Amiram Eldar tells me that Mathematica considers -1 times a prime to be a prime. Select[Range[-10, 10], PrimeQ] {-7, -5, -3, -2, 2, 3, 5, 7} This is wrong, and dangerous (it has led people to make mistakes in sequences). If negative numbers were primes we would lose unique factorization, a cornerstone of mathematics.