[math-fun] Factorizations of 1 + n + n^2

At least for the first few positive n, the factorization of 1 + n + n^2 contains a prime larger than n. The first counterexample is at n=16; here 1 + n + n^2 = 273 = 3*7*13. I've only explored the question by hand, but so far I've found no counterexamples for the special case when n is prime. Can somebody with a few free minutes find one?