## 5 more j(tau) factors

```    Subject: 5 more j(tau) factors
Date: Wed, 21 Oct 1998 12:24:20 +0000
From: Allan MacLeod <MACL-MS0@wpmail.paisley.ac.uk>
To: kc2h-msm@asahi-net.or.jp

Hello,

5 more j(tau) factorisations

Coefficient 238 of j(tau)

Input number is
3112858486243848741739131778939181857119774283471696992138257866586006789 (73 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=922854873
Step 1 took 528846ms for 39102834 muls, 3 gcdexts
********** Factor found in step 1: 1968659459974281164163644803

Found probable prime factor of 28 digits: 1968659459974281164163644803

Probable prime cofactor 1581207186683529080136952943951740982039221463 has 46 digits

Coefficient 271 of j(tau)

Input number is
37613225907173288688481728932396563231126442456488058118966647207590196645783 (77 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=1980207801
Step 1 took 526538ms for 39102834 muls, 3 gcdexts
Step 2 took 259011ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 574675279120534993991971813

Found probable prime factor of 27 digits: 574675279120534993991971813

Probable prime cofactor 65451268348858487179305195578252378121776715871691 has 50 digits

Coefficient 274 of j(tau)

Input number is
22919754025359421868666485233015084977561456582047061187124202576135227114455452177 (83 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=1427477798
Step 1 took 608296ms for 39102834 muls, 3 gcdexts
Step 2 took 290000ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 606522088868231200072816219199

Found probable prime factor of 30 digits: 606522088868231200072816219199

Probable prime cofactor 37788819972126042926456266887620042649483061930069423 has 53 digits

Coefficient 296 of j(tau)

Input number is
420520143826354214366964469185045478569606571077050777003962722980352024115136941 (81 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=807291476
Step 1 took 1834945ms for 39102834 muls, 3 gcdexts
Step 2 took 558022ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 619009209118396757718329

Found probable prime factor of 24 digits: 619009209118396757718329

Probable prime cofactor 679343921918812837300007554282988125079932680512886852629 has 57 digits

Coeffcient 299 of j(tau)

Input number is
49751374571632516197900101874447501584827294490848988264550243029947119709404877212754279 (89
digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=744301
Step 1 took 2797582ms for 39102834 muls, 3 gcdexts
Step 2 took 1471703ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 51625874472420368827383090424733

Found probable prime factor of 32 digits: 51625874472420368827383090424733

Probable prime cofactor 963690689601989211468133286890333562607716781846348151763 has 57 digits

Allan MacLeod
```

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