Given $ q\in \mathbb Z[X]$ , then for big enough $ n$ : $ $ m\equiv q(p_n)\pmod{p_{n+1}}\;\wedge\; 0\leq m<p_{n+1}\iff\exists k\in \mathbb Z:m=q(-2k).$ $ https://math.stackexchange.com/questions/2645854/a-conjecture-concerning-primes-and-perhaps-prime-gaps This also seems to be a generalization of Opperman’s conjecture. What is the intuition about this? Are there counterexamples?Read more