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

[Martin Fuller]

The Alpertron link can use special properties of a number to factor it more efficiently, so it is better to start from 2^eulerphi(3^7)-1.  The complete factorisation comes back in seconds.

http://www.alpertron.com.ar/ecm.htm

Input: 2^(2*3^6)-1
Output:
= 3 ^ 7 x 7 x 19 x 73 x 163 x 487 x 1459 x 2593 x 71119 x 80191 x 87211 x 
97687 x 135433 x 139483 x 262657 x 379081 x 97685839 x 227862073 x 272010961 
x 3110690934667 x 16753783618801 x 192971705688577 x 3712990163251158343 x 
10429407431911334611 x 918125051602568899753 x 216892513252489863991753 x 
1102099161075964924744009 x 664728004346558283448724389870269691211809 x 
393063301203384521164229656203691748263012766081190297429488962985651210769817 
x 
101213745778143742250901040788003424950068418098259161142719688891708905138274462262307761 

There are 29 prime factors excluding 3^7, so the conjecture still holds.

Unfortunately 2^(2*3^7)-1 contains a 402 digit unfactored composite, so the next term is hard.

Martin Fuller

--- On Fri, 21/11/08, Hans Havermann <pxp at rogers.com> wrote:

> From: Hans Havermann <pxp at rogers.com>
> Subject: [seqfan] Re: Artur (by way of O. Gérard) Help Needed for factorization
> To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
> Date: Friday, 21 November, 2008, 3:35 PM
> > 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 ?
> 
> http://www.alpertron.com.ar/ecm.htm