## E84 and j(tau)(225)

```    Subject: E84 and j(tau)(225)
Date: Thu, 22 Oct 1998 09:50:36 +0000
From: Allan MacLeod <MACL-MS0@wpmail.paisley.ac.uk>
To: kc2h-msm@asahi-net.or.jp

Hello,

(a) Factor of Euler number E84

Input number is
17090572074142215353815758080777485783407404674013679738319308238903492554230168384294571193045226324509 (104 digits)

Using B1=11000000, B2=1100000000, polynomial x^60, sigma=147697541
Step 1 took 2958516ms for 144056910 muls, 3 gcdexts
Step 2 took 1399890ms for 57653166 muls, 91544 gcdexts

********** Factor found in step 2: 739762335239015186706527735192795520726707

Found probable prime factor of 42 digits: 739762335239015186706527735192795520726707

Probable prime cofactor 23102787557601588721456558705317833928862314134208348372143087 has 62 digits

I tested the primality of both factors with UBASIC APRT-CL code.

(b) Factor of coefficient 225 of elliptic modular function j(tau)

Input number is 96779643607491989576101728743207853412483479805211096782700669078777 (68 digits)

Using B1=3000000, B2=300000000, polynomial x^30, sigma=1925897902
Step 1 took 406538ms for 39102834 muls, 3 gcdexts
Step 2 took 191483ms for 16480797 muls, 29004 gcdexts

********** Factor found in step 2: 113253187875038244275802455408944537

Found probable prime factor of 36 digits: 113253187875038244275802455408944537

Probable prime cofactor 854542334951993581782069995175521 has 33 digits

Allan MacLeod
```

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