The factorization of primorials +/- 1

[Joppe_Bos]

Originally Posted by rogue

Have you done any P-1 or P+1 factoring on these numbers?

When I started the extensions I began (after some trial dividing) with P-1 and P+1 factoring but only using very the small bound 1e8 on most of the numbers. Do you think it is useful to apply these algorithms with higher bounds (on primorials +/- 1) ("useful" as in higher chance to find new factors)?

[rogue]

Originally Posted by Joppe_Bos

When I started the extensions I began (after some trial dividing) with P-1 and P+1 factoring but only using very the small bound 1e8 on most of the numbers. Do you think it is useful to apply these algorithms with higher bounds (on primorials +/- 1) ("useful" as in higher chance to find new factors)?

From experience with ECMNet and its users, I have seen projects typically do P-1/P+1 at two or three levels above ECM. What I mean that if you are using the optimal B1 bounds to find a factor of 40 digits using ECM, then these projects would use P-1/P+1 with a B1 to find a factor of around 50 digits. They do this because only 1 P-1 and 3 P+1 attempts are made vs the thousands of ECM curves when looking for larger factors.

I will admit that I don't know the probabilities of ECM at 40 vs P-1 at 50 to find a factor so I can't say if that is truly the best way to attack a number.

[fivemack]

P159+: 5000 curves at 3e6, no factor found. Now running P158+

[Joppe_Bos]

I found the following factor:
P132# - 1 (c275) = p37 * c239
With p37 = 2431390407440486232451468669562714353

And decided to indeed do some p-1 factoring with higher bounds on some numbers.
I ran p-1 algorithm on P160# - 1 and P158# - 1 with bound 1e10, no factor found.

ECM curves:
Done 2500 curves on P129# - 1 with B1=3e6
Done 4700 curves on P154# - 1 with B1=3e6
Done 2700 curves on P155# - 1 with B1=3e6
Done 2655 curves on P156# - 1 with B1=3e6

Done 3655 curves on P160# - 1 with B1=11e6
Done 3320 curves on P158# - 1 with B1=11e6
Done 4715 curves on P100# - 1 with B1=11e6

Tables have been updated.

[fivemack]

P158+: 5000 curves at 3e6, no factor found. Now running P157+

[fivemack]

P157+: 5000 curves run. Found prime factor 141156872758003104279732595198340416361 of 39 digits, twice. Now running P155+

Cofactor is C319 5286317743460950065887041375988078879243672764150473678391112267615160185151156322106301951613113510177963758768568055446828290792555065532448155893846572315643987303227951437312976286585207581282181218030471416481281012945936608642654030178433097215759259893329230740214095253518602774370050599715112869266964471702131

[Joppe_Bos]

Four new factors found; P138# - 1 is completely factored.

P133# - 1 (c313) = p39 * c274
with p39 = 808823054396726705208944607100082721043

P138# - 1 (c307) = p38 * p269
With p38 = 96179166277977241951912544193004581067

P151# - 1 (c284) = p33 * p35 * c217
With p33 = 162389066092101684831595375705859
and p35 = 24683713090857359137423637093261839

And new curves:

Done 5750 curves on P109# - 1 with B1=11e6
Done 5750 curves on P110# - 1 with B1=11e6
Done 5460 curves on P111# - 1 with B1=11e6

Done 2680 curves on P130# - 1 with B1=3e6
Done 2500 curves on P132# - 1 with B1=3e6
Done 2500 curves on P133# - 1 with B1=3e6
Done 2500 curves on P134# - 1 with B1=3e6
Done 2500 curves on P137# - 1 with B1=3e6
Done 2560 curves on P143# - 1 with B1=3e6
Done 2500 curves on P146# - 1 with B1=3e6
Done 2500 curves on P153# - 1 with B1=3e6

Tables have been updated.

[Joppe_Bos]

Originally Posted by fivemack

P157+: 5000 curves run. Found prime factor 141156872758003104279732595198340416361 of 39 digits, twice. Now running P155+

Cofactor is C319 5286317743460950065887041375988078879243672764150473678391112267615160185151156322106301951613113510177963758768568055446828290792555065532448155893846572315643987303227951437312976286585207581282181218030471416481281012945936608642654030178433097215759259893329230740214095253518602774370050599715112869266964471702131

Nice result!

The result will be in the tables within a few seconds!

[fivemack]

Thanks! I notice that you haven't filled in your factorisation of P77+ in the tables.

[Joppe_Bos]

Originally Posted by fivemack

Thanks! I notice that you haven't filled in your factorisation of P77+ in the tables.

Thanks for spotting this mistake! I fixed the error.

[fivemack]

P155+, 5000 curves @ 3e6, no factor. Stopping for the time being.