Originally Posted by

**hhh**
Wow. You meant B1> current levels, though, right?

B1 less than 1.08e9.

How did you come up with your B1/B2-bounds?

I did something like this on the particular CPU / memory combination I am mainly using:

Code:

for i in `seq 1 300`; do
./ecm-time -v -inp 24737.991.inp -maxmem 4000 ${i}e7 >> timings-4g.txt
done

And similar for 8000 MiB RAM. Among the output, gmp-ecm reports the following interesting lines:

Code:

Using B1=2520000000, B2=77978684123358, polynomial Dickson(30), sigma=1683006743
dF=1048576, k=6, d=11741730, d2=19, i0=196
Expected number of curves to find a factor of n digits:
40 45 50 55 60 65 70 75 80 85
30 96 338 1303 5454 24566 118242 608303 3288378 1.9e+07
[...]
Expected time to find a factor of n digits:
40 45 50 55 60 65 70 75 80 85
18.06d 57.24d 201.29d 2.13y 8.91y 40.12y 193.09y 993.37y 5370y 30569y

I selected B1 levels and default B2 level which gave the lowest expected time to find a factor of given size. For the machines I have been using the optmal B1 is 1080000000 for 65 digit factors using up to 4 GB RAM for stage 2, and 2520000000 for 70 digit factors using up to 8 GB ram for stage 2. This test is using a modified gmp-ecm to get expected times for factors > 65 digits.