Let $R$ be an integral domain, is it true that if $R$ is atomic, then it must contain a prime element?
If not, what is a counterexample?
I know that if an element is prime, then if $I$ is the ideal generated by it, then $R/I$ must be an integral domain. However, $R$ being an atomic integral domain doesn't really help for that, since even if we take the ideal generated by an irreducible element $a,$ there can still be nonunique factorizations of $ka=rs$ such that $r$ and $s$ are not multiples of $a.$
I'm stuck on how to approach the problem in other ways and I can't really get a sense of if it's even true or not.
Any help would be greatly appreciated!