125

This number is a composite.

125 = 11² + 2² (the sum of prime squares). [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]