Justin C. Walker on Sat, 25 Mar 2006 07:10:35 +0100

 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
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I'm beginning to like the cut of his jibberish.
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```