Consecutive primes and IP sets

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 pₙ₊₁-pₙ=m for infinitely many n. In this note, we show that every IP set of even natural numbers contains infinitely many de Polignac numbers.