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The millionth number with at least one million prime factors

Problem 615 Published on Sunday, 3rd December 2017, 10:00 am; Solved by 314

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.