## j(tau) n=305,311,320,322

```    Subject: j(tau) n=305,311,320,322
Date: Fri, 23 Oct 1998 09:52:06 +0000
From: Allan MacLeod <MACL-MS0@wpmail.paisley.ac.uk>
To: kc2h-msm@asahi-net.or.jp

Hello,

I have moved on to the 301-400 range - but still looking at 286 and 300.

Some initial results follow.

Allan MacLeod

Coefficient 305 of j(tau)

Input number is
53352823741698078108418229083086034591925361228061538158216295077590112417383062059 (83 digits)

Using B1=1000000, B2=100000000, polynomial x^18, sigma=234721933
Step 1 took 198406ms for 12986907 muls, 3 gcdexts
Step 2 took 98791ms for 5771003 muls, 12687 gcdexts

********** Factor found in step 2: 60703299950406299574319

Found probable prime factor of 23 digits: 60703299950406299574319

Probable prime cofactor 878911423024556291381309745853675869456127098853710859979461 has 60 digits

Coefficient 311 of j(tau)

Input number is
8361890555234230927543464274611833871011778408934926959565973922342163003434649992062146786481
(94 digits)

Using B1=1000000, B2=100000000, polynomial x^18, sigma=1434091968
Step 1 took 227637ms for 12986907 muls, 3 gcdexts
Step 2 took 115439ms for 5771003 muls, 12687 gcdexts

********** Factor found in step 2: 4222146784193785718420871953839

Found probable prime factor of 31 digits: 4222146784193785718420871953839

Probable prime cofactor 1980483148179066618128535828120708514112043563485341629775358879 has 64 digits

Coefficient 320 of j(tau)

Input number is
48932443303170443032606156718511981082282238050532412531409083661453007 (71 digits)

Using B1=1000000, B2=100000000, polynomial x^18, sigma=1534537918
Step 1 took 167857ms for 12986907 muls, 3 gcdexts
Step 2 took 85769ms for 5771003 muls, 12687 gcdexts

********** Factor found in step 2: 760127428465995410947631

Found probable prime factor of 24 digits: 760127428465995410947631

Probable prime cofactor 64374000293504018001955105402287923828922988897 has 47 digits

Coefficient 322 of j(tau)

Input number is
3758890848671601110573491002932127687316907406011356712936024953 (64 digits)

Using B1=1000000, B2=100000000, polynomial x^18, sigma=1236331051
Step 1 took 142637ms for 12986907 muls, 3 gcdexts
Step 2 took 73022ms for 5771003 muls, 12687 gcdexts

********** Factor found in step 2: 9867321886381473198530317

Found probable prime factor of 25 digits: 9867321886381473198530317

Probable prime cofactor 380943369635026156366730766777635521309 has 39 digits
```

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