In this paper, we show that there are infinitely many primes of the form `2`m+m2 such that 2`m is prime, and that the number of such primes satisfies the expected asymptotic formula. We show this by adapting the proof of a result of Fouvry and Iwaniec who showed that there are infinitely many primes of the form `2 + m2 with ` prime.
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