M1061...

[thomasn]

[Fri Dec 3 02:13:49 2004]
M1061 completed 200 ECM curves, B1=44000000, B2=4290000000


Thomas

[thomasn]

Originally Posted by Mystwalker

Is the multiplier really 1? After all, these curves have been done with gmp-ecm and higher bounds than 100 * B1...

Hmm. I belive so : I based that on post #114 (and also the README of gmp-ecm) which has this table :

       digits D  optimal B1      B2        expected curves N(B1,B2,D)
          15        2e3         1.2e5             30
          20       11e3         1.4e6             90
          25        5e4         1.2e7            240
          30       25e4         1.1e8            500
          35        1e6         8.4e8           1100
          40        3e6         4.0e9           2900
          45       11e6        2.6e10           5500
          50       43e6        1.8e11           9000
          55       11e7        6.8e11          22000
          60       26e7        2.3e12          52000
          65       85e7        1.3e13          83000
          70       29e8        7.2e13         120000

          Table 1: optimal B1 and expected number of curves to find a
          factor of D digits.

So at the time I posted the summary we had done 179 of 22000 curves.
*stops to think*
I see that I did not specify the expected number of curves for that level. Sorry for that. I will do that in the future.

Thomas

[Xyzzy]

Just for fun, here are save files for 60, 65 and 70 digits...

[thomasn]

[Sun Dec 5 18:15:32 2004]
M1061 completed 200 ECM curves, B1=44000000, B2=4290000000

edit : From George's page I see that only 2007 curves remain for B=44000000. I have done 800 curves and will mail George.

Thomas

[geoff]

Completed 200 curves: B1=11e7, B2=52e9, Dickson(12) polynomial (multiplier 0.61)

According to rho.gp, with B1=11e7, B2=43e9 and k=5, increasing the polynomial from degree 12 to degree 30 increases the effectiveness of the curve for finding 55 digit factors by 4.6%, and on my P4 (if gmp-ecm is used for the whole curve) increases the time per curve by only 3.3%.

But if mprime was used to do stage one of the curve, the time increase per curve is 7.9%. (because stage two then accounts for a larger proportion of the curve).

By default gmp-ecm switches from using the degree 12 to using the degree 30 polynomial at about B2=31e9, so if using mprime to do stage one this should be advanced. I haven't worked out the ideal crossover point, but it is above 86e9 for M1061 curves, probably much higher.

[Wolf]

M1061 completed 100 ECM curves, B1=44000000, B2=4290000000

Also did these at the 55 digit level:-
M1061 completed 5 ECM curves, B1=110000000, B2=4290000000

How many 'standard' GMP-ECM curves are these equivalent to?

[geoff]

Originally Posted by Wolf

Also did these at the 55 digit level:-
M1061 completed 5 ECM curves, B1=110000000, B2=4290000000

How many 'standard' GMP-ECM curves are these equivalent to?

Each is worth 0.35 gmp-ecm default curves, not bad for such a small stage two, but if you used gmp-ecm to do do the stage two step -- even if you only spent the same itime n stage two that Prime95 did -- you could increase that to 0.45 or more.

[thomasn]

[Wed Dec 8 06:35:47 2004]
M1061 completed 200 ECM curves, B1=44000000, B2=4290000000

Thomas

PS : I will be offline until monday.

[Wolf]

Originally Posted by geoff

Each is worth 0.35 gmp-ecm default curves, not bad for such a small stage two, but if you used gmp-ecm to do do the stage two step -- even if you only spent the same itime n stage two that Prime95 did -- you could increase that to 0.45 or more.

Thanks for the info, I was just curious. I don't think I'll be any more curves at that level.

[thomasn]

[Fri Dec 17 18:07:08 2004]
M1061 completed 200 ECM curves, B1=44000000, B2=4290000000

Thomas

[thomasn]

Since so few curves remain for B1=44M I will try to mail George with curves as they are posted.

Summary:
Wolf : 100 curves (8 dec).
thomasn : 400 curves.

I have emailed George the 500 curves done since last summary.

Thomas