Fermat, Euler and Wilson · Challenge problem

$2^{340} \equiv 1 \pmod{341}$, although $341$ is composite

$2^{340} \not\equiv 1 \pmod{341}$, which proves $341$ is composite

$2^{340} \equiv 1 \pmod{341}$, which proves $341$ is prime

$2^{340} \not\equiv 1 \pmod{341}$, although $341$ passes every Fermat test