# [seqfan] Re: Large gaps between primes

Charles Greathouse charles.greathouse at case.edu
Tue Jan 17 00:20:01 CET 2012

```That's useful, but not what I'm looking for.  I might need the fifth
gap of length 200, for example, if f is false for the first four.

For example, consider finding the lonely numbers A051650 which I
worked on recently (and have an ongoing search to 10^12 for).  The
next term I'm looking for corresponds to a prime gap at least 248 in
length, but it's considerably larger than the minimal gap of that
length.  Right now I'm going through each prime in turn, but the
average prime gap is around 26 where I'm searching, so being able to
search just the rare few with length >= 248 would be a tremendous
speedup.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Jan 16, 2012 at 5:09 PM, RGWv <rgwv at rgwv.com> wrote:
> Dear Charles,
>
>   Is what you are looking for https://oeis.org/A000230 ?
>
> Bob.
>
> -----Original Message----- From: Charles Greathouse Sent: Monday, January
> 16, 2012 3:51 PM To: Sequence Fanatics Discussion list Subject: [seqfan]
> Large gaps between primes
> 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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