Probability of factor (TF)

[nuggetprime]

Hi,
Is there a formula / excel spreadsheet anywhere which lets me calculate the probablility that I find a factor for Mn by trial factoring from x to x+1 bits, with no previously known factor?

Thanks,
nugget

[Mini-Geek]

http://mersenne-aries.sili.net/credit.php (put in a TF assignment and factoring range, as part of the result it says the chance of finding a factor)
That's the easiest way, since it applies the formula for you.
The actual formula is at:
http://www.mersenne.org/various/math.php

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

Pretty simple.
But note that this only counts starting at about log_2(p) bits, since all factors must be of the form 2kp+1.

Whether there is a previously known factor does not make a difference in the distribution of further factors, but the TF depth does.

[Mr. P-1]

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

That only applies if no prior factoring work has been done, which could have found a factor in that range. If that isn't the case, for example if a P-1 test has been done on the exponent, then the probability of finding a factor with TF will be less.