## The millionth number with at least one million prime factors

### Problem 615

Consider the natural numbers having at least 5 prime factors, which don't have to be distinct.

Sorting these numbers by size gives a list which starts with:

- 32=2⋅2⋅2⋅2⋅2
- 48=2⋅2⋅2⋅2⋅3
- 64=2⋅2⋅2⋅2⋅2⋅2
- 72=2⋅2⋅2⋅3⋅3
- 80=2⋅2⋅2⋅2⋅5
- 96=2⋅2⋅2⋅2⋅2⋅3
- ...

So, for example, the fifth number with at least 5 prime factors is 80.

Find the millionth number with at least one million prime factors.

Give your answer modulo 123454321.