P751
 

Can Richard or Paul reveal the parameters used for 2,751+?

Sizes of factor bases, large prime bounds, sieve region boundaries/length
of the sieve lines etc.??

Hi Bob,

I can help with this. We used f(x)=2*x^6+1 and g(x)=x-m with common root 2^125.

We used a factorbase bound of 30M on each side and large prime limit of 500M on each side.

Line lengths were 180M, 126M and 90M, longer lines being used at smaller b's but the bulk of the sieving with 90M. I don't know the exact boundaries at which the line lengths changed (Richard has the details).

We've sieved about 45M lines so far and have collected about 43.6M relations. Richard indicated that after some filtering tests, we may need to sieve a bit longer before we can get a manageable matrix.

-Don

[QUOTE=dleclair]Hi Bob,

I can help with this. We used f(x)=2*x^6+1 and g(x)=x-m with common root 2^125.

We used a factorbase bound of 30M on each side and large prime limit of 500M on each side.

Line lengths were 180M, 126M and 90M, longer lines being used at smaller b's but the bulk of the sieving with 90M. I don't know the exact boundaries at which the line lengths changed (Richard has the details).

We've sieved about 45M lines so far and have collected about 43.6M relations. Richard indicated that after some filtering tests, we may need to sieve a bit longer before we can get a manageable matrix.

-Don[/QUOTE]


Hi,

Your line lengths *appear* to be sub-optimal, but since your factor base
is smaller than optimal, this may be OK. The lines close to the origin
seem about right, but at larger b's (say b > 10M) they should only
be 20-30M in length...


An optimal factor base would be "about" 35% bigger .


I understand very well the need to make the matrix as small as possible.

Note that for 2,791+ I am using factor base bounds of 24M, with a number
that is 70 bits smaller than yours....I estimate my matrix will have 4M rows.
My LP bound is 700M.

Thanks for the info.

Bob