# 72

This number is a composite.

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

72 is the only number of the form *p*^{q} * *q*^{p} 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: {19^{2} - 17^{2}} and {11^{2} - 7^{2}}. [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]