mersenneforum.org > Math Probability of factor (TF)
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 2011-03-18, 20:11 #1 nuggetprime     Mar 2007 Austria 2×151 Posts Probability of factor (TF) 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
2011-03-18, 21:28   #2
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

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
Quote:
 the chance of finding a factor between 2X and 2X+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.

Last fiddled with by Mini-Geek on 2011-03-18 at 21:32

2011-03-19, 22:14   #3
Mr. P-1

Jun 2003

7·167 Posts

Quote:
 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.

Last fiddled with by Mr. P-1 on 2011-03-19 at 22:14

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