Low n ECM Factoring Reservation

[ltd]

To make handling of the ECM reservations easier i have moved it to this thread.
Here is a list of the values that need ECM work.
All other noted p-1 results by gribozavr
P+1 work done so far (gribozavr)
237019*2^1006+1: P+1: 3 runs with B1=1e9, B2=1e12. No factor found.

P-1 work done so far (gribozavr)
P-1 on all composites: B1=1e7, B2=1e10. (done by gribozavr)
237019*2^1006+1 (P-1: B1=1e10 B2=1e13)
152267*2^1059+1 (P-1: B1=1e10 B2=1e13)
258317*2^1359+1 (P-1: B1=1e9 B2=1e12) [obsolete, prime found]
265711*2^1824+1 (P-1: B1=1e10, B2=1e13) [obsolete, prime found]

B1=11000000 (4590 curves) (45 digit level)
237019*2^1006+1 :2250 curves done by hhh [unreserved]
152267*2^1059+1 gribozavr [reserved]
168451*2^1116+1 :2250 curves done by hhh [unreserved]
79817*2^1191+1
222113*2^1221+1
152267*2^1707+1

265711*2^1128+1 [obsolete, prime found]
258317*2^1167+1 [obsolete, prime found]
258317*2^1311+1 [obsolete, prime found]
258317*2^1359+1 [obsolete, prime found]


B1=3000000 (2440 curves) (40 digit level)
237019*2^1726+1

258317*2^1479+1 [obsolete, prime found]
265711*2^1824+1 gribozavr [reserved] [obsolete, prime found]
222361*2^1912+1 [obsolete, prime found]

7 numbers left.

Results found:

16128337303431960646300665617239669 | 149183*2^1309+1 has a factor B1=1000000, B2=839549779 (ecm default). by gribozavr
57502772233796094957626382483691 | 237019*2^1330+1: Factor found in step 2:by Mystwalker
1109963100575400207621326621023 | 90527*2^1511+1: Factor found in step 2: by fetofs
4956781252585267514049309709366520124023 | 265711*2^1344+1: Factor found in step 2: by gribozavr
72747115712011935356411692471357381223 | 79309*2^1694+1: ECM: 220 curves with B1=3e6, B2=4016636513 (ecm default). Factor found in step 2: by gribozavr
896948379820920588037275255750180735407209 | 237019*2^1582+1: B1=3e6, B2=5706890290, polynomial Dickson(6), sigma=1483464917032609 found by hhh

[VJS]

Have you guys done p-1 factoring on these numbers. Wlipp said he generally does a p-1 and then 3 p+1 3 levels higher than they ecm.

Personally I'd suggest since this is all in good fun.

make sure each k/n pair is B1=B2=4.2G this is the limit of proth, took a little less than a day for a n=991.

[geoff]

If you want to make the most of your CPU time then you should probably use Prime95 for the stage one step on these numbers (at least until the next version of gmp-ecm comes out). On a 2.66GHz P4 the Prime95 24.14 times for 258317*2^1167+1 with B1=1,000,000 are:
stage 1: 23.6 sec
stage 2: 11.6 sec

for gmp-ecm 6.0.1 on the same number with B2=100*B1:
stage 1: 94.8 sec
stage 2: 7.9 sec (B2=100*B1)
stage 2: 30.3 sec (gmp-ecm default)

The higher the exponent the more of an advantage Prime95 will have over gmp-ecm.

[gribozavr]

Originally Posted by geoff

If you want to make the most of your CPU time then you should probably use Prime95 for the stage one step on these numbers (at least until the next version of gmp-ecm comes out).

That would be great. I've put GmpEcmHook=1 into prime.ini, but I can't get mprime to factor number of form k.2^n+1. Under Advanced/ECM I can enter only 2^n+/-1. How can it be done?

[Joe O]

ECM2=24737,2,991,1,11000000,2420000000,10

will do 10 curves on 24737.2^991+1 with B1=11000000 and B2=2420000000

Now since you want to do only stage1 put B2 =1 not zero one!

ECM2=24737,2,991,1,11000000,1,10

Don't forget to use B1 =1 and B2= the prime95 B1 value followed by a - and the B2 value you want when you run the ECM

ecm6-k7.exe -dickson 12 -resume resume23.txt >>ECM6A-output23.txt 1 11000000-18000000000

[Mystwalker]

From the readme file of gmp-ecm6.0:

In summary, we advise the following method:

0 - choose a target factor size of D digits
1 - choose optimal B1 and B2 values to find factors of D digits (cf Table 1)
2 - run once P-1 with 10*B1, and the default B2 chosen by GMP-ECM
3 - (optional) run 3 times P+1 with 5*B1, and the default B2
4 - run N(B1,B2,D) times ECM with those B1 and B2, where N(B1,B2,D) is the
expected number of ECM curves with step 1 bound B1, step 2 bound B2,
to find a factor of D digits (cf above table).
5 - if no factor is found, either increase D by 5 digits and go to 0, or use
another factorization method (MPQS, GNFS)

P+1 factoring is not really useful when you're not trying to factor Fermat/Jacobi (?) numbers, so just try P-1 with B1=1e7 (35 digit level) or B1=3e7 (40 digit level).

4.2G would be somewhere between 60 and 65 digit - here, P-1 is not efficient anymore anyway. Plus, you'd have big problems with B2...

[geoff]

Originally Posted by gribozavr

I have a question: does it really make sense to increase B2 to "spend as many time in stage 2 as in stage 1"?

For the current implementations of ECM, probably not.

You can work out for yourself exactly what the optimal B2 value to use by running gmp-ecm with the -v parameter on a few curves using different values of B2. Note the expected time to find a factor for each curve, and use the B2 value that minimises this time.

In my experience on a P4 the optimal value for B2 is usually quite close to when the time spent in stage two is about half of the stage one time, regardless of whether you use GMP-ECM or mprime for stage one.

If you use GMP-ECM for both stages then the default B2 is fine for smaller numbers, but it seems to become too small as the size of the number increases. This might depend a bit on the hardware used. If your machine is relatively more efficient in the stage one code than a P4 then the smaller B2 might be reasonable.

Note that GMP-ECM may not use the exact value of B2 that you specify on the command line, the actual value used is the B2' value shown at the beginning of stage 2 when using the -v switch.

[gribozavr]

If anyone wants to run only stage 1 of ECM/P-1/P+1, I can continue and run stage 2. Especially P-1/P+1 -- I have 1Gb of ram, so I can do stage 2, but stage 1with B1=1e10 is rather long (265711*2^1824+1 P-1 stage 1 with B1=1e10 took about 30 hours).

[ltd]

Hi,

if somebody is interested to do some ecm work i have set up an ecmnet server. It contains all the not reserved composited from this thread plus some more from the beta test ranges.

The server is reachable under: www.psp-project.de
port: 8194

If possible put your nickname into the "id=" in ecmnetclient.cfg.
If not please mail me for which psp nickname i should use for the email address that is reported from cemnet in case you find a factor.

And no sorry i have no ecmnet client as binary ready for download.

Lars

[gribozavr]

Just an update: I'm still working on reserved composites and have some unreported curves. I'm working split-stage: Celeron 1.2Ghz does stage 1, Athlon64 3000+ does stage 2.

[ltd]

@gribozavr:

Your reservations will stay untouched and it will be allways possible to reserve other k/n pairs for local ecm testing. They will be disabled on the ecmnet then.

I am only playing with the server and it was easy to set up the ecmnet server so i did it.

Lars