Extension to the Base 2 tables from 1300 to 1500, LM to 3000

[ryanp]

Got an ECM hit on the 2+ table yesterday.

GMP-ECM 7.0.5-dev [configured with GMP 6.2.0, GWNUM 30.4, --enable-asm-redc, --enable-assert] [ECM]
Due to incompatible licenses, this binary file must not be distributed.
Input number is (2^1361+1)/228211667657412909230323001705434042549018058879196001936615244070298287105666185870832703670953992780536531240215594078779119204857385398683700824873931077687558812068274836107 (234 digits)
Using B1=850000000, B2=15892628251516, polynomial Dickson(30), sigma=1:3479069830
Step 1 took 2572853ms
Step 2 took 495384ms
********** Factor found in step 2: 6901216084212062896491856436448111443188245170307294941500166249
Found prime factor of 64 digits: 6901216084212062896491856436448111443188245170307294941500166249
Composite cofactor ((2^1361+1)/228211667657412909230323001705434042549018058879196001936615244070298287105666185870832703670953992780536531240215594078779119204857385398683700824873931077687558812068274836107)/6901216084212062896491856436448111443188245170307294941500166249 has 170 digits

I'm going to take the remaining c170 via GNFS.

[xilman]

Originally Posted by ryanp

Got an ECM hit on the 2+ table yesterday.

...

I'm going to take the remaining c170 via GNFS.

Nice work!

Interesting the second stage took so much less time than the first. To me that suggests you could raise B2 substantially unless it takes too much memory. Theoretical optimum is to spend equal effort in each stage.

[charybdis]

Originally Posted by xilman

Theoretical optimum is to spend equal effort in each stage.

Hmmm, can you point me to a reference for this? Surely the optimum ratio is implementation dependent?

[mathwiz]

Originally Posted by xilman

Nice work!

Interesting the second stage took so much less time than the first. To me that suggests you could raise B2 substantially unless it takes too much memory. Theoretical optimum is to spend equal effort in each stage.

Would that be better than just letting GMP-ECM pick a B2?

[VBCurtis]

Originally Posted by charybdis

Hmmm, can you point me to a reference for this? Surely the optimum ratio is implementation dependent?

This "spend equal time on stage 1 and stage 2" was pushed really hard by RDS years ago, and the paper he wrote that caused him to push this so hard itself showed stage 2 using much less time than stage 1. Explanations about the difference ranged from "implementation hiccup, it's theoretically correct" to a big shrug.

When using GMP-ECM, stage 2 time half of stage 1, or a bit less (like 40%), appears optimal via experiment. Alas, GMP-ECM itself does not follow that by default when B1 is above 300M or so, as shown by Ryan's result here.