167

This number is a prime.

It is conjectured that every positive integer may be written as the sum of seven nonnegative cubes except these seventeen: {15, 22, 23, 50, 114, 167, 175, 186, 212, 231, 238, 239, 303, 364, 420, 428, 454}. This conjecture has been tested to 10³⁴ and proven for numbers divisible by four. [Caldwell]