The number, 1406357289, is a 0 to 9 pandigital number because it is made up of each of the digits 0 to 9 in some order, but it also has a rather interesting sub-string divisibility property.

Pentagonal numbers are generated by the formula, Pn=n(3n1)/2. The first ten pentagonal numbers are:

Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:

It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.

The series, 11 + 22 + 33 + … + 1010 = 10405071317.