## 7 j(tau) factors

Subject: 7 j(tau) factors
Date: Tue, 20 Oct 1998 09:44:14 +0000
From: Allan MacLeod <MACL-MS0@wpmail.paisley.ac.uk>
To: kc2h-msm@asahi-net.or.jp

Hello,

The following factorisations came out since yesterday.

I hope they are all correct.

Allan MacLeod

Coefficient 206 of j(tau)

Input number is
564386218452270364501008898336266888170878134561029254425893288164873639 (72 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=279010231
Step 1 took 524780ms for 39102834 muls, 3 gcdexts
Step 2 took 259176ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 8048472077794618479177924127

Found probable prime factor of 28 digits: 8048472077794618479177924127

Probable prime cofactor 70123398950390496070831154521987243837499257 has 44 digits

Coefficient 239 of j(tau)

Input number is
3170756627628359212534428849556413815566711458583370115514225135133369 (70 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=2001400162
Step 1 took 508241ms for 39102834 muls, 3 gcdexts
Step 2 took 247033ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 207016596854848512026048321189129

Found probable prime factor of 33 digits: 207016596854848512026048321189129

Probable prime cofactor 15316436825843305733909895474515008561 has 38 digits

Coefficient 244 of j(tau)

Input number is
63348649096645859123873254444337918441210639726394831791247870277788469 (71 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=575785678
Step 1 took 518956ms for 39102834 muls, 3 gcdexts
Step 2 took 256593ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 282531828248971894048189

Found probable prime factor of 24 digits: 282531828248971894048189

Probable prime cofactor 224217743852993237836488431287334608745077538521 has 48 digits

Coefficient 246 of j(tau)

Input number is
12111702484760388672099175697284430346807391001494260651559936519167617 (71 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=402762777
Step 1 took 517087ms for 39102834 muls, 3 gcdexts
Step 2 took 251759ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 136688621206493688742012197899

Found probable prime factor of 30 digits: 136688621206493688742012197899

Probable prime cofactor 88607979053818973163107294464172031458083 has 41 digits

Coefficient 254 of j(tau)

Input number is
1087994220677090328141739405228025291206041390942123988684670530408182711662669 (79 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=2022864818
Step 1 took 595384ms for 39102834 muls, 3 gcdexts
Step 2 took 282308ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 158705171042408251984281997

Found probable prime factor of 27 digits: 158705171042408251984281997

Probable prime cofactor 6855442790747901861419959561172474096685445760483777 has 52 digits

Coefficient 265 of j(tau)

Input number is
853287334375712558552011498885949656604275857903543626908317235494387112389658319 (81 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=710918811
Step 1 took 598406ms for 39102834 muls, 3 gcdexts
Step 2 took 283572ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 29136145209252317157037

Found probable prime factor of 23 digits: 29136145209252317157037

Probable prime cofactor 29286212305969261643055786803806899197169227020287653105387 has 59 digits

Coefficient 281 of j(tau)

Input number is
5916973305353979800229611104928981453142888482543660547598578848929478276989 (76 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=554387643
Step 1 took 417692ms for 39102834 muls, 3 gcdexts
Step 2 took 202417ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 4532332679165069863235959

Found probable prime factor of 25 digits: 4532332679165069863235959

Probable prime cofactor 1305502866670410321080972453513418706699201991392171 has 52 digits

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