A property of the ring of integers of cyclotomic fields Let $t$ be a positive integer and consider $\mathbb Q(\zeta_t)$ a cyclotomic field. It is known that its ring of integer is $R=\mathbb Z[\zeta_t]$. I would like to know why there exists a nonzero prime ideal $P$ of $R$ that does not contain $t$. 

Probably it is not so difficult to prove it, so I would appreciate some hints about it.
Correct me if I'm wrong, but try considering a prime $p$ that doesn't divide $t$. $(p)$ might not be prime but there are primes above it.
Correct me if I'm wrong, but try considering a prime $p$ that doesn't divide $t$. $(p)$ might not be prime but there are primes above it.