## j(tau) n=357, 366, 370, 372, 375, 377, 379, 384, 400

``` Subject: 9 j(tau) factors
Date: Mon, 23 Nov 1998 14:08:17 +0000
From: Allan MacLeod <MACL-MS0@wpmail.paisley.ac.uk>
To: kc2h-msm@asahi-net.or.jp

Hello,

A good set of results from weekend runs.

Allan MacLeod

(a) Coefficient 357 of j(tau)

Input number is
448973801095749176356764834684577571277828781812908804252439920940926694283633711 (81 digits)

Found probable prime factor of 29 digits: 31799734193280750753215438243

Found probable prime factor of 22 digits: 7479199439113171736831

Found probable prime factor of 31 digits: 1887740943417220480300562633467

(b) Coefficient 366 of j(tau)

Input number is
885773318366352083696661415745275514243780602308359217167242402428424411913 (75 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=911345017
Step 1 took 518296ms for 39102834 muls, 3 gcdexts
Step 2 took 250989ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 30672771482346523637860253641846663

Found probable prime factor of 35 digits: 30672771482346523637860253641846663

Probable prime cofactor 28878163777151734244771777801059567936751 has 41 digits

(c) Coefficient 370 of j(tau)

Input number is
4742139160778584634999279378165077837830793599559760642194482810193316372851515309192413 (88
digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=321606260
Step 1 took 715164ms for 39102834 muls, 3 gcdexts
Step 2 took 333132ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 75142159029257729028306408719

Found probable prime factor of 29 digits: 75142159029257729028306408719

Probable prime cofactor 63108902140170892307050334015158697658733746677800990003027 has 59 digits

(d) Coefficient 372 of j(tau)

Input number is
3758595903779715624810432674165891082286024007742869225093343218285671334303099 (79 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=719714486
Step 1 took 614615ms for 39102834 muls, 3 gcdexts

********** Factor found in step 1: 448722920432070362952017

Found probable prime factor of 24 digits: 448722920432070362952017

Probable prime cofactor 8376206635846916363218001504553170388389072908118279947 has 55 digits

(e) Coefficient 375 of j(tau)

Input number is
931500718935856646022797989022655791546674497990567017335028342937825788385340807 (81 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=757334451
Step 1 took 617472ms for 39102834 muls, 3 gcdexts

********** Factor found in step 1: 1661546626244413532232959086501

Found probable prime factor of 31 digits: 1661546626244413532232959086501

Probable prime cofactor 560622677824770760953503054659315588753835793285307 has 51 digits

(f) Coefficient 377 of j(tau)

Input number is
1181038649076153908548839567676911136653316499165143601145860034465917094436784512226009 (88
digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=141701046
Step 1 took 696318ms for 39102834 muls, 3 gcdexts
Step 2 took 326868ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 152887657388868566018114043767

Found probable prime factor of 30 digits: 152887657388868566018114043767

Probable prime cofactor 7724878968301484935974608265644835568373756813221850362927 has 58 digits

(g) Coefficient 379 of j(tau)

Input number is
21512391742570334725889028465264118569350294332178034640293186489425388434772635789 (83 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=150900777
Step 1 took 495769ms for 39102834 muls, 3 gcdexts

********** Factor found in step 1: 11721651610947544116337

Found probable prime factor of 23 digits: 11721651610947544116337

Probable prime cofactor 1835269675007115805538287769083278167365210098794158056850397 has 61 digits

(h) Coefficient 384 of j(tau)

Input number is
205700345642827895916321998923105482358871959329280540929366078648784105664732559331 (84 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=207802051
Step 1 took 596758ms for 39102834 muls, 3 gcdexts
Step 2 took 284450ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 86261402616325382288717389

Found probable prime factor of 26 digits: 86261402616325382288717389

Probable prime cofactor 2384616287283718748789662733088031439325883068431527370479 has 58 digits

(i) Coefficient 400 of j(tau)

Input number is
25354450474102326863344916965786708305686793937140587681875015812451642610720712321556986454087 (95 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=1620399683
Step 1 took 576703ms for 39102834 muls, 3 gcdexts
Step 2 took 278626ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 237839918988848682577895977

Found probable prime factor of 27 digits: 237839918988848682577895977

Probable prime cofactor 106603006685732561273905404078604492420760879643455286026456343944431 has 69
digits
```

E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima