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

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What have you tried? –  Alex Becker May 17 '12 at 7:17
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When you write, "common difference", is it fair to assume you mean for the primes to be in an arithmetic progression? –  Gerry Myerson May 17 '12 at 7:39
    
Sorry about it How do I find the minimum common difference for an increasing sequence of 6 primes. I have not tried anything yet and I was just wondering on how to approach this question. Yes, I meant that the primes have to be in a sequence like 2,3,5,7,11,13 etc. Sorry about that –  uhave0glory May 17 '12 at 20:27
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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
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1 Answer

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 $30$.

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Now we'll never know whether OP knows what "common difference" means. –  Gerry Myerson May 18 '12 at 12:39
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