https://zenodo.org/records/10971571 Please take a look carefully at above link and verify it. Thanks!

For each $n\in\mathbb{N},$ let $S_n$ be the set of prime factors of $n! + 1$. By Wilson's theorem, we have $\ p\mid (p-1)!+1\ $ for every prime $p.$ Therefore, $\displaystyle\bigcup_{n=1}^{\infty} S_n \supset \bigcup_{n \text{ is prime }} S_{n-1} = \mathbb{P},\ $ the set of primes. Trivially, thi...