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-   -   ECM on small Generalised Fermat numbers (https://www.mersenneforum.org/showthread.php?t=13784)

 alpertron 2010-09-02 13:37

[QUOTE=R.D. Silverman;228164]Check Brent's tables!!!![/QUOTE]
Notice that my ECM applet already checks for factors included in Brent's tables, which is old: updated 11 September 2009 according to his Web site.

 fivemack 2010-09-03 10:20

115^128+1 completed (250 curves at 1e7 were enough); result in factordb.com
101^128+1 also completed

So: 400 curves at 1e7 on the not-previously-fully-factored numbers in {94..115}^128+1. This took one night on 16 threads on a macpro.

35^128+1 currently finishing linalg

 fivemack 2010-09-03 21:15

35^128+1 = 2 * 769 * 77310721 * 465774259823008864434412748488285224928909076514051885029488061896961 * P118

 ET_ 2010-09-03 21:25

[QUOTE=fivemack;228351]35^128+1 = 2 * 769 * 77310721 * 465774259823008864434412748488285224928909076514051885029488061896961 * P118[/QUOTE]

69 digits by ECM?!?

Luigi

 mdettweiler 2010-09-03 21:48

[quote=ET_;228359]69 digits by ECM?!?

Luigi[/quote]
It looks like this was either SNFS or GNFS (probably SNFS):
[quote=fivemack;228259]35^128+1 currently finishing linalg[/quote]

 Andi47 2010-09-04 04:24

[QUOTE=mdettweiler;228361]It looks like this was either SNFS or GNFS (probably SNFS):[/QUOTE]

SNFS-197 with a quintic? Or did I miss something?

 fivemack 2010-09-04 07:49

yes; x^5+35^2, x=35^26; alim=rlim=15M, Q=7.5M-17.5M, 28-bit large primes. 494 CPU-hours sieving on 8x K10+3x core2, 48 CPU-hours on 4xphenom to do the matrix step. A trivial exercise.

 ET_ 2010-09-04 08:21

[QUOTE=fivemack;228259]

35^128+1 currently finishing linalg[/QUOTE]

:blush:

 geoff 2010-09-13 05:36

I found this p44 factor after about 500 curves with B1=11e6: 14571454116637488440882751359138387691414529 | 8^(2^8) + 5^(2^8)

If anyone wanted to finish some of these off with GNFS, I think the two smallest
remaining composites (with bases <= 12) are now:

11^(2^8) + 3^(2^8) = 2 . 3430486387626057217 . 1826300595737909153428993580626433 . 132980092956629419115138154564331009 . 11765487608073254883107740674172674049 . C143

8^(2^8) + 5^(2^8) = 206102775026177 . 25083346678208656976952833 . 14571454116637488440882751359138387691414529 . C149

 R. Gerbicz 2010-09-13 05:46

[QUOTE=geoff;229528]I found this p44 factor after about 500 curves with B1=11e6: 14571454116637488440882751359138387691414529 | 8^(2^8) + 5^(2^8)

If anyone wanted to finish some of these off with GNFS, I think the two smallest
remaining composites (with bases <= 12) are now:

11^(2^8) + 3^(2^8) = 2 . 3430486387626057217 . 1826300595737909153428993580626433 . 132980092956629419115138154564331009 . 11765487608073254883107740674172674049 . C143

8^(2^8) + 5^(2^8) = 206102775026177 . 25083346678208656976952833 . 14571454116637488440882751359138387691414529 . C149[/QUOTE]

That p44 has been found by J. Becker on 2009-10-26, see: [URL="http://www.leyland.vispa.com/numth/factorization/anbn/UPDATE.txt"]http://www.leyland.vispa.com/numth/factorization/anbn/UPDATE.txt[/URL]

 geoff 2010-09-13 06:21

[QUOTE=R. Gerbicz;229530]That p44 has been found by J. Becker on 2009-10-26, see: [URL="http://www.leyland.vispa.com/numth/factorization/anbn/UPDATE.txt"]http://www.leyland.vispa.com/numth/factorization/anbn/UPDATE.txt[/URL][/QUOTE]

Thanks, I didn't know about that project. So it looks like two projects have been working independently on some of these numbers :-(

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