Do there exist three 2-digit 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 5-tuples of primes that are arithmetic progressions, and 15 6-tuples, the biggest being:
{6922547,6922577,6922607,6922637,6922667,6922697}.
I haven't found any satifying 7-tuples, though I have no doubt that such creatures exist. I wonder the following:
Given a positive integer n>3, does there always exist an n-tuple 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 2004-10-24 16:10:34 |
re: Arithmetic progression
