# a question on Euclid Numbers

Let $p_n$ be the $n$-th prime, numbers $E_n=p_1\cdot\ldots\cdot p_n+1$ are called Euclid numbers.

https://en.wikipedia.org/wiki/Euclid_number

It is not known if there are infinitely many primes among $E_n$'s.

The second open question is if all Euclid numbers are squarefree. Are Euclid numbers squarefree?

Are any two distinct Euclid numbers relatively prime? Is this known?

No. Check the notes here. The first example is $E_7$ and $E_{17}$...