669063983112026p+1)^{1}$ , $(6112642941587097453450p+1)^{1}$ $\bigr]$
$b=36, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(106p+1)^{1}$ , $(214p+1)^{1}$ , $(330p+1)^{1}$ , $(69454p+1)^{1}$ , $(9034779076p+1)^{1}$ , $(29642236066p+1)^{1}$ , $(55534837614p+1)^{1}$ $\bigr]$
$b=36, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(696p+1)^{1}$ , $(210930p+1)^{1}$ , $(45240265509426766516560p+1)^{1}$ , $(117986674726269375000980p+1)^{1}$ $\bigr]$
$b=36, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(10p+1)^{1}$ , $(171706p+1)^{1}$ , $(24394276816975853386p+1)^{1}$ , $(9592620665748327437386015717410p+1)^{1}$ $\bigr]$
$b=36, p=47,$ $\bigl[$ $(19806624p+1)^{1}$ , $(959805024p+1)^{1}$ , $(379185492759918p+1)^{1}$ , $(11373990733208995562354210295740970p+1)^{1}$ $\bigr]$
$b=37, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(9p+1)^{1}}$ $\bigr]$
$b=37, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(22p+1)^{1}$ $\bigr]$
$b=37, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(854p+1)^{1}$ $\bigr]$
$b=37, p=7,$ $\bigl[$ $(10p+1)^{1}$ , $(5305828p+1)^{1}$ $\bigr]$
$b=37, p=11,$ $\bigl[$ $(242p+1)^{1}$ , $(168714578928p+1)^{1}$ $\bigr]$
$b=37, p=13,$ $\bigl[$ $(520447060290772020p+1)^{1}$ $\bigr]$
$b=37, p=17,$ $\bigl[$ $(36p+1)^{1}$ , $(6421910p+1)^{1}$ , $(11145621031338p+1)^{1}$ $\bigr]$
$b=37, p=19,$ $\bigl[$ $(232270p+1)^{1}$ , $(207028357345956358564p+1)^{1}$ $\bigr]$
$b=37, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(80218692623300p+1)^{1}$ , $(16312031186341160p+1)^{1}$ $\bigr]$
$b=37, p=29,$ $\bigl[$ $(8p+1)^{1}$ , $(1332p+1)^{1}$ , $(12012588p+1)^{1}$ , $(48764732p+1)^{1}$ , $(649144962702212912p+1)^{1}$ $\bigr]$
$b=37, p=31,$ $\bigl[$ $(12448219888363578p+1)^{1}$ , $(9552571707276461630169909132p+1)^{1}$ $\bigr]$
$b=37, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(54p+1)^{1}$ , $(216p+1)^{1}$ , $(450p+1)^{1}$ , $(468p+1)^{1}$ , $(275478801534p+1)^{1}$ , $(1132525014960671351301574p+1)^{1}$ $\bigr]$
$b=37, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(18p+1)^{1}$ , $(72p+1)^{1}$ , $(685948772p+1)^{1}$ , $(2631011896617552829918750974252733139169956p+1)^{1}$ $\bigr]$
$b=37, p=43,$ $\bigl[$ $(2315730084p+1)^{1}$ , $(18563866636674p+1)^{1}$ , $(2241649260640652392p+1)^{1}$ , $(2283356760270989476p+1)^{1}$ $\bigr]$
$b=37, p=47,$ $\bigl[$ $(254p+1)^{1}$ , $(3616964906p+1)^{1}$ , $(85211785844516p+1)^{1}$ , $(3690396605767344283683782583190758381678p+1)^{1}$ $\bigr]$
$b=38, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ , $(6p+1)^{1}$ $\bigr]$
$b=38, p=3,$ $\bigl[$ $(494p+1)^{1}$ $\bigr]$
$b=38, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(38936p+1)^{1}$ $\bigr]$
$b=38, p=7,$ $\bigl[$ $(441759006p+1)^{1}$ $\bigr]$
$b=38, p=11,$ $\bigl[$ $(20366p+1)^{1}$ , $(2616524408p+1)^{1}$ $\bigr]$
$b=38, p=13,$ $\bigl[$ $(6p+1)^{1}$ , $(34p+1)^{1}$ , $(20464958209534p+1)^{1}$ $\bigr]$
$b=38, p=17,$ $\bigl[$ $(8p+1)^{1}$ , $(251130p+1)^{1}$ , $(1952550657418016p+1)^{1}$ $\bigr]$
$b=38, p=19,$ $\bigl[$ $(49840p+1)^{1}$ , $(1558120054802659015318p+1)^{1}$ $\bigr]$
$b=38, p=23,$ $\bigl[$ $(2586722019380p+1)^{1}$ , $(42718457843872412594p+1)^{1}$ $\bigr]$
$b=38, p=29,$ $\bigl[$ $(8p+1)^{1}$ , $(758264p+1)^{1}$ , $(37679766834860p+1)^{1}$ , $(1084036734107386790p+1)^{1}$ $\bigr]$
$b=38, p=31,$ $\bigl[$ $(1186p+1)^{1}$ , $(54421986p+1)^{1}$ , $(132170277479912775526557543585646p+1)^{1}$ $\bigr]$
$b=38, p=37,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(694p+1)^{1}$ , $(157470p+1)^{1}$ , $(3736028402673770733141724725685147097856598p+1)^{1}$ $\bigr]$
$b=38, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(632p+1)^{1}$ , $(3468p+1)^{1}$ , $(544468534152048p+1)^{1}$ , $(5700637827992739767941351236155388p+1)^{1}$ $\bigr]$
$b=38, p=43,$ $\bigl[$ $(20019256p+1)^{1}$ , $(67677841074p+1)^{1}$ , $(2059345683416554p+1)^{1}$ , $(241543538603234028683925894p+1)^{1}$ $\bigr]$
$b=38, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(8205580829950374p+1)^{1}$ , $(936560500913056853807176671495800268142141667215734p+1)^{1}$ $\bigr]$
$b=39, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{3}}$ , $(2p+1)^{1}$ $\bigr]$
$b=39, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(74p+1)^{1}$ $\bigr]$
$b=39, p=5,$ $\bigl[$ $(6p+1)^{1}$ , $(38p+1)^{1}$ , $(80p+1)^{1}$ $\bigr]$
$b=39, p=7,$ $\bigl[$ $(408p+1)^{1}$ , $(180576p+1)^{1}$ $\bigr]$
$b=39, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(230p+1)^{1}$ , $(146596772p+1)^{1}$ $\bigr]$
$b=39, p=13,$ $\bigl[$ $(10p+1)^{1}$ , $(12p+1)^{1}$ , $(47527174301614p+1)^{1}$ $\bigr]$
$b=39, p=17,$ $\bigl[$ $(18410p+1)^{1}$ , $(5525374307406481730p+1)^{1}$ $\bigr]$
$b=39, p=19,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(7720p+1)^{1}$ , $(5621520298p+1)^{1}$ , $(7905975948p+1)^{1}$ $\bigr]$
$b=39, p=23,$ $\bigl[$ $(26p+1)^{1}$ , $(3030236p+1)^{1}$ , $(107731674666310047386430p+1)^{1}$ $\bigr]$
$b=39, p=29,$ $\bigl[$ $(10806770p+1)^{1}$ , $(170935155990270p+1)^{1}$ , $(8079206543537924420p+1)^{1}$ $\bigr]$
$b=39, p=31,$ $\bigl[$ $(46p+1)^{1}$ , $(2701959287940p+1)^{1}$ , $(3515774802606p+1)^{1}$ , $(1370914330959148p+1)^{1}$ $\bigr]$
$b=39, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(114425692585032610p+1)^{1}$ , $(83462924297286510763866403996692174p+1)^{1}$ $\bigr]$
$b=39, p=41,$ $\bigl[$ $(70376p+1)^{1}$ , $(87723998p+1)^{1}$ , $(8070004397184816p+1)^{1}$ , $(32012010252271830477134276790p+1)^{1}$ $\bigr]$
$b=39, p=43,$ $\bigl[$ $(4132p+1)^{1}$ , $(4995835554p+1)^{1}$ , $(4176555406875743695964099536591273523194784680030p+1)^{1}$ $\bigr]$
$b=39, p=47,$ $\bigl[$ $(3339532115037190861424706p+1)^{1}$ , $(2149668999357344130120643095641092060074243498p+1)^{1}$ $\bigr]$
$b=40, p=2,$ $\bigl[$ $(20p+1)^{1}$ $\bigr]$
$b=40, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(182p+1)^{1}$ $\bigr]$
$b=40, p=5,$ $\bigl[$ $(525128p+1)^{1}$ $\bigr]$
$b=40, p=7,$ $\bigl[$ $(600146520p+1)^{1}$ $\bigr]$
$b=40, p=11,$ $\bigl[$ $(6p+1)^{1}$ , $(13520p+1)^{1}$ , $(98119542p+1)^{1}$ $\bigr]$
$b=40, p=13,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(52p+1)^{1}$ , $(532p+1)^{1}$ , $(21743133444p+1)^{1}$ $\bigr]$
$b=40, p=17,$ $\bigl[$ $(14p+1)^{1}$ , $(19482698p+1)^{1}$ , $(32734853521268p+1)^{1}$ $\bigr]$
$b=40, p=19,$ $\bigl[$ $(3709553400053981106612685560p+1)^{1}$ $\bigr]$
$b=40, p=23,$ $\bigl[$ $(7844899016461984392419175027870680p+1)^{1}$ $\bigr]$
$b=40, p=29,$ $\bigl[$ $(25484560225615538815207780725022104332449160p+1)^{1}$ $\bigr]$
$b=40, p=31,$ $\bigl[$ $(36p+1)^{1}$ , $(418p+1)^{1}$ , $(2635170786871244571360083473476465660766p+1)^{1}$ $\bigr]$
$b=40, p=37,$ $\bigl[$ $(61270p+1)^{1}$ , $(31008984p+1)^{1}$ , $(5673117076p+1)^{1}$ , $(239767779032353425503564990346p+1)^{1}$ $\bigr]$
$b=40, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(11568p+1)^{1}$ , $(104402p+1)^{1}$ , $(57593190769711620190436p+1)^{1}$ , $(760050173978545481762892p+1)^{1}$ $\bigr]$
$b=40, p=43,$ $\bigl[$ $(11073924p+1)^{1}$ , $(436900336p+1)^{1}$ , $(51573396633001585336166554076273087254583624404p+1)^{1}$ $\bigr]$
$b=40, p=47,$ $\bigl[$ $(27441148308p+1)^{1}$ , $(837832086463711259796048332524406845917240211569456655086356p+1)^{1}$ $\bigr]$

Mizar/みざー

$b=41, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ , $\color{magenta}\bm{(3p+1)^{1}}$ $\bigr]$
$b=41, p=3,$ $\bigl[$ $(574p+1)^{1}$ $\bigr]$
$b=41, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(115856p+1)^{1}$ $\bigr]$
$b=41, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(16175604p+1)^{1}$ $\bigr]$
$b=41, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(12086p+1)^{1}$ , $(409037730p+1)^{1}$ $\bigr]$
$b=41, p=13,$ $\bigl[$ $(910p+1)^{1}$ , $(8536p+1)^{1}$ , $(1355076042p+1)^{1}$ $\bigr]$
$b=41, p=17,$ $\bigl[$ $(11871524p+1)^{1}$ , $(19048520654685116p+1)^{1}$ $\bigr]$
$b=41, p=19,$ $\bigl[$ $(660p+1)^{1}$ , $(4601256408p+1)^{1}$ , $(5273725020378p+1)^{1}$ $\bigr]$
$b=41, p=23,$ $\bigl[$ $(1236p+1)^{1}$ , $(37687084615716p+1)^{1}$ , $(547720397847354p+1)^{1}$ $\bigr]$
$b=41, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(12p+1)^{1}$ , $(8582p+1)^{1}$ , $(2387535122p+1)^{1}$ , $(143304687698714708912222p+1)^{1}$ $\bigr]$
$b=41, p=31,$ $\bigl[$ $(12p+1)^{1}$ , $(179452p+1)^{1}$ , $(97452010p+1)^{1}$ , $(12755763878382067187303688888p+1)^{1}$ $\bigr]$
$b=41, p=37,$ $\bigl[$ $(6p+1)^{1}$ , $(40p+1)^{1}$ , $(490p+1)^{1}$ , $(53144619718587649974651071725993458350340840384p+1)^{1}$ $\bigr]$
$b=41, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(42740p+1)^{1}$ , $(501638p+1)^{1}$ , $(45777056368068366p+1)^{1}$ , $(144541160724182866775451164798p+1)^{1}$ $\bigr]$
$b=41, p=43,$ $\bigl[$ $(22p+1)^{1}$ , $(1373496044481710216987073085176803772201247491467384961973279696p+1)^{1}$ $\bigr]$
$b=41, p=47,$ $\bigl[$ $(211873717432520990p+1)^{1}$ , $(1661578309932553580132556p+1)^{1}$ , $(4324040965783192788675732344p+1)^{1}$ $\bigr]$
$b=42, p=2,$ $\bigl[$ $\color{magenta}\bm{(21p+1)^{1}}$ $\bigr]$
$b=42, p=3,$ $\bigl[$ $(4p+1)^{1}$ , $(46p+1)^{1}$ $\bigr]$
$b=42, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(36p+1)^{1}$ , $(320p+1)^{1}$ $\bigr]$
$b=42, p=7,$ $\bigl[$ $(550p+1)^{1}$ , $(208588p+1)^{1}$ $\bigr]$
$b=42, p=11,$ $\bigl[$ $(90p+1)^{1}$ , $(270p+1)^{1}$ , $(540243246p+1)^{1}$ $\bigr]$
$b=42, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(9230694p+1)^{1}$ , $(373301716p+1)^{1}$ $\bigr]$
$b=42, p=17,$ $\bigl[$ $(68118p+1)^{1}$ , $(4878586099436480016p+1)^{1}$ $\bigr]$
$b=42, p=19,$ $\bigl[$ $(12p+1)^{1}$ , $(24p+1)^{1}$ , $(238p+1)^{1}$ , $(78021162p+1)^{1}$ , $(12707343634p+1)^{1}$ $\bigr]$
$b=42, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(10495273430p+1)^{1}$ , $(2020237995701914962630p+1)^{1}$ $\bigr]$
$b=42, p=29,$ $\bigl[$ $(932954p+1)^{1}$ , $(3687986493861306388853699860229119148p+1)^{1}$ $\bigr]$
$b=42, p=31,$ $\bigl[$ $(840360562p+1)^{1}$ , $(6320553257717001009285083863417274008p+1)^{1}$ $\bigr]$
$b=42, p=37,$ $\bigl[$ $(16p+1)^{1}$ , $(90p+1)^{1}$ , $(51902170p+1)^{1}$ , $(65657724p+1)^{1}$ , $(1163771198368p+1)^{1}$ , $(1908379402997760754p+1)^{1}$ $\bigr]$
$b=42, p=41,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(20p+1)^{1}$ , $(20213883728p+1)^{1}$ , $(9734562827862979680p+1)^{1}$ , $(190981917693631709217368018p+1)^{1}$ $\bigr]$
$b=42, p=43,$ $\bigl[$ $(323494p+1)^{1}$ , $(82380728325158281932240916p+1)^{1}$ , $(72583578385580806891729918924080p+1)^{1}$ $\bigr]$
$b=42, p=47,$ $\bigl[$ $(6p+1)^{1}$ , $(3606p+1)^{1}$ , $(4973484p+1)^{1}$ , $(10131514854860150p+1)^{1}$ , $(1907179313020967448811741571555240832968p+1)^{1}$ $\bigr]$
$b=43, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{2}}$ , $\color{magenta}\bm{(5p+1)^{1}}$ $\bigr]$
$b=43, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(210p+1)^{1}$ $\bigr]$
$b=43, p=5,$ $\bigl[$ $(700040p+1)^{1}$ $\bigr]$
$b=43, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(834p+1)^{1}$ , $(22620p+1)^{1}$ $\bigr]$
$b=43, p=11,$ $\bigl[$ $(548918p+1)^{1}$ , $(333127746p+1)^{1}$ $\bigr]$
$b=43, p=13,$ $\bigl[$ $(3147003890626906200p+1)^{1}$ $\bigr]$
$b=43, p=17,$ $\bigl[$ $(38p+1)^{1}$ , $(3339432404p+1)^{1}$ , $(223995696218p+1)^{1}$ $\bigr]$
$b=43, p=19,$ $\bigl[$ $(12p+1)^{1}$ , $(142p+1)^{1}$ , $(222p+1)^{1}$ , $(2442p+1)^{1}$ , $(112497080460418p+1)^{1}$ $\bigr]$
$b=43, p=23,$ $\bigl[$ $(489742948766520p+1)^{1}$ , $(3412725237124906844p+1)^{1}$ $\bigr]$
$b=43, p=29,$ $\bigl[$ $(18p+1)^{1}$ , $(362p+1)^{1}$ , $(110620788167832p+1)^{1}$ , $(10940912695925673676224p+1)^{1}$ $\bigr]$
$b=43, p=31,$ $\bigl[$ $(228p+1)^{1}$ , $(1216528p+1)^{1}$ , $(1250458671214898695534225154654127952p+1)^{1}$ $\bigr]$
$b=43, p=37,$ $\bigl[$ $(318802068p+1)^{1}$ , $(347511256p+1)^{1}$ , $(29675202644794p+1)^{1}$ , $(10602126222819291224934p+1)^{1}$ $\bigr]$
$b=43, p=41,$ $\bigl[$ $(306p+1)^{1}$ , $(5504379692380579152p+1)^{1}$ , $(1923717930765368923218518197181682729050p+1)^{1}$ $\bigr]$
$b=43, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(2800p+1)^{1}$ , $(461051720287959860546654630714149530213163508879542555636680p+1)^{1}$ $\bigr]$
$b=43, p=47,$ $\bigl[$ $(2314643472145050780p+1)^{1}$ , $(276113919215486167226230218422822017942956495873945896p+1)^{1}$ $\bigr]$
$b=44, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{2}}$ , $(2p+1)^{1}$ $\bigr]$
$b=44, p=3,$ $\bigl[$ $(2p+1)^{1}$ , $(94p+1)^{1}$ $\bigr]$
$b=44, p=5,$ $\bigl[$ $(767052p+1)^{1}$ $\bigr]$
$b=44, p=7,$ $\bigl[$ $(34p+1)^{1}$ , $(166p+1)^{1}$ , $(3816p+1)^{1}$ $\bigr]$
$b=44, p=11,$ $\bigl[$ $(576p+1)^{1}$ , $(399240502452p+1)^{1}$ $\bigr]$
$b=44, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(24p+1)^{1}$ , $(366p+1)^{1}$ , $(4792p+1)^{1}$ , $(842694p+1)^{1}$ $\bigr]$
$b=44, p=17,$ $\bigl[$ $(854p+1)^{1}$ , $(818165981578493619914p+1)^{1}$ $\bigr]$
$b=44, p=19,$ $\bigl[$ $(12p+1)^{2}$ , $(61980p+1)^{1}$ , $(333197926701746640p+1)^{1}$ $\bigr]$
$b=44, p=23,$ $\bigl[$ $(6p+1)^{1}$ , $(44p+1)^{1}$ , $(21074p+1)^{1}$ , $(16518587882p+1)^{1}$ , $(2457053200574p+1)^{1}$ $\bigr]$
$b=44, p=29,$ $\bigl[$ $(338p+1)^{1}$ , $(660254408p+1)^{1}$ , $(1953407517514729731454403999382p+1)^{1}$ $\bigr]$
$b=44, p=31,$ $\bigl[$ $(664053120185089594713450746753165812758083837700p+1)^{1}$ $\bigr]$
$b=44, p=37,$ $\bigl[$ $(22962738p+1)^{1}$ , $(4751748596697973037073542170552846242337595502126p+1)^{1}$ $\bigr]$
$b=44, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(1218p+1)^{1}$ , $(101940p+1)^{1}$ , $(18867895001252243772p+1)^{1}$ , $(1018951686112736595360637181300p+1)^{1}$ $\bigr]$
$b=44, p=43,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(17645846112396p+1)^{1}$ , $(772589460181554267822501062575631729019755747269854p+1)^{1}$ $\bigr]$
$b=44, p=47,$ $\bigl[$ $(14p+1)^{1}$ , $(90p+1)^{1}$ , $(3254p+1)^{1}$ , $(4774674062178p+1)^{1}$ , $(8187805773708p+1)^{1}$ , $(2347230917370585046592861762092224p+1)^{1}$ $\bigr]$
$b=45, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $\color{magenta}\bm{(11p+1)^{1}}$ $\bigr]$
$b=45, p=3,$ $\bigl[$ $(6p+1)^{1}$ , $(36p+1)^{1}$ $\bigr]$
$b=45, p=5,$ $\bigl[$ $(294p+1)^{1}$ , $(570p+1)^{1}$ $\bigr]$
$b=45, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(10p+1)^{1}$ , $(589224p+1)^{1}$ $\bigr]$
$b=45, p=11,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(8p+1)^{1}$ , $(3233773502268p+1)^{1}$ $\bigr]$
$b=45, p=13,$ $\bigl[$ $(10p+1)^{1}$ , $(28820400p+1)^{1}$ , $(110522830p+1)^{1}$ $\bigr]$
$b=45, p=17,$ $\bigl[$ $(90p+1)^{1}$ , $(11110559912966141932770p+1)^{1}$ $\bigr]$
$b=45, p=19,$ $\bigl[$ $(30819918383205726135290410530p+1)^{1}$ $\bigr]$
$b=45, p=23,$ $\bigl[$ $(6p+1)^{1}$ , $(751090906657030539235839710327256p+1)^{1}$ $\bigr]$
$b=45, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(1091866653697410152p+1)^{1}$ , $(368037958485086120429310p+1)^{1}$ $\bigr]$
$b=45, p=31,$ $\bigl[$ $(61050p+1)^{1}$ , $(596760p+1)^{1}$ , $(27900388p+1)^{1}$ , $(43012293966351363803561368p+1)^{1}$ $\bigr]$
$b=45, p=37,$ $\bigl[$ $(40p+1)^{1}$ , $(684564p+1)^{1}$ , $(82686139489494p+1)^{1}$ , $(371594962742184p+1)^{1}$ , $(5742906832123054p+1)^{1}$ $\bigr]$
$b=45, p=41,$ $\bigl[$ $(285833854426726730p+1)^{1}$ , $(2861402874637726968571496688468560269288550090p+1)^{1}$ $\bigr]$
$b=45, p=43,$ $\bigl[$ $(456p+1)^{1}$ , $(4000p+1)^{1}$ , $(12829810p+1)^{1}$ , $(913835558307805131540p+1)^{1}$ , $(885534227647924179320814876p+1)^{1}$ $\bigr]$
$b=45, p=47,$ $\bigl[$ $(24p+1)^{1}$ , $(3292004p+1)^{1}$ , $(1102921367534969652313724p+1)^{1}$ , $(26825204875159537171844116644493479774p+1)^{1}$ $\bigr]$
$b=46, p=2,$ $\bigl[$ $\color{magenta}\bm{(23p+1)^{1}}$ $\bigr]$
$b=46, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{1}$ , $(34p+1)^{1}$ $\bigr]$
$b=46, p=5,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(183078p+1)^{1}$ $\bigr]$
$b=46, p=7,$ $\bigl[$ $(1383548118p+1)^{1}$ $\bigr]$
$b=46, p=11,$ $\bigl[$ $(66p+1)^{1}$ , $(128p+1)^{1}$ , $(16526p+1)^{1}$ , $(21170p+1)^{1}$ $\bigr]$
$b=46, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(12p+1)^{1}$ , $(42p+1)^{1}$ , $(1852p+1)^{1}$ , $(815274p+1)^{1}$ $\bigr]$
$b=46, p=17,$ $\bigl[$ $(80p+1)^{1}$ , $(17756754006612992813898p+1)^{1}$ $\bigr]$
$b=46, p=19,$ $\bigl[$ $(45754381311911904630505119102p+1)^{1}$ $\bigr]$
$b=46, p=23,$ $\bigl[$ $(9750p+1)^{1}$ , $(396272p+1)^{1}$ , $(644376p+1)^{1}$ , $(5586848544692760p+1)^{1}$ $\bigr]$
$b=46, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(8p+1)^{1}$ , $(50p+1)^{1}$ , $(1190p+1)^{1}$ , $(75554p+1)^{1}$ , $(1342122311604p+1)^{1}$ , $(21661472029818p+1)^{1}$ $\bigr]$
$b=46, p=31,$ $\bigl[$ $(22p+1)^{1}$ , $(256p+1)^{1}$ , $(63676p+1)^{1}$ , $(1621042p+1)^{1}$ , $(4681099073625471540298190190p+1)^{1}$ $\bigr]$
$b=46, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(60673398498275728p+1)^{1}$ , $(59736423897279117824764230150892529574p+1)^{1}$ $\bigr]$
$b=46, p=41,$ $\bigl[$ $(228p+1)^{1}$ , $(618p+1)^{1}$ , $(340816095837900231250845481719993269006023782346521210380p+1)^{1}$ $\bigr]$
$b=46, p=43,$ $\bigl[$ $(2964p+1)^{1}$ , $(10957285750p+1)^{1}$ , $(2712590818435538461637549267197917616025437954250500p+1)^{1}$ $\bigr]$
$b=46, p=47,$ $\bigl[$ $(20p+1)^{1}$ , $(349604883792348336956p+1)^{1}$ , $(43156155084557638511362051925699379406221897076454p+1)^{1}$ $\bigr]$
$b=47, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{4}}$ , $\color{magenta}\bm{(1p+1)^{1}}$ $\bigr]$
$b=47, p=3,$ $\bigl[$ $(12p+1)^{1}$ , $(20p+1)^{1}$ $\bigr]$
$b=47, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(6p+1)^{1}$ , $(2924p+1)^{1}$ $\bigr]$
$b=47, p=7,$ $\bigl[$ $(6p+1)^{1}$ , $(36589854p+1)^{1}$ $\bigr]$
$b=47, p=11,$ $\bigl[$ $(12246p+1)^{1}$ , $(36269014590p+1)^{1}$ $\bigr]$
$b=47, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(172p+1)^{1}$ , $(1080816p+1)^{1}$ , $(5481936p+1)^{1}$ $\bigr]$
$b=47, p=17,$ $\bigl[$ $(210p+1)^{1}$ , $(594p+1)^{1}$ , $(125138678p+1)^{1}$ , $(444168878p+1)^{1}$ $\bigr]$
$b=47, p=19,$ $\bigl[$ $(22p+1)^{1}$ , $(3434066914p+1)^{1}$ , $(2463607348997412p+1)^{1}$ $\bigr]$
$b=47, p=23,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(288272814p+1)^{1}$ , $(1780351296634228271130884p+1)^{1}$ $\bigr]$
$b=47, p=29,$ $\bigl[$ $(12710093684p+1)^{1}$ , $(6297023310322813036437676506803708p+1)^{1}$ $\bigr]$
$b=47, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(3090p+1)^{1}$ , $(161001148623269117950105888899853883567656p+1)^{1}$ $\bigr]$
$b=47, p=37,$ $\bigl[$ $(4036p+1)^{1}$ , $(10428p+1)^{1}$ , $(751798622872101258368946391145048520663678238960p+1)^{1}$ $\bigr]$
$b=47, p=41,$ $\bigl[$ $(2978p+1)^{1}$ , $(8216p+1)^{1}$ , $(127399730p+1)^{1}$ , $(493570593752p+1)^{1}$ , $(43876028013013819047456921192888p+1)^{1}$ $\bigr]$
$b=47, p=43,$ $\bigl[$ $(4p+1)^{1}$ , $(30p+1)^{1}$ , $(130116744p+1)^{1}$ , $(321519720629840441106132794791365059001344268519305794p+1)^{1}$ $\bigr]$
$b=47, p=47,$ $\bigl[$ $(36p+1)^{1}$ , $(5441329636101351307971032557210128p+1)^{1}$ , $(4142702830129770814192942535749872588p+1)^{1}$ $\bigr]$
$b=48, p=2,$ $\bigl[$ $\color{magenta}\bm{(3p+1)^{2}}$ $\bigr]$
$b=48, p=3,$ $\bigl[$ $(4p+1)^{1}$ , $(60p+1)^{1}$ $\bigr]$
$b=48, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(108p+1)^{1}$ , $(182p+1)^{1}$ $\bigr]$
$b=48, p=7,$ $\bigl[$ $(10p+1)^{1}$ , $(25132426p+1)^{1}$ $\bigr]$
$b=48, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(3578p+1)^{1}$ , $(6658726488p+1)^{1}$ $\bigr]$
$b=48, p=13,$ $\bigl[$ $(24p+1)^{1}$ , $(67990p+1)^{1}$ , $(42477764542p+1)^{1}$ $\bigr]$
$b=48, p=17,$ $\bigl[$ $(79785304560p+1)^{1}$ , $(35170814621760p+1)^{1}$ $\bigr]$
$b=48, p=19,$ $\bigl[$ $(98340418295036133766447327248p+1)^{1}$ $\bigr]$
$b=48, p=23,$ $\bigl[$ $(1165585502p+1)^{1}$ , $(7190207990p+1)^{1}$ , $(97270579541616p+1)^{1}$ $\bigr]$
$b=48, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(110004147354221339702p+1)^{1}$ , $(22224958534200527053260p+1)^{1}$ $\bigr]$
$b=48, p=31,$ $\bigl[$ $(330312p+1)^{1}$ , $(880506809613787505862358970587469631915720p+1)^{1}$ $\bigr]$
$b=48, p=37,$ $\bigl[$ $(1776658p+1)^{1}$ , $(535671828p+1)^{1}$ , $(70912060309836886916381634485355307224814p+1)^{1}$ $\bigr]$
$b=48, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(98p+1)^{1}$ , $(1326822779799010693439039925192445871388020790068105710885032p+1)^{1}$ $\bigr]$
$b=48, p=43,$ $\bigl[$ $(10p+1)^{1}$ , $(852p+1)^{1}$ , $(1880346717797556p+1)^{1}$ , $(761558600393734160618306746400131027281650770p+1)^{1}$ $\bigr]$
$b=48, p=47,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(264p+1)^{1}$ , $(1070p+1)^{1}$ , $(257900148p+1)^{1}$ , $(13282140734454067860520310015687285940226436616869699136p+1)^{1}$ $\bigr]$
$b=49, p=2,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(2p+1)^{2}$ $\bigr]$
$b=49, p=3,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(6p+1)^{1}$ , $(14p+1)^{1}$ $\bigr]$
$b=49, p=5,$ $\bigl[$ $(2p+1)^{1}$ , $(38p+1)^{1}$ , $(560p+1)^{1}$ $\bigr]$
$b=49, p=7,$ $\bigl[$ $(4p+1)^{1}$ , $(16p+1)^{1}$ , $(130p+1)^{1}$ , $(676p+1)^{1}$ $\bigr]$
$b=49, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(102p+1)^{1}$ , $(26678p+1)^{1}$ , $(976940p+1)^{1}$ $\bigr]$
$b=49, p=13,$ $\bigl[$ $(4p+1)^{1}$ , $(17577832p+1)^{1}$ , $(1242166800p+1)^{1}$ $\bigr]$
$b=49, p=17,$ $\bigl[$ $(824p+1)^{1}$ , $(162801864p+1)^{1}$ , $(1710518485200p+1)^{1}$ $\bigr]$
$b=49, p=19,$ $\bigl[$ $(22p+1)^{1}$ , $(18480p+1)^{1}$ , $(213580878p+1)^{1}$ , $(238640354758p+1)^{1}$ $\bigr]$
$b=49, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(134p+1)^{1}$ , $(1368687973772p+1)^{1}$ , $(148743192065657154p+1)^{1}$ $\bigr]$
$b=49, p=29,$ $\bigl[$ $(2p+1)^{1}$ , $(4397940p+1)^{1}$ , $(2459204240862p+1)^{1}$ , $(13878904119884395374300p+1)^{1}$ $\bigr]$
$b=49, p=31,$ $\bigl[$ $(10p+1)^{1}$ , $(12p+1)^{1}$ , $(682p+1)^{1}$ , $(314658p+1)^{1}$ , $(174855062812668p+1)^{1}$ , $(129002847722563368p+1)^{1}$ $\bigr]$
$b=49, p=37,$ $\bigl[$ $(4p+1)^{1}$ , $(6p+1)^{1}$ , $(78p+1)^{1}$ , $(129874192148440966702200p+1)^{1}$ , $(420871483788716993979075904p+1)^{1}$ $\bigr]$
$b=49, p=41,$ $\bigl[$ $(2p+1)^{1}$ , $(118278p+1)^{1}$ , $(219512p+1)^{1}$ , $(500388p+1)^{1}$ , $(39908750p+1)^{1}$ , $(1902671112p+1)^{1}$ , $(106393642347050455026702p+1)^{1}$ $\bigr]$
$b=49, p=43,$ $\bigl[$ $(22p+1)^{1}$ , $(462p+1)^{1}$ , $(486p+1)^{1}$ , $(3804p+1)^{1}$ , $(5470p+1)^{1}$ , $(88350p+1)^{1}$ , $(110460p+1)^{1}$ , $(3860549019591832p+1)^{1}$ , $(50989234006306480p+1)^{1}$ $\bigr]$
$b=49, p=47,$ $\bigl[$ $(291974824457930p+1)^{1}$ , $(1354925787157841499138p+1)^{1}$ , $(13945048714777403283142177443781785786p+1)^{1}$ $\bigr]$
$b=50, p=2,$ $\bigl[$ $\color{magenta}\bm{(1p+1)^{1}}$ , $(8p+1)^{1}$ $\bigr]$
$b=50, p=3,$ $\bigl[$ $(850p+1)^{1}$ $\bigr]$
$b=50, p=5,$ $\bigl[$ $(1275510p+1)^{1}$ $\bigr]$
$b=50, p=7,$ $\bigl[$ $\color{red}\bm{(1p+0)^{1}}$ , $(325385256p+1)^{1}$ $\bigr]$
$b=50, p=11,$ $\bigl[$ $(2p+1)^{1}$ , $(90p+1)^{1}$ , $(6698p+1)^{1}$ , $(5394312p+1)^{1}$ $\bigr]$
$b=50, p=13,$ $\bigl[$ $(48237606p+1)^{1}$ , $(30559167936p+1)^{1}$ $\bigr]$
$b=50, p=17,$ $\bigl[$ $(8p+1)^{1}$ , $(2549411408p+1)^{1}$ , $(15425372447334p+1)^{1}$ $\bigr]$
$b=50, p=19,$ $\bigl[$ $(2208321908194p+1)^{1}$ , $(4882749221564488p+1)^{1}$ $\bigr]$
$b=50, p=23,$ $\bigl[$ $(2p+1)^{1}$ , $(39570320p+1)^{1}$ , $(24728110166434202581555824p+1)^{1}$ $\bigr]$
$b=50, p=29,$ $\bigl[$ $(7584p+1)^{1}$ , $(38514179755480569438p+1)^{1}$ , $(53360402892373722360p+1)^{1}$ $\bigr]$
$b=50, p=31,$ $\bigl[$ $(5898p+1)^{1}$ , $(938952p+1)^{1}$ , $(20032848814570p+1)^{1}$ , $(9275429222255204514922p+1)^{1}$ $\bigr]$
$b=50, p=37,$ $\bigl[$ $(11582053886317936p+1)^{1}$ , $(936494111770236847974581535998069371207558p+1)^{1}$ $\bigr]$
$b=50, p=41,$ $\bigl[$ $(639279711927342p+1)^{1}$ , $(317541228513501577192296p+1)^{1}$ , $(6633328190336453728379400p+1)^{1}$ $\bigr]$
$b=50, p=43,$ $\bigl[$ $(1362p+1)^{1}$ , $(190445700341651692622804680p+1)^{1}$ , $(11250013525316669428509851354024732224p+1)^{1}$ $\bigr]$
$b=50, p=47,$ $\bigl[$ $(330p+1)^{1}$ , $(488p+1)^{1}$ , $(3368601906p+1)^{1}$ , $(662483235030916928p+1)^{1}$ , $(17591365619983127882254169976686386146p+1)^{1}$ $\bigr]$

Mizar/みざー

素因数の形に言及していそうな部分:

If $p$ is an odd prime, then every prime $q$ that divides $R_p^{(b)}$ must be either $1$ plus a multiple of $2p$ , or a factor of $b - 1$ . For example, a prime factor of $R_{29}$ is $62003 = 1 + 2\cdot 29\cdot 1069$ . The reason is that the prime p is the smallest exponent greater than $1$ such that $q$ divides $b^p - 1$ , because $p$ is prime. Therefore, unless $q$ divides $b - 1$ , $p$ divides the Carmichael function of $q$ , which is even and equal to $q - 1$ .

$p$ が奇素数の場合、 $R_p^{(b)}$ を割るすべての素数 $q$ は $2p$ の倍数に $1$ を加えた数か、 $b - 1$ の素因数のどちらかでなければならない。例えば、 $R_{29}$ の素因数は $62003 = 1 + 2 \cdot 29 \cdot 1069$ である。これは、 $p$ が素数なので、 $q$ が $b^p - 1$ を割るような $1$ より大きい最小の指数が素数 $p$ であるからである。したがって、 $q$ が $b - 1$ を割らない限り、 $p$ は $q$ のカーマイケル関数を割り、 $q - 1$ に等しい偶数であることがわかる。

Properties of the Carmichael function

In this section, an integer $\displaystyle n$ is divisible by a nonzero integer $\displaystyle m$ if there exists an integer $\displaystyle k$ such that $\displaystyle n=km$ . This is written as

$\displaystyle m\mid n$ .

Order of elements modulo n

Let $a$ and $n$ be coprime and let $m$ be the smallest exponent with $a^m\equiv 1 (\operatorname{mod}n)$ , then it holds that

$\displaystyle m\,|\,\lambda (n)$ .

That is, the order $m := \operatorname{ord}_n(a)$ of a unit $a$ in the ring of integers modulo $n$ divides $\lambda(n)$ and

$\displaystyle \lambda (n)=\max\{\operatorname{ord}_{n}(a)\,\colon\,\operatorname{gcd}(a,n)=1\}$

カーマイケル関数の性質

この節では、整数 $\displaystyle n$ が非零整数 $\displaystyle m$ で割り切れるのは、 $\displaystyle n=km$ のような整数 $\displaystyle k$ が存在するときである、とする。これは次のように書かれる。

$\displaystyle m\mid n$ .

法 n の位数

$a$ と $n$ を互いに素な数とし、 $m$ を、 $a^m\equiv 1 ( \operatorname{mod}n)$ を満たす最小の指数とすると、以下の式が成り立つ。

$\displaystyle m\,|\,\lambda (n)$ .

すなわち、整数環 modulo $n$ における単位 $a$ の位数 $m := \operatorname{ord}_n(a)$ が $\lambda(n)$ を割り、かつ

$\displaystyle \lambda (n)=\max\{\operatorname{ord}_{n}(a)\,\colon\,\operatorname{gcd}(a,n)=1\}$

Mizar/みざー

https://ja.wikipedia.org/wiki/位数

数学において位数 (いすう、英: order [1])とは，階数・次数などと同じくある種の指標 (index) として働く数に用いられる。

"order" は、ものによっては、「位数」ではなく、階数もしくは次数と和訳される（各々を参照のこと）。

群 $G$ の位数とは、群 $G$ の元の数のことである。

群 $G$ の元 $g$ の位数とは、 $e$ を $G$ の単位元として、 $g^n = e$ を満たす最小の正の整数 $n$ のことである。そのような $n$ が存在しないときは、 $g$ の位数は $\infty$ とする。

初等整数論における位数とは、互いに素な正の整数 $m$ と整数 $a$ に対して $a^d \equiv 1 (\operatorname{mod} m)$ なる合同式が成り立つような最小の正の整数 $d$ のことである。このような $d$ を、 $m$ を法とする $a$ の位数（multiplicative order of $a$ modulo $m$ ）と呼び、 $\operatorname{ord}_m(a)$ や $\operatorname{O}_m(a)$ などと記す。

Mizar/みざー

素数 $p$ での円分多項式は $\Phi_p(x)=x^{p-1}+x^{p-2}+\cdots+x^2+x+1=(x^p-1)/(x-1)$ なので、このとき、素数 $p$ での円分多項式と、基数 $b$ での $p$ 桁のレピュニット $R_p(b)=b^{p-1}+b^{p-2}+\cdots+b^2+b+1=(b^p-1)/(b-1)$ は同じ形をしている。

性質

実際に円分多項式を計算すると以下のようになる。

$\begin{align*}\Phi_{1}&=x-1\\\Phi_{2}&=(x^2-1)/\Phi_1&&=x+1\\\Phi_{3}&=(x^3-1)/\Phi_1&&=x^2+x+1\\\Phi_{4}&=(x^4-1)/\Phi_1\Phi_2&&=x^2+1\\\Phi_{5}&=(x^5-1)/\Phi_1&&=x^4+x^3+x^2+x+1\\\Phi_{6}&=(x^6-1)/\Phi_1\Phi_2\Phi_3&&=x^2-x+1\\\Phi_{7}&=(x^7-1)/\Phi_1&&=x^6+x^5+x^4+x^3+x^2+x+1\\\Phi_{8}&=(x^8-1)/\Phi_1\Phi_2\Phi_4&&=x^4+1\\\Phi_{9}&=(x^9-1)/\Phi_1\Phi_3&&=x^6+x^3+1\\\Phi_{10}&=(x^{10}-1)/\Phi_1\Phi_2\Phi_5&&=x^4-x^3+x^2-x+1\\\Phi_{11}&=(x^{11}-1)/\Phi_1&&=x^{10}+x^9+x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1\\\Phi_{12}&=(x^{12}-1)/\Phi_1\Phi_2\Phi_3\Phi_4\Phi_6&&=x^4-x^2+1\\\end{align*}$
円分多項式の次数はその性質上オイラーの $\varphi$ 関数を用いれば $\varphi(n)$ に等しい。また、上記の例では係数が $1, -1, 0$ しか現れないが、必ずそうなるわけではない。実際 $\Phi_{105}(x)$ がそうでない最小の例で係数に $-2$ が現れる。
$\begin{align*}\Phi_{105}(x)&=x^{48}+x^{47}+x^{46}-x^{43}-x^{42}-2 x^{41}-x^{40}-x^{39}+x^{36}\\&\qquad\quad+x^{35}+x^{34}+x^{33}+x^{32}+x^{31}-x^{28}-x^{26}-x^{24}\\&\qquad\quad-x^{22}-x^{20}+x^{17}+x^{16}+x^{15}+x^{14}+x^{13}+x^{12}\\&\qquad\quad-x^9-x^8-2 x^7-x^6-x^5+x^2+x+1\end{align*}$

補題７ $a$ を $2$ 以上の整数とする。このとき、任意の整数 $k$ に対して、 $\Phi_a(k)$ の素因数は $a$ の約数であるか、ある自然数 $n$ を用いて $an+1$ と書ける。

証明. $X^a−1=\Phi_a(X)F(X)$ と書ける（ $F(X)\in\mathbb{Z}[X]$ ）。 $X=k$ を代入することにより $k^a−1=\Phi_a(k)F(k)$ を得る。 $\Phi_a(k)\ne\pm 1$ のときを考えればよい。 $\Phi_a(k)$ の素因数を勝手にとって $p$ とする。このとき、 $k^q\equiv 1(\operatorname{mod}p)$ が成り立つ。よって、 $k$ の $(\mathbb{Z}/p\mathbb{Z})^\times$ における位数を $e$ とすればある自然数 $b$ が存在して $a=eb$ と書ける。 $b\ge 2$ のときを考える。このとき、 $X^e-1$ と $\Phi_a(X)$ は共通因数をもたない（ $X^e-1$ の根は $1$ の原始 $a$ 乗根ではない）ので、 $X^e−1\mid F(x)$ である。その商を $G(x)\in\mathbb{Z}[X]$ とすれば

$\Phi_a(X)G(X)=X^{e(b−1)}+X^{e(b−2)}+⋯+X^e+1$
が成り立つ。 $X$ に $k$ を代入して、 $e$ の定義より成り立つ $k^e\equiv 1(\operatorname{mod}p)$ を適用することにより、 $b\equiv\Phi_a(k)G(k)\equiv 0(\operatorname{mod}p)$ が従う。よって、 $p\mid a=eb$ 、すなわち $p$ は $a$ の約数である。次に $a=e$ と仮定する。このときはFermatの小定理によって $e\mid p−1$ である。すなわち、ある自然数 $n$ が存在して $p=an+1$ が成り立つ。 $\mathbf{Q.E.D.}$