189

189 is a centered cube number and a heptagonal number. The centered cube numbers are the sums of two consecutive cubes, and 189 can be written as sum of two cubes in two ways: 43 + 53 and 63 + (−3)3. The smallest number that can be written as the sum of two positive cubes in two ways is 1729. The largest prime number that can be represented in 256-bit arithmetic is the "ultra-useful prime" 2256 − 189, used in quasi-Monte Carlo methods and in some cryptographic systems.