Mathematics, applications of mathematics to life in general, and my life as a mathematician.

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

Only for p=3

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.

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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## Konstantin:

Only for p=3

30 December 2021, 12:15 am## 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.

30 December 2021, 9:49 am## 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.

30 December 2021, 12:37 pm