A Power Problem

Problem. For how many prime numbers p, the expression 2p + p2 is a prime?



  1. Konstantin:

    Only for p=3

  2. JBL:

    On the other hand it seems that the expression is exactly 3 times a prime more than occasionally: 5, 7, 17, 43, 61, 73, … is not in the OEIS.

  3. Carl Feynman:

    The expression should be a multiple of three half of the time, assuming a reasonable proposition: primes are equally distributed between multiples of three plus one, and multiples of three plus two. Consider the values of the expression modulo 3.

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