Trial factoring result expectation

[glebm]

I have run trial factoring on a bunch of numbers and got no factors for any.
I wonder, what is the expectation of there being a factor for a given exponent and a range?

[Batalov]

...the chance of finding a factor between 2^X and 2^X+1 is about 1/X.

(and more useful info at http://www.mersenne.org/various/math...rial_factoring )

So if you are taking on the new trial factoring assignments of, say, 72 bits in size, you will be finding them at a rate of ~1 for each 72 assignments. However if you will try to trial factor something that had been already factored, the chances are near 0 (but not exactly zero, because there's always a chance that the previous computer made a mistake, e.g. because it was overclocked). So, that's why you will do best by connecting to a server that hands out useful work tasks. The server keeps track of finished work.

[kladner]

Originally Posted by glebm

I have run trial factoring on a bunch of numbers and got no factors for any.
I wonder, what is the expectation of there being a factor for a given exponent and a range?

Hang in there. It is a wonderful feeling when you find your first factor. At this point, I run TF on 2 gtx580s and still see long dry spells. In spite of that, I am running well ahead of the "Predicted" (by GPU72) number of factors. It almost seems that factors come in "showers" sometimes. You may be surprised some morning by more than one factor.

[glebm]

Thank you! Came back from work today and saw not 1 but 4 factored results! Poisson processes are weird.
It's an especially cold July in London but I am warm thanks to trial factoring.

[kladner]

Originally Posted by glebm

Thank you! Came back from work today and saw not 1 but 4 factored results! Poisson processes are weird.
It's an especially cold July in London but I am warm thanks to trial factoring.

Cheers!