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Old 2010-04-15, 22:23   #1
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Feb 2006
Cambridge, England

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Default 2801^79-1; thoughts on duplication sampling

I've run a reasonable number of simulations (one more to go), aiming for half a billion raw relations with 32-bit large primes. 16e is a lot slower than 15e; sieving should be on the rational side; the run will probably take 250 million CPU-seconds or so.

I tried doing some experiments to determine duplication rates, on cases where I have the whole sieving run to work on, but I've not been able to get estimates which behave anything like the real answer - I over-estimate the duplication rate enormously, and under-estimate the yield.

My estimate for yield was simply to count relations in the first 1% of the range and scale up; this gives the wrong answer (a strong over-estimate for small Q and a strong under-estimate for larger Q) whether I scale up by the ratio of the number of prime ideals or just by the ratio of the width of the Q ranges.

My assumption for duplication was that, if sieving a region Q0 < Q < Q1, that I should count with a factor 1/N a relation that has N factors between Q0 and Q1 on the appropriate side; that gave results which are 20% too low. OK, no relation can ever appear more than three times because there are only ever two large primes, but very few relations appear as many as three times so that's not what was causing the discrepancies.
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