List-all-primes-p-for-which-p-2-and-p-4-are-also-primes-

Question Number 765 by prakash jain last updated on 09/Mar/15

List all primes p for which p + 2 and p + 4

are also primes .

Answered by rishabh last updated on 09/Mar/15

p = 3 is the only such number .

Let us assume there is a prime p > 3 .

Since p is not divisible by 3,

p = 3 k + 1 or 3 k + 2 where k \in N, k ⩾ 1

If p = 3 k + 1 then p + 2 is divisible by 3 .

If p = 3 k + 2 then p + 4 is divisible by 3 .

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