20130215, 19:21  #1 
Feb 2013
2^{3} Posts 
Best Way to find large factors
Hello,
Which tests are more likely to find out large factors: Trial Factoring or P1? I know that a trial factoring test will run for a day or so, what about P1 tests, how long usually they run for? Best Regards 
20130215, 19:45  #2 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
Mmm. About equal, on a wall clock time basis. (At least, even to within a factor of 2, I think.)
If you're trying to decide which worktype to do, with a CPU, P1 is definitely way more in demand. 
20130215, 19:54  #3 
Banned
"Luigi"
Aug 2002
Team Italia
2^{2}·3·401 Posts 

20130215, 21:34  #4 
"Brian"
Jul 2007
The Netherlands
6305_{8} Posts 
You mention large factors. It becomes inefficient and infeasible for trial factoring to look further than about 2^70 for CPUs or 2^73 for GPUs in the range of Mersenne numbers currently being fully tested for primality, but P1 factoring can turn up much larger factors than this if you are lucky.

20130215, 21:54  #5 
Einyen
Dec 2003
Denmark
17·181 Posts 
P1 will also run in around 1 day (anywhere from 12 hours to 23 days probably) depending on how much RAM you give it and how fast your CPU is.
It's almost a "waste" now to trialfactor on a CPU since GPU's are so much faster at it and P1 is more needed atm, but it is of course up to you what you want to do. For P1 you should give at least 300 Mb RAM for every thread that runs P1, and the more the better. 
20130215, 22:10  #6  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Quote:
Of course this is a much better response to OP's question. Sorry OP Here's some links with "interesting" P1 factors. "Bits" means log base 2 of the factor, so the number of characters in its binary representation (which is roughly log2(10)~3.3 as many times as decimal digits). As Brian mentions, TF can only go up to 73 or 74 bits effectively, while these (admittedly rare) P1 factors are north of 100 bits. Even discounting these rare ones, almost any P1 job that finds a factor (somewhere between 1 in 20 and 1 in 60) will be larger than what TF can find. 

20130217, 16:12  #7  
"Jerry"
Nov 2011
Vancouver, WA
1,123 Posts 
Quote:
[clarification]edit: properly = without error [/clarification] Last fiddled with by flashjh on 20130217 at 16:13 

20130217, 19:48  #8 
"Brian"
Jul 2007
The Netherlands
6305_{8} Posts 
Is that true now? It didn't use to be. P1 used to be performed before the last bit or two of TF, so theoretically the P1 factoring could find a factor which the subsequent TF would otherwise have found.

20130217, 20:20  #9 
"Jerry"
Nov 2011
Vancouver, WA
1123_{10} Posts 
I don't remember that, but it's possible that was done because it was mathematically better to P1 before spending more CPU time on TF.

20130217, 20:36  #10 
"Brian"
Jul 2007
The Netherlands
7×467 Posts 
Yes, that was the reason. I appreciate that the TF situation has changed radically since GPUto72 began, and I know you are very heavily involved in that yourself, whilst I am not, so I was just wondering how it works nowadays with the timing of the P1 factoring relative to the extra TF bits which GPUs can turn in.

20130217, 21:28  #11 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
I meant what was in the realm of possibility. So, for instance, P1 could find a low75 bit factor (or 74 bit)  that's within the range of what TF *can* do, even if no exponents are supposed to be taken that high.

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