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Vector programming techniques for testing, generating and factoring prime numbers
When the cache of known primes KP
is long, finding primes to an x
close to PT
is faster (KP where KP<=x
) is faster than sieving. But finding primes to an x
much smaller than PT
is slower, because it requires KP
comparisons to select.
If we knew the highest prime below x
in KP
we could find it fast (because KP
is sorted) and select with (KP?hp)#KP
.
But we don’t. Is there a way to test items of KP
for <=x
and stop when we find the first?
Otherwise we could use a test on PT
and x
to decide when to select from KP
and when to sieve.
Interestingly, sieving from scratch turns out to be (much, much) faster than reconstructing the bitmap from KP
.
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