GMP-ECM test

[ATH]

I tried to run a curve on the c402 from http://www.mersenneforum.org/showthread.php?t=4194 with B1=43M and it took over 1 hour.

That made me want to test how number of digits influence ecm time on my P4 prescott 3.4 Ghz. Here is the data: ECM.txt.

I used Excel to do regression analysis:

B1=11000: step1=0.0349*digits^1.7104 (R^2=0.999) step2=0.1781*digits^1.3103 (R^2=0.9932)

B1=50000: step1=0.1591*digits^1.7104 (R^2=0.9988) step2=1.0627*digits^1.2673 (R^2=0.9912)

B1=250000: step1=0.7849*digits^1.7128 (R^2=0.9989) step2=5.8206*digits^1.2521 (R^2=0.9953)

B1=1000000: step1=2.9016*digits^1.7281 (R^2=0.9989) step2=20.656*digits^1.2157 (R^2=0.9972)

B1=3000000: step1=8.6296*digits^1.7331 (R^2=0.999) step2=55.839*digits^1.222 (R^2=0.9964)

B1=11000000: step1=30.745*digits^1.7373 (R^2=0.9989) step2=162.64*digits^1.2442 (R^2=0.998)

B1=43000000: step1=122.4*digits^1.7336 (R^2=0.999) step2=349.18*digits^1.3057 (R^2=0.9846)
(step2 probably affected by high memory usage for B1=43M since B2 is very high, R^2 value not close to 1)

[ATH]

I tried to check the constants infront of the power series in step1 as a function of B1 and got:
constants(step1)=(3*10^-6)*B1 (R^2=1)

The constants infront of step2 power series as a function of B2 didn't fit as good:
constants(step2)=(3*10^-5)*B2^0.6488 (R^2=0.9896)


So it seems step1 time roughly is proportional to B1*digits^1.7
and step2 time roughly proportional to B2^0.6*digits^1.3.