Best Way to find large factors

[mahnouman]

Hello,
Which tests are more likely to find out large factors:
Trial Factoring or P-1?

I know that a trial factoring test will run for a day or so, what about P-1 tests, how long usually they run for?

Best Regards

[Dubslow]

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, P-1 is definitely way more in demand.

[ET_]

Originally Posted by Dubslow

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, P-1 is definitely way more in demand.

...especially if you have lots of RAM.

Luigi

[Brian-E]

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 P-1 factoring can turn up much larger factors than this if you are lucky.

[ATH]

P-1 will also run in around 1 day (anywhere from 12 hours to 2-3 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 P-1 is more needed atm, but it is of course up to you what you want to do.

For P-1 you should give at least 300 Mb RAM for every thread that runs P-1, and the more the better.

[Dubslow]

Originally Posted by Brian-E

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 P-1 factoring can turn up much larger factors than this if you are lucky.

<insert ATH's avatar here>

Of course this is a much better response to OP's question. Sorry OP

Here's some links with "interesting" P-1 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) P-1 factors are north of 100 bits. Even discounting these rare ones, almost any P-1 job that finds a factor (somewhere between 1 in 20 and 1 in 60) will be larger than what TF can find.

[flashjh]

Originally Posted by Dubslow

Even discounting these rare ones, almost any P-1 job that finds a factor (somewhere between 1 in 20 and 1 in 60) will be larger than what TF can find.

It will always be larger if TF was done properly.

[clarification]edit: properly = without error
[/clarification]

[Brian-E]

Originally Posted by flashjh

It will always be larger if TF was done properly.

[clarification]edit: properly = without error
[/clarification]

Is that true now? It didn't use to be. P-1 used to be performed before the last bit or two of TF, so theoretically the P-1 factoring could find a factor which the subsequent TF would otherwise have found.

[flashjh]

I don't remember that, but it's possible that was done because it was mathematically better to P-1 before spending more CPU time on TF.

[Brian-E]

Originally Posted by flashjh

I don't remember that, but it's possible that was done because it was mathematically better to P-1 before spending more CPU time on TF.

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 P-1 factoring relative to the extra TF bits which GPUs can turn in.

[Dubslow]

Originally Posted by flashjh

It will always be larger if TF was done properly.

[clarification]edit: properly = without error
[/clarification]

I meant what was in the realm of possibility. So, for instance, P-1 could find a low-75 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.