Not quite a PrimeNet P-1 record

[S485122]

I had the pleasure today, after a very long P-1 dry spell, of finding a big factor with Prime95 : 784897778891064591942839363373697049558744749633 (159 bits and 48 digits) is a factor of M39122179.

It is the 7th largest factor in the PrimeNet tables, the bigger factors where found for very small exponents :

Exponent  Places  Factor
727       98      17606291711815434037934881872331611670777491166445300472749449436575622328171096762265466521858927
523       69      160188778313202118610543685368878688932828701136501444932217468039063
751       66      227640245125324450927745881868402667694620457976381782672549806487
809       61      4148386731260605647525186547488842396461625774241327567978137
997       57      167560816514084819488737767976263150405095191554732902607
971       53      23917104973173909566916321016011885041962486321502513
39122179  48      784897778891064591942839363373697049558744749633
3343      47      21395366139013330348249888032891790630577329313
2683      46      3019483344963149568756116899590804134821111103
4177      45      467039490551109991900169555492443530235814719
17504141  45      426315489966437174530195419710289226952407399

It earned me 0,287 factoring credit (it had been trial factored up to 68 bits.)

The computer I did it on (Quad 6700, 64 bits OS, 4GB of memory) earns 0,307 P90 CPU years a day per core doing LL work, 0,137 doing trial factoring and 0,009 doing P-1 work. Actually that last figure should be someting like -0,068 since P-1 factoring slows the other cores... Credit earning is not a reason to do P-1 work.

[alpertron]

It appears that you found two prime factors of M39122179 because

784897778891064591942839363373697049558744749633 = 26207295509565505207993 x
29949590891764532677185481

[S485122]

Originally Posted by alpertron

It appears that you found two prime factors of M39122179 because

784897778891064591942839363373697049558744749633 = 26207295509565505207993 x
29949590891764532677185481

Yes that was a possibility since P-1 does not always find the smallest factor. :-(

Anyway after spending 44 core days on 35 exponents in P-1 stage 1 and 2 without success, I am still satisfied. So far I did a total of 88 P-1 and four times the program found a factor.

[alpertron]

The lowest prime factor has 75 bits so you would not have found it without p-1.

[Mr. P-1]

Originally Posted by S485122

Yes that was a possibility since P-1 does not always find the smallest factor. :-(

This is true, however it is not the explanation for your result.

Rather, what happened was that in this instance there were two prime factors that were k-smooth to the bounds of your P-1 test:

26207295509565505207993-1 = 2^3 . 3 . 7 . 43 . 150107 . 617761 . 39122179

29949590891764532677185481-1 = 2^3 . 3 . 5 . 173 . 1861 . 2087 . 9494491 . 39122179

In this situation, the P-1 test returns the product of the factors, an interesting outcome, but by no means exceptional, and certainly not record-breaking.