P-1 Factoring

I read the mersennewiki page on P-1 factoring. In short, that is some crazy stuff.

I'm interested in understanding the method for no better reason than wanting to understand it. Maybe I just missed something, maybe something is missing, but I don't really know. A few questions come to mind.

What purpose do the relative primes serve in the process? I currently have one worker running P-1, using 5337MB of memory and it said something about 129 relative primes (or some number in that ballpark).


What are "curves" as far as P-1 factoring is concerned?


If this hasn't been addressed yet (probably has), why does having more available memory help? The readme.txt, I am quite sure, is very dated. It says the program would run an exponent of 50 million on 85MB of RAM just fine, though 170MB would be better yet 250MB would be ideal. In the example, 400MB of 512MB was allocated during low memory usage times.

The times where a person had half a gig of memory in their system are far behind us, yet the computing can't have changed very much since then, and the exponents I am working on aren't very far above 50 million either. Yet, I have still read in this forum that several gigabytes is great.

Is it just a matter of getting a little bit more out of the process with massively diminishing returns? Larger B1 and B2 bounds, maybe? I remember when I got an Out Of Memory in Minecraft, a long, long time ago, running on 512MB, I could allocate 2048MB and barely avoid the overload. Yet, if I made my demonic experiments just a tiny bit bigger, even 14336MB wasn't enough.

[TheMawn]

Also, I've allocated 6144MB of Memory to the program.

Worker #1 reached stage 2 first and took 5537MB of RAM (running 192 relative primes).

When worker #2 reached stage 2, it detected 739MB of leftover RAM and allocated 725MB to the worker. It runs 19 relative primes.

Should I try to balance out the allocation, or does Prime95 know what it's doing?

[cheesehead]

Originally Posted by Unregistered

What are "curves" as far as P-1 factoring is concerned?

P-1 factoring doesn't use "curves".

ECM (Elliptic Curve Method) factoring uses curves.

If this hasn't been addressed yet (probably has), why does having more available memory help?

P-1 stage 2 allocates workareas in order to store certain computed values so that it has to compute them only once, and can thereafter just use the stored values. (ECM stage 2 also does this.)

The more "available memory", the more workareas that (P-1 or ECM) stage 2 can allocate, and thus the more duplicate computations it can skip, speeding up that stage.