I've finally reached an important milestone - I've sieved the GFN range
for exponent 131072 up to p=50*10^15 (in fact, most of the way up to 65Q).
I've analysed the densities, the rates, and the range sizes, and finally
come up with some tentative conclusions about sieving depth.
The highlights are:
- That for this exponent the wide sieve algorithm seems _24_ times faster
than the old trial division method.
- That the old trial division technique would have stopped being useful, as
it would be slower that just PRPing, _quite a long time ago_.
- The true sieve is still noticably faster than PRPing, and should continue
I've put the data from which I drew those conclusions on the slightly tidied
I'd appreciate it if those familiar with GFN testing could read over the
data and verify that I've not made some horrendous boob.
Those who've dealt with a part of the 131072 range who can verify that my
timings appear realistic. Some really surprised me, in particular my second
point above that the trial division technique is now utterly redundant for
the range (which was effectively my target in the first place, anything more
is pure bonus). I'd really like confirmation of that proto-fact.
Pretty please ;-)
First rule of Factor Club - you do not talk about Factor Club.
Second rule of Factor Club - you DO NOT talk about Factor Club.
Third rule of Factor Club - when the cofactor is prime, or you've trial-
divided up to the square root of the number, the factoring is over.
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