The millionth number with at least one million prime factors (noch nicht übersetzt)
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.