Originally Posted by

**mr fantastic** Hmmmm ..... Just because n^2 + 2 produces some numbers that aren't prime, that's not a proof that the equation does not produce infinitely many primes. All it proves is that the equation does not always produce a prime ......

To show that n^2 + 2 does not produce an infinite number of primes, it's needed to show that it produces only a finite number of primes. Soroban has done half the work, since if n is even you always get an even number => no primes.

So you need to show that when n is odd, n = 2m + 1 say, there are only a finite number of primes. In other words there are NOT an infinite number of primes of the form (2m + 1)^2 + 2 = 4m^2 + 4m + 3 ......