Factors of j(tau) n=179

    Subject: Factors of j(tau) n=179
    Date: Thu, 15 Oct 1998 11:50:34 +0000
    From: Allan MacLeod <MACL-MS0@wpmail.paisley.ac.uk>
    To: kc2h-msm@asahi-net.or.jp


You recently added coefficients of the elliptic modular function j(tau)
to your tables. This morning - 15 Oct 1998 - the only coefficient
unfactored between 100 and 200 was number 179. 

I have managed to factor it with GMP-ECM. Here is the output

GMP-ECM 3, by P. Zimmermann (Inria), 17 Sep 1998, with contributions from
T. Granlund, P. Leyland, C. Curry, A. Stuebinger, G. Woltman, JC. Meyrignac.
Input number is 
24955627382335707905782461261751597173516369235750661180545899333506711 (71 digits)

Using B1=1000000, B2=100000000, polynomial x^18, sigma=1805537839
Step 1 took 362307ms for 12986907 muls, 3 gcdexts
Step 2 took 108627ms for 5771003 muls, 12687 gcdexts

********** Factor found in step 2: 1985254459399353768421421

Found probable prime factor of 25 digits: 1985254459399353768421421

Probable prime cofactor 
     12570493048979790321053802851574262126929809491 has 47 digits

I will try to do some of the 200-300 range.

Allan MacLeod


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