# Interesting Primes

Number Theory Level pending

A prime is interesting if it can be written in the form $$3a^2-b^2$$ for positive integers $$a, b$$. It turns out that a prime $$p>3$$ is interesting if and only if it is equal to $$x \pmod y$$ for some positive integers $$x, y$$. Find $$x+y$$.

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