<s>[INST] If $a,b,c,a^2+b^2+c^2$ are primes, then $a$ or $b$ or $c$ is equal to $3$ Given primes $a,b,c$ such that $a^2+b^2+c^2$ is prime, then $3\in\{a,b,c\}$.
Tested for $a,b,c<500$.
 [/INST] If $p\neq3$, $p$ a prime, then $p^2\equiv1\pmod3$. So if $3\notin\{a,b,c\}$ then $3\mid a^2+b^2+c^2$.
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