Dyson’s rank of a partition witnesses Ramanujan’s first two congruences for p(n): \(p(5n+4)\equiv 0\pmod 5\) and \(p(7n+5)\equiv 0\pmod 7\) . However, the 5- and 7-divisibility outside of these arithmetic progressions is not always witnessed by the rank. In this paper, we find statistics witnessing every instance of m-divisibility of P(n, d), the number of partitions of n into exactly d parts. We call these statistics “supercranks," and we give several examples. We conjecture that these examples, along with just one other known supercrank, are the only supercranks for P(n, d) modulo any m.
