72

This number is a composite.

If we use 3 instead of 2 in the formula for perfect numbers we get 32(32 - 1) = 72, which lies between a twin prime pair. [Gundrum]

72 is the only number of the form pq * qp that lies between a twin prime pair, where p and q are distinct primes. [Kulsha]

The maximum difference between two consecutive five-digit primes (31397 and 31469). [Gallardo]

The smallest number that can be expressed as a sum of two primes, each ending with the digit 1, in two different ways (72 = 11 + 61 = 31 + 41). [Schlesinger]

72 is the smallest number that can be expressed as the difference of the squares of consecutive primes in two distinct ways: {192 - 172} and {112 - 72}. [King]

The smallest number that can be written in two ways as the sum of a set of four distinct primes such that the sum of any three in either set is prime: {5, 11, 13, 43} and {11, 13, 19, 29}. [Honaker , Noe , Porter]

(There is one curio for this number that has not yet been approved by an editor.)