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