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 Prime Time Revisited (Posted on 2004-10-22)
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

 See The Solution Submitted by SilverKnight Rating: 3.0000 (8 votes)

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 re: Arithmetic progression | Comment 11 of 17 |
(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

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