This number is a composite.
If you consider the alphabet as an extension of the decimal system (base 36), the difference in the numerically expressed words SIXTY and FOUR is equal to 47180851, which is prime. [Nothdurft]
The number 264 + 1 was factored by Landry in 1880. [Kraitchik]
Using A = 1, B = 2, ..., Z = 26, the sum of all the letter values in the word names of the numbers from 1 to 64 is a prime (7369). If 0 (whose alpha-numeric value is 64) is included, the sum is yet another prime (7433). [Trotter]
The smallest power of 2 with no prime neighbor. [Necula]
The smallest square that creates two primes if concatenated with its previous and next squares, i.e., 6449, 6481. [Loungrides]
The first occurrence of a composite number whose factorization with exponents contains exactly one circular loop on each side of the equals sign (64 = 2^6). [Honaker]