125

This number is a composite.

125 = (10² + 5²) or (11² + 2²), i.e., the sum of prime squares in two ways. [Sladcik]

125 = 5³ (a prime cube). It is the smallest number which is both a sum of distinct prime squares and a prime cube. [Kulsha]

Conjecture by Zhi-Wei Sun to be the largest power (5³) for which there is no prime between it and the previous power (11²). The other prime gaps between powers are in (2³, 3²), (2⁵, 6²) and (5², 3³). [Caldwell]

The smallest prime cube (p^3), where (p+3) = the digit-sum of (p^3) = another prime cube. Note that 125 = π(12)^π(5). [Worrom]

125 = sigma(prime(1*25)) + prime(1) + 25. [Worrom]