If n is prime, N + 2 is prime and N > 10, we prove that N + (n + 2) is a multiple of 12

If n is prime, N + 2 is prime and N > 10, we prove that N + (n + 2) is a multiple of 12

From the question, we get that n is not an even number, not a multiple of 3;
So the sum of the digits of n is 3K + 1 or 3K + 2;
Because n + 2 is prime, n is 3K + 2;
So n + 1 is 3K + 3, a multiple of 3; it is even
The original formula is n + N + 2 = 2 (n + 1);
N + 1 is a multiple of two and three and a multiple of six;
So the original formula is a multiple of 12

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