The largest integer n for which  (n) = n/4. [Woods]
120 = 31 + 32 + 33 + 34. [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]
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