[seqfan] Large gaps between primes
Charles Greathouse
charles.greathouse at case.edu
Mon Jan 16 21:51:30 CET 2012
It's often useful to use A002386 to check prime-gap related
conjectures or sequences, since you can check to a great height (15 *
10^17) with just 75 numbers. But sometimes I find myself in the
position of working with sequences where large -- but not necessarily
record -- prime gaps are needed. Is there a sequence that has
something like this, a less-strict version of A002386? (Less strict
than A085237, as well.)
If not, perhaps something should be added to the OEIS. Any ideas for
a good way of doing this? I wouldn't want to add something as
arbitrary as "Primes p followed by at least 200 composites" but that's
the basic idea. (Aside from being arbitrary, that should contain
almost all primes, asymptotically.) "Primes followed by a gap at
least x times the average gap" for some x is maybe a little better,
but still not quite there. Useful, but much too arbitrary: a sequence
with the first 100 primes starting a prime gap of a given length.
Basically, imagine you're finding terms for a sequence where the prime
gap following each term is increasing, but a term p is only included
if f(p) is true for some predicate f. A somewhat more forgiving
version of A002386 could greatly speed calculation. (Of course you'd
still have to find the sequence, but then you could use it for many
sequences with different functions f.)
Charles Greathouse
Analyst/Programmer
Case Western Reserve University
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