# 120

This number is a composite.

The largest integer *n* for which π(*n*) = *n*/4. [Woods]

120 = 3^{1} + 3^{2} + 3^{3} + 3^{4}. [Sladcik]

120^120-119^119 is prime. [Dobb]

120 is the smallest composite number of the form x! whose digit sum and x are primes. [Capelle]

All primes (except 2 and 3) are of form 6*n +/- 1. Note that 120 = 6*20 is the first number such that 6n+1 or 6n-1 does not contain a prime. [Luhn]

120 is the smallest three-digit number that may be expressed as the difference between the squares of consecutive primes in two different ways (120 = 31^2 - 29^2 = 17^2 - 13^2). [King]

The smallest possible sum for a set of six distinct double-digit primes such that the sum of any five is prime: {11, 13, 17, 19, 23, 37}. [Loungrides]

The smallest number whose the sum of the reciprocals of its divisors is an odd prime. [Loungrides]