20031210, 22:12  #1 
Sep 2002
1226_{8} Posts 
How large a factor can P1 testing find ?
In trial factoring for the bigger mersennes it will test factors that are upto 72 bits long ( to just below 2^72 ).
The software may support slighty higher for factor overide but not sure about it. What is the max size factor P1 factoring can find in either stage 1 or stage 2 ? Why is that ( whatever it is ) the limit ? memory, software, math ? Perhaps, this is also a math question. 
20031211, 00:00  #2 
Mar 2003
New Zealand
13×89 Posts 
See http://www.loria.fr/~zimmerma/records/Pminus1.html for the largest factors found by the P1 method.
I don't know of any theoretical upper limit. I think this is what makes P1 factoring more interesting than trial factoring, there is always the possibility that you will find a record factor. 
20031211, 00:09  #3 
Nov 2003
10100101_{2} Posts 
There is no hard limit, only a probable one. P1 factoring finds factors p of a number if all of the factors of p1 are less than a certain limit most people call B1. Using an extension, p1 factoring finds all factors p if all but one factor of p1 is less than B1, and the remaining factor is less than B2. It is conceivable that this method could find an arbitrarily large factor, it is just highly unlikely. Almost all factors found by this method will be less than 35 or 40 digits.

20031211, 00:48  #4 
Sep 2002
2·331 Posts 
Thanks for the informative replies,
I checked the link and for the largest mersenne listed 2^17504141  1 , it had a p1 factor = 426315489966437174530195419710289226952407399 which is 45 digits ( roughly 149 bits), it is much larger than what is produced from trial factoring (72 bits at the upper end). The summary of the conditions for stage 1 and stage 2 answered alot about p1 that was vaque before. 
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