How large a factor can P-1 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 P-1 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.

See [url]http://www.loria.fr/~zimmerma/records/Pminus1.html[/url] for the largest factors found by the P-1 method.

I don't know of any theoretical upper limit. I think this is what makes P-1 factoring more interesting than trial factoring, there is always the possibility that you will find a record factor.

There is no hard limit, only a probable one. P-1 factoring finds factors p of a number if all of the factors of p-1 are less than a certain limit most people call B1. Using an extension, p-1 factoring finds all factors p if all but one factor of p-1 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.

Thanks for the informative replies,

I checked the link and for the largest mersenne listed 2^17504141 - 1 , it had a p-1 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 p-1 that was vaque before.