Let $p$ be a prime number such that $p\equiv 1 \pmod 9$. My question is the following:

Is the prime number $p$ representable in the form $x^2+ny^2$?

for some integer $n$ which doesn't depend on $p$.

Is there an integer $n\ge1$ such that every prime $p\equiv1\pmod{9}$ is representable in the form $x^2+ny^2$?

Let $p$ be a prime number such that $p\equiv 1 \pmod 9$. My question is the following:

Is the prime number $p$ representable in the form $x^2+ny^2$?

for some integer $n$

Let $p$ be a prime number such that $p\equiv 1 \pmod 9$. My question is the following:

Is the prime number $p$ representable in the form $x^2+ny^2$?

for some integer $n$ which doesn't depend on $p$.