ECM on small Generalised Fermat numbers - Page 2

alpertron · 2010-09-02, 13:37

Quote:

Originally Posted by R.D. Silverman

Check Brent's tables!!!!

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:

Originally Posted by fivemack

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

69 digits by ECM?!?

Luigi

mdettweiler · 2010-09-03, 21:48

Quote:

Originally Posted by ET_

69 digits by ECM?!?

Luigi

It looks like this was either SNFS or GNFS (probably SNFS):

Quote:

Originally Posted by fivemack

35^128+1 currently finishing linalg

Andi47 · 2010-09-04, 04:24

Quote:

Originally Posted by mdettweiler

It looks like this was either SNFS or GNFS (probably SNFS):

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:

Originally Posted by fivemack

35^128+1 currently finishing linalg

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:

Originally Posted by geoff

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

That p44 has been found by J. Becker on 2009-10-26, see: http://www.leyland.vispa.com/numth/f...nbn/UPDATE.txt

geoff · 2010-09-13, 06:21

Quote:

Originally Posted by R. Gerbicz

That p44 has been found by J. Becker on 2009-10-26, see: http://www.leyland.vispa.com/numth/f...nbn/UPDATE.txt

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

2010-09-03, 10:20	#13
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 6424₁₀ Posts	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 Last fiddled with by fivemack on 2010-09-04 at 07:50

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2010-09-03, 21:15	#14
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2³·11·73 Posts	35^128+1 = 2 * 769 * 77310721 * 465774259823008864434412748488285224928909076514051885029488061896961 * P118

2010-09-04, 07:49	#18
fivemack (loop (#_fork)) Feb 2006 Cambridge, England 2³×11×73 Posts	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.

2010-09-13, 05:36	#20
geoff Mar 2003 New Zealand 2205₈ Posts	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