# MCD for an increasing arithmetic sequence of 6 primes

Find the minimum common difference for an increasing sequence of 6 prime numbers

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I think you have missed my point. What do you mean by "common" in the phrase, "common difference"? Does the sequence $2,3,5,7,11,13$ that you gave have a common difference? Anyway, when you have figured out what you mean, why not try to solve something simpler first, say, 3 prime numbers instead of 6; if you succeed with that, think about 4 prime numbers, then 5, consider the patterns you are finding, I'm sure you'll be able to work out an answer for 6 (and if not you can come back here and show what you were able to do and we'll go on from there). – Gerry Myerson May 18 '12 at 7:08
The minimum common difference must be a multiple of $30$, because if the difference is odd then every other number will be even, and if the difference is not a multiple of $3$ then two of the numbers will be a multiple of $3$, and one of the numbers will be a multiple of $5$ if the common difference is not a multiple of $5$.
$7,37,67,97,127,157$ has difference $30$.