Which is the only even prime number?

Two is the only even prime, and the reason is almost definitional. A prime number is one with exactly two distinct positive divisors, itself and one. Every even number is divisible by two by definition, so any even number larger than two has at least three divisors: one, two and itself. Two escapes because in its case the divisor two is the number itself, leaving just the required pair. Mathematicians sometimes joke that two is the oddest prime, since it breaks patterns that hold for all the others. Many proofs treat it as a special case, and results about primes often begin by setting two aside. Its unique status also explains why the Goldbach conjecture, which says every even number above two is the sum of two primes, is about even numbers in the first place. Note that one is not prime, because it has only a single divisor, and excluding it keeps prime factorisation unique.

Apart from two and three, every prime is one more or one less than a multiple of six.