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Old 2011-09-21, 12:42   #2
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jasonp's Avatar
Oct 2004

67318 Posts

o(1) means 'this can't be zero, but we expect it to drop to zero much faster than all the other terms grow'. The temptation to make it zero and keep going is overwhelming.

Incidentally, in practice the asymptotic bound on the factor base size is extremely conservative; you would be better off actually forcing the bound to a given size and choosing that size to optimize the actual runtime of your program. Don't be surprised if the best B goes down as the sieving speed increases.
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