Five consecutive positive odd numbers, none of which can be expressed as a sum of two prime powers

Chen, Yong-Gao

doi:10.1090/S0025-5718-04-01674-6

Five consecutive positive odd numbers, none of which can be expressed as a sum of two prime powers
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Math. Comp. 74 (2005), 1025-1031 Request permission

Abstract:

In this paper, we prove that there is an arithmetic progression of positive odd numbers for each term $M$ of which none of five consecutive odd numbers $M, M-2, M-4, M-6$ and $M-8$ can be expressed in the form $2^n \pm p^\alpha$, where $p$ is a prime and $n, \alpha$ are nonnegative integers.

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