Justin C. Walker on Sat, 25 Mar 2006 07:10:35 +0100 |
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MPQS behavior |
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 ----------- I'm beginning to like the cut of his jibberish. -----------