Maximum number of distinct prime factors of numbers below $2^{64}$

Question

What is the maximum number of distinct prime factors of numbers below $2^{64}$? I'm interested in the exact count, not just an estimate.

In other words, what is the largest $\omega(n)$, where $n < 2^{64}$?

Answer 1

The number with the most distinct prime factors will have the form

$$2\cdot 3\cdot 5\cdot 7\cdots$$

So all you need is to multiply all primes until you reach $2^{64}$.