p-1 testing ram vs finding a factor
 

Does anyone have the relationship between ram and "chance of finding a factor is and estimated x.xx%"

im also assumeing that it increases time. is that true?

[QUOTE=crash893]Does anyone have the relationship between ram and "chance of finding a factor is and estimated x.xx%"

im also assumeing that it increases time. is that true?[/QUOTE]

Noone does. There is no such relationship. The probability of finding
a factor with P-1 does not depend upon RAM, assuming a certain minimal
(and modest) amount of ram; say 32 Mbytes. Step 1 storage requirements
are negligible. Step 2 can be implemented in chunks that fit in available memory.

Of course, Step 2 will run somewhat slower, depending on the
machine, implementation, and amount of available memory. But your query
did not specify run time requirements.

The probability of finding a factor does indeed increase with the run time.
See my joint paper with Sam Wagstaff Jr: "A Practical Analysis of the
Elliptic Curve Factoring Algorithm", Mathematics of Computation, for
exact analysis.

It appears that the original poster performs P-1 on numbers of about ten million digits (for Lone Mersenne Hunters). The step 2 will require several hundreds of MB to run smoothly with Prime95 bounds.

[QUOTE=alpertron]It appears that the original poster performs P-1 on numbers of about ten million digits (for Lone Mersenne Hunters). The step 2 will require several hundreds of MB to run smoothly with Prime95 bounds.[/QUOTE]


His question was not implementation specific. Nor was it time-constrained.
And one can perform classical time-space tradeoffs in the implementation of
step 2.

I can write code that will execute P-1 in ~64MB, even for numbers in the
10 million digit range. Step 2 will not be convolution based and will therefore
require extra time to run, but it will still be quite a bit faster than Step 1.

If the O.P. meant to ask about a specific implementation and meant to
include time constraints, he did not so indicate. His question was purely
about memory.

Well here is what i noticed as i raised the availble memory for p-1 testing on my computer

[IMG]http://i5.tinypic.com/1530ks6.png[/IMG]

the estimated likelyhood of finding a factor went up as i increased the allowed ram

What i was wondering is

is this type of curve the same for all computers or does it depened on something else as well ( like type of memory or cpu or number that im testing)

[QUOTE=crash893]is this type of curve the same for all computers or does it depened on something else as well ( like type of memory or cpu or number that im testing)[/QUOTE]
Assuming you are using prime95, the allocated memory determines the optimal B1 & B2 bound which in turn determines the probability of finding a factor. Other factors include size of the exponent (yes, this does affect the bounds and the probability), and the amout of trial factoring done.

The type of memory or cpu has _no_ effect on the bounds selection logic or probability.

[QUOTE=crash893]Well here is what i noticed as i raised the availble memory for p-1 testing on my computer

[IMG]http://i5.tinypic.com/1530ks6.png[/IMG]

the estimated likelyhood of finding a factor went up as i increased the allowed ram

What i was wondering is

is this type of curve the same for all computers or does it depened on something else as well ( like type of memory or cpu or number that im testing)[/QUOTE]

Actually, you did not do what you claimed. You did not "raise available
memory for p-1 testing". What you did was "raise available memory for
p-1 testing using prime95 to do the computation".

If you were to use a different piece of software, you would get different results.

When you start a mathematical discussion, you must be more careful to
state ALL your constraints and assumptions.

"p-1 testing" is not the same as "p-1 testing with prime95".

Now, if the Title of this sub-forum were "Prime95 Software", instead of
just "Software", I would concede that the default assumption was that
prime95 was being used.

But this is the software subforum of the Great Internet Mersenne Prime Search forum, so it should be clear that Prime95 is used, if no other software package is mentioned.

[QUOTE=alpertron]But this is the software subforum of the Great Internet Mersenne Prime Search forum, so it should be clear that Prime95 is used, if no other software package is mentioned.[/QUOTE]

I don't know. The 'math' subforum discusses lots of math not related
to GIMPS, as does the 'hardware' subforum. I've seen software discussed herein that is not prime95.

But wouldnt the assumption be that it is prime95 unless otherwise stated?

either way i think there is a lot of hair spliting going on.

Within the context of P-1 factoring for [url=http://mersenneforum.org/forumdisplay.php?f=30]Mersenne-aries[/url], using Prime95 on Windows, making more RAM available does increase the chance of finding a factor. As a very rough guideline, you might ideally want to allocate at least (Mdigits / 20) GB of RAM, although it'll still work fine (at a marginally lower chance of finding a factor) at a half or quarter of that. For example, for M30xxxxxx you might want to allocate 30/20=1.5GB RAM, although you can get by with 400MB.