3 problems

Let $N>24476$ be a non-square satisfying $N\equiv 0,2\pmod{6}$. Nonsquare prime-square representation conjecture. Then there exist primes $p$ and $q$ such that … By Hua's theorem,…

Let $\mathcal A=\{n\in\mathbb N:n\equiv 4\pmod{24}\}$. A representation as a sum of four squares of primes is an expression … with each $p_i$ prime. Four prime squares representati…

Sums-of-squares-of-primes conjecture. Every sufficiently large integer in $\mathcal{A}_j$ can be represented as the sum of $j$ squares of primes, and consequently