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I have a confusion over understanding of the statement "3 consecutive odd prime integers".

I was looking at a question, where they considered 3 consecutive odd integers that are prime (in this case only 3, 5, 7 will satisfy as after this set every 3 consecutive no. will have at least 1 number a multiple of 3).

But I took it as 3 consecutive prime integers that are odd. Ex. 3,5,7 and 13, 17, 19 and much more.

Is it called as 3 consecutive integers that are prime, or 3 consecutive prime integers that are odd?

Goutham
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    I would interprete it as three consecutive primes (which are then always all odd , unless we speak of the triple $(2,3,5)$) – Peter Sep 28 '21 at 17:41
  • Probably depends on the context. I think this is often an example in intro proof books to show there is only 1 prime triple ${3,5,7}$, for the reason you mentioned. This is analogous to the unsolved twin prime conjecture. – Brian Lai Sep 28 '21 at 17:48
  • For every integer $n$ you have that exactly one of $n,n+2,n+4$ is a multiple of three. Any positive integer that is a multiple of three (with the exception of $3$ itself) is necessarily composite and not prime. It follows that the only choice of $n$ such that $n,n+2,n+4$ are all prime is $n=3$ itself. Any other choice of $n$ you would have at least one composite number among $n,n+2,n+4$. – JMoravitz Sep 28 '21 at 17:52
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    @JMoravitz The author noticed this as well. – Peter Sep 28 '21 at 18:36
  • @peter the purpose of my comment was to rephrase and remove reference to the word consecutive as it was ambiguous what sequence it was in reference to – JMoravitz Sep 28 '21 at 19:07

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