Conjecture (compatible primes, Lagrange’s conjecture)

If n is greater than 1 and p is the greatest prime less than n^2 and q is the smallest prime greater than (n+1)^2, and n^2 – p = 2 and q – (n+1)^2 = 1, then p and q are compatible primes.
keywords:
[Mathematics]
[Number Theory]