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

[A.N.W.Hone at kent.ac.uk]

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
> could do advanced prime
> factorization on a fast computer system, but I cannot find the 
> link again.
> 
> Could someone send me the link again ?
> 
> Best wishes,
> 
> ARTUR
> 
> 
> _______________________________________________
> 
> Seqfan Mailing list - http://list.seqfan.eu/
>