Do there exist three 2digit primes such that:
 Any two of the three, averaged, produce another prime, and
 The average of all three is prime
(In reply to
Arithmetic progression by Brian Smith)
Interesting thought, Brian, and I thought at first that such creatures don't exist ... silly me!
Of the first 500,000 primes, there are 135 5tuples of primes that are arithmetic progressions, and 15 6tuples, the biggest being:
{6922547,6922577,6922607,6922637,6922667,6922697}.
I haven't found any satifying 7tuples, though I have no doubt that such creatures exist. I wonder the following:
Given a positive integer n>3, does there always exist an ntuple artithmetic progression of primes? Is there always an infinite number of these?
These are probably classic results in number theory or something harder than the twin prime conjecture; I don't know. Anyone?

Posted by owl
on 20041024 16:10:34 