# [seqfan] Re: Artur (by way of O. Gérard) Help Needed for factorization

A.N.W.Hone at kent.ac.uk A.N.W.Hone at kent.ac.uk
Thu Nov 20 18:13:43 CET 2008

```Hi -

Maple found the factors

227862073,97687,80191,379081

of the first number (N) in a split-second on my desktop PC using the command

ifactor(N , easy)

which I guess must be similar to the routine you wrote.

After dividing out the above prime factors to get the second number (M), I tried

isprime(M)

(probabilistic primality test)

which immediately returned the answer "false".

To get the prime factors of M I will need to wait a while...maybe somebody else has a better
machine/software.

All the best
Andy

----- Original Message -----
From: Olivier Gerard <olivier.gerard at gmail.com>
Date: Thursday, November 20, 2008 4:54 pm
Subject: [seqfan] Artur (by way of O. Gérard) Help Needed for factorization
To: Sequence Fanatics Discussion list <seqfan at seqfan.eu>

> Dear Jack,
>
> Could you confirm my conjecture that the number of prime
> divisors of numbers
> (2^EulerPhi[3^n] - 1)/3^n is 0,1 or a prime number
>
> a(n)=0, 0, 1, 3, 5, 11, 19
>
> because you have good algorithmm for finding small divisors, you
> may be able to
> find total number for some n>7
>
> Mathematica tried factoring on my machine
>
> 1330560206356479874437581808691225710711634173623638361001698161624807\
> 9279126427105233053103284238007262282978961283301626482919922623957738\
> 2611453884961785422078720891479787457044659989325136247370735966256412\
> 9863013583118913903182578923381081567912635533663584632871383920445968\
> 5713267042987
>
> for three days.
>
> I have written a procedure to extract relatively quickly "small"
> divisors and now I have to factor
>
> 1966382802018295849983426140507775310581529713937897353137000391612422\
> 8278817175390596880190641015445045632436171849324612595906231468275752\
> 7061637282120947925875224843503921645170678491988278295011723585321614\
> 64349494218512454182166238160960541165661049938151951871347
>
> and the next prime divisor should be of the form 486 k + 1 and
> k>1000001
> And a general question to all seqfans:
> ==============================
>
> someone sent on the list about one year ago a link to a server
> where I
> factorization on a fast computer system, but I cannot find the
>
> Could someone send me the link again ?
>
> Best wishes,
>
> ARTUR
>
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>

```