37

This number is a prime.

The degree of the first polynomial discovered whose set of positive values is the set of primes as the variables range over the natural numbers. Matijasevic showed this was possible in 1971, and Jones, Sato, Wada, and Wiens provided an example of such a polynomial with 26 variables (and degree 25) in 1976. It can conveniently be written down using the 26 letters of the English alphabet.