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The Addition of Primes and Power

Abstract Let k ≥ 2 be an integer. Let Ek (N) be the number of natural numbers not exceeding N which are not the sum of a prime and a k-th power of a natural number. Assuming the Riemann Hypothesis for all Dirichlet L-functions it is shown that Ek (N) ≪ N1-1/25k.