Factors & Multiples · Medium problem

Every prime greater than $3$ is one more or one less than a multiple of $6$.

Every number that is one more or one less than a multiple of $6$ is prime.

The product of the first $k$ primes, plus $1$, is always prime.

If $n > 1$ has no prime factor up to $\sqrt[3]{n}$, then $n$ is prime.