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]
125 = 53 is the number of primes between 193 and 203. Can you find another example where the number of primes between consecutive cubes is also a cube? [Honaker]