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 2020-04-15, 10:48 #1 fivemack (loop (#_fork))     Feb 2006 Cambridge, England 13·491 Posts Yields with 16e This is a 16e factorisation of a GNFS-200.0 number (and about a third complete) I am a little surprised that, with alim=rlim=400M, I'm seeing the yield increasing monotonically as Q goes down all the way from 300M to 200M ... I've generally expected the peak yield to be roughly at Q=lim Maybe I should start this kind of large job by sieving 1M slots at 20M intervals then filling in the gaps. Much narrower sieve regions will just pick up Poisson noise rather than a 10% yield difference. Actually the noise is much worse than Poisson, because there's a roughly Poisson process at each prime ideal plus non-uniform distributions of the prime ideals; if I fit a linear trend to the yield and look at $\left| \frac{Y-f(X)}{\sqrt{f(X)}} \right|$ then the median is about seven. Attached Thumbnails   Last fiddled with by fivemack on 2020-04-15 at 10:49
2020-04-19, 13:45   #2
fivemack
(loop (#_fork))

Feb 2006
Cambridge, England

13×491 Posts

Quote:
 Originally Posted by fivemack This is a 16e factorisation of a GNFS-200.0 number (and about a third complete) I am a little surprised that, with alim=rlim=400M, I'm seeing the yield increasing monotonically as Q goes down all the way from 300M to 200M ... I've generally expected the peak yield to be roughly at Q=lim Maybe I should start this kind of large job by sieving 1M slots at 20M intervals then filling in the gaps. Much narrower sieve regions will just pick up Poisson noise rather than a 10% yield difference. Actually the noise is much worse than Poisson, because there's a roughly Poisson process at each prime ideal plus non-uniform distributions of the prime ideals; if I fit a linear trend to the yield and look at $\left| \frac{Y-f(X)}{\sqrt{f(X)}} \right|$ then the median is about seven.
Dividing out by the counts of prime ideals (which are just length(polrootsmod(f,p)) ) gives something with much nicer statistical properties - the linear fit has an r^2 of 0.998 rather than 0.957, and you immediately see the <1% outliers caused by a segfault in the middle of some of the subintervals. This suggests that 100kQ slots with prime-ideal correction would be fine for yield estimation; in fact, looking at the first subinterval of each block, 10kQ slots at 10M intervals look to produce a pretty close fit.

Last fiddled with by fivemack on 2020-04-19 at 14:08

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