There are 24,061,467,864,032,622,473,692,149,727,991 partitions of 1000 as unordered sums of positive integers.

A partition of a positive integer n is a collection of positive integers (order unimportant) whose sum is n. The integers in a partition are called parts. We denote by p(n) the number of partitions of n, and by p(n, k) the number of partitions of n into exactly k parts. Clearly,

p(n) =

p(n, k).