- for prime(N) if gap = 3 then both 2N + 1 and 2N + 7 are composite and their prime factor either 3 or 5 or 3 and 5.And the converse is not true.

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[Non-text portions of this message have been removed] - for prime(N) if gap = 3 then both 2N + 1 and 2N + 7 are composite and

their prime factor either 3 or 5 or 3 and 5.And the converse is not

true. - kadickv wrote:
> for prime(N) if gap = 3 then both 2N + 1 and 2N + 7 are composite and

3 always divides one of N, N+2, N+4.

> their prime factor either 3 or 5 or 3 and 5.

By "gap = 3" I assume you mean that N and N+4 are consecutive primes.

Then 3 must divide N+2. And then 3 divides 2*(N+2) = 2N+4.

This means 3 also divides 2N+1 and 2N+7.

We know that 5 doesn't divide 2N or 2*(N+4) = 2N+8.

Then 5 must divide exactly one of 2N+1, 2N+4, 2N+7.

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Jens Kruse Andersen