Frank Hornung found the largest factor ever found using P-1. M17504141 is divisible by the 45-digit factor 426315489966437174530195419710289226952407399
Paul Zimmermann maintains a list of P-1 records here: http://www.loria.fr/~zimmerma/records/Pminus1.html
My, that's a beauty. It is amazingly smooth,
p45-1 = 2 3 191 307 593 839 3593 3989 4051 6691 152429 2349679 17504141
Since the 17504141 part is known in advance, mere B1=152429, B2=2349679 would find this factor. Can you tell us which bounds were actually used? Another surprise is that p-1 is squarefree.
I hope that, with more P-1 being routinely done as part of GIMPS operations, a 50 digit factor will be found someday. That would give some more credit back to P-1 which has been in the shadows of ECM for a long time now. Sure, the majority of factors is much easier to find with ECM, but there are quite a lot for which P-1 is more efficient than any other method, and the above p45 is a splendid example of that.
Alex
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