# [seqfan] Fwd: [Prime] Help in Factoring Needed!

Max Alekseyev maxale at gmail.com
Sat Nov 22 19:07:35 CET 2008

Artur,

As Alexander Kruppa pointed out in the GIMPS maillist you'd better use
Cunningham tables while factoring numbers of the form 2^n - 1 or 2^n +
1.
Otherwise you may be wasting time doing a job that was already done by someone.

Regards,
Max

---------- Forwarded message ----------
From: Alexander Kruppa <kruppa at in.tum.de>
Date: Thu, Nov 20, 2008 at 10:11 AM
Subject: Re: [Prime] Help in Factoring Needed!
To: grafix at csl.pl, The Great Internet Mersenne Prime Search list
<prime at hogranch.com>

Artur wrote:
> Dear Prime Gurus,
> I would like to ask about factorizing following number on prime factors:
> N=1966382802018295849983426140507775310581529713937897353137000391612422\
> 8278817175390596880190641015445045632436171849324612595906231468275752\
> 7061637282120947925875224843503921645170678491988278295011723585321614\
> 64349494218512454182166238160960541165661049938151951871347
> Smallest prime factor is of the form 486k+1 and k>10^6 and probably for
> biggest factors of N k is divisable be powers of 3 range 2-5
>
> For any help I would like to thank on advance!
>
> Best wishes
> ARTUR

This is a cofactor of 2^729+1 which is already completely factored by
the Cunningham project, http://homes.cerias.purdue.edu/~ssw/cun/index.html

The relevant lines in the Main Tables, Table 2+ are

1   3
3  (1) 3*
9  (1,3) 3*.19
27  (1,3,9) 3*.87211
81  (1,3,9,27) 3*.163.135433.272010961
243  (1,3,9,27,81)
3*.1459.139483.10429407431911334611.918125051602568899753
729  (1,3,9,27,81,243) 3*.227862073.3110690934667.
.216892513252489863991753.1102099161075964924744009.P78

The "729" line gives the primitive prime factors, the other ones the
prime factors of algebraic factors.

Alex
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