primes in arithmetic progressions

[Joshua Zucker]

It looks to me like
  http://hjem.get2net.dk/jka/math/aprecords.htm#minimalend
gives the next two terms of several of the sequences.  But it says
"smallest known" -- implying that for those next two, the minimal is
not yet proven to be really the smallest.

I think it's a very tough problem to come up with more terms!

If someone can find ANY terms for n > 23, that'd be impressive enough,
and then proving that it's minimal is a whole 'nother problem.

For those two, where we have those "smallest known" to work from, if
someone wants to write a distributed engine to share the work of
checking that they're really minimal, I'm happy to run part of it on a
few OS X machines around my work and home.  Given that the last terms
of the arithmetic progressions known have 15 or 16 digits, though,
that's a lot of primes to check!

--Joshua Zucker


On 1/25/06, N. J. A. Sloane <njas at research.att.com> wrote:
> Dear Seqfans,
>
> The biggest news in number theory in many years is the Green-Tao paper,
> http://xxx.arxiv.org/math.NT/0404188
>
> Andrew Granville has a new paper in which he investigates some
> consequences of this work:
>  Andrew Granville, <a href="http://www.dms.umontreal.ca/~andrew/PDF/PrimePatterns.pdf">Prime number patterns</a>
>
> I have added 9 sequences from his paper to the OEIS:
> see A113827-A113835.
>
> It might add to the reputation of the OEIS if seqfans could extend
> some of these sequences!
>
> They won't be visible until the next upgrade, in about 10 minutes
>
> Neil
>
>