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]

Printed from the PrimePages <t5k.org> © G. L. Honaker and Chris K. Caldwell