MPQS behavior

["Justin C. Walker" <justin@mac.com>]

Hi, all,

This is a somewhat involved post; I hope it makes sense, and  
apologize in advance if it is totally obvious:

For various reasons, I decided to compare my G5 PowerMac and my Core  
Duo MacBook Pro in the following computation: I computed the  
coefficients of
     eta(x)^6*eta(3*x)^6
to a precision of 310, and then started a loop to factor each.

The two systems were neck and neck (:-}) until the coefficient for  
n=186.  Then I got this:

PowerPC:
186:  
489374912706076771525100405333124116411054140808019375469349301329808748 
04891650866221688438

  *** factor: Warning: MPQS: factoring this number will take several  
hours.
[2, 1; 3, 2; 7, 1; 11, 1; 557810501066166798560937148699439400223, 1;  
63298262031087966002932642338205110362839613755121, 1]

Core Duo:
186:  
489374912706076771525100405333124116411054140808019375469349301329808748 
04891650866221688438
  *** factor: Warning: MPQS: factoring this number will take several  
hours:
N =  
353084352601786992442352384800233850224425787018772998174133695043152054 
86934813034791983.
[2, 1; 3, 2; 7, 1; 11, 1; 557810501066166798560937148699439400223, 1;  
63298262031087966002932642338205110362839613755121, 1]

In order to get to the factorization, it took the PowerPC box much  
longer.

A side question: what is the significance of the "N=" line from the  
Core Duo?  And why do I get it only on the Core Duo?

At this point, the PowerPC has been chewing on this for roughly twice  
as long as the Core Duo (the Core Duo has been sleeping a lot :-}).   
However, the PowerPC is up to n=193, while the Core Duo is up to n=204.

I know there is randomness in the factorization algorithms; is this  
the explanation for the long time in MPQS?

BTW, up to the present, n=186 is the only one to invoke MPQS.

Thanks!

Regards,

Justin

--
Justin C. Walker, Curmudgeon at Large
Institute for the Absorption of Federal Funds
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I'm beginning to like the cut of his jibberish.
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