3. Find all non-negative integers $a, b$ such that $a^{4}+4 b^{4}$ is a prime.

Find all non-negative integers $a, b$ such that $a^{4}+4 b^{4}$ is a prime.
3. From $a^{4}+4 b^{4}=\left(a^{2}+2 a b+2 b^{2}\right)\left(a^{2}-2 a b+2 b^{2}\right)$, we know that when at least one of $a, b$ is zero, $a^{4}+4 b^{4}$ is not a prime number, so only when $a=b=1$, $a^{4}+4 b^{4}=5$ is a prime number.