Consecutive primes and IP sets

2024/03/15 by William D. Banks, Banks, William D.
Computer Science · #Computability, Logic, AI Algorithms

paper · pdf · doi:10.48550/arxiv.2403.10637

Abstract

For an infinite set M of natural numbers, let FS(M) be the set of all nonzero finite sums of distinct numbers in M. An IP set is any set of the form FS(M). Let p_n denote the n-th prime number for each n ≥ 1. A de Polignac number is any number m such that p_n+1-p_n=m for infinitely many n. In this note, we show that every IP set of even natural numbers contains infinitely many de Polignac numbers.

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