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Old 2005-12-06, 12:42   #1
R.D. Silverman
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Nov 2003

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Default Stopping on a dime?

I am nearly done sieving 2,1402L.

Last night I did my first filtering pass on the data. The results
show (theoretically) that I could proceed with the LA if I wanted to....

I had a bare excess of 78 equations over ideals and a matrix of about
6.8 million rows.... I have never before seen such a small excess on the
first filter pass. Usually, I still have a defficiency after the first pass.

I will sieve for another two days. This will yield enough relations to
cut the matrix in half and thereby save about 3 weeks of Linear Algebra

I ran into a bug in my lattice siever when I did some initial experiments
on 2,781-. I was using a reciprocal quintic. This number is only 9 bits
bigger than 2,1402L, but I was only getting a tiny fraction of the
expected yield. I then tried 2,820+, (with a quartic), but this dumped
core. I am guessing that with the size of the factor bases I am using,
that polynomials lower than degree 6 are smooth so often that I am
running out of space to store some data. I need to investigate.
Unfortunately, I am swamped with real work, and don't have the time
right now. I have therefore switched to 2,1011+. I will do 2,781- at
a later time if someone else doesn't do it first.
R.D. Silverman is offline