A partition with no hook lengths divisible by a is called an a-core partition. For two coprime numbers a and b, a partition is called an (a,b)-core partition if it is both a-core and b-core partition. It is well-known that the number of a-core partitions is infinite, and Anderson proved the number of (a,b)-core partitions is a rational Catalan number. Inspired by work of Johnson, we give an expression for the number of (a,b,c)-core partitions. This is ongoing work with Jineon Baek and Myungjun Yu.