Conjecture (odd power of 2; 3; Lagrange’s conjecture)

If n is greater than 2 and p is the largest prime less than n^2 and q is the smallest prime greater than (n+1)^2, and q – (n+1)^2 = 3, then n^2 – p is an odd power of 2.
keywords:
[Mathematics]
[Number Theory]