Finding cyclic group $\mathbb{Z}^*_n$ of prime order

It can be proven that multiplicative group of integers modulo N defined as

$ \mathbb{Z}^*_N = \{ i∈Z : 1≤i≤N−1\; AND\; gcd(i,N)=1 \} $

is cyclic for a prime N and that if it is of prime order, then every non-identity element in the group is a generator of this group.

How can I find such N?

I wrote a simple program and brute-forced for i $ \mathbb ∈\; [1, 300 000]$ and found no group of prime order so far.