> There are infinitely many primes that can be formulated by squaring two whole numbers and adding them together. [...] By insisting that one of the numbers yo

> There are infinitely many primes that can be formulated by squaring two whole numbers and adding them together. [...] By insisting that one of the numbers you’re squaring be odd, perhaps [...] makes the problem much harder. Does it? For any number a, a^2 = a (mod 2), and primes greater than 2 are all odd, so if a prime p = a^2 + b^2, doesn't one of a or b have to be odd? Reducing mod 2, p = 1 (mod 2), a^2 + b^2 = 1 (mod 2), a + b = 1 (mod 2), so either a = 0 (mod 2) and b = 1 (mod 2) or vice-versa? edit: If Euler proved infinitely many such primes exist then "With this in hand, Green and Sawhney proved Friedlander and Iwaniec’s conjecture: There are infinitely many primes that can be written as p^2 + 4q^2." makes no sense without a further condition of p or q, let (in my notation) a=p be odd and b=2q be even. Now having finished the article, I think this was just sloppy writing, and the actual accomplishment is related to the post-perhaps clause: one of p or q has to itself be a perfect square? Anyway, I have very little certainty about what was actually accomplished from reading this article.