Euler Prime. Let a prime number generated by Euler's prime-generating polynomial be known as an Euler prime. Then the first few Euler primes occur for , 2, ..., 39, 42, 43, 45, ... (OEIS A056561), corresponding to the primes 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, ... (OEIS A005846).