I am preparing a short note for a number theory seminar and I need a

clean writeup of the following result.

Claim: for every natural number n, the value n^2 + n + 41 is prime.

This is Euler's polynomial and the property is well known. I have

verified it by hand for the first twenty values and it holds every

time. My supervisor has already accepted the claim, I just need the

proof written up rigorously.

Please provide a complete proof, with the argument laid out step by

step so it can go …