My choice of 3M as my sieve range was a curious one. As the sieving algorithm has roughly O(n^(1/2)) behaviour, where n is the range of the exponents (500000..3000000 would be 2500000), I have several criteria to balance:
1) n not too large,
a) as it's slower
b) as several k would crack early, everything beyond that would be 'waste'
c) as sieving next year is quicker than sieving this year! (~Moore's law)
2) n not too small,
a) as then the overhead of sieving vs. testing would increase
b) as O(n^(1/2)) still favours large n, being better than linear
If fewer than half of them have split by 3M then I'd say I got the balance
right. If more than 8, I'd say we sieved too large a zone.
For the future, the ones that reach n=2M probably should have sieving in a
band of about 3M-20M started, with the same reasons as above.
Just gut feel.
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