Find the sum of three-digit numbers, each of which is the product of four unequal primes.

Let’s solve this problem by brute force.

Suppose there is no two in the prime factorization.

Then, the minimum product is 3 * 5 * 7 * 11 = 1155.

This means that the sought-for three-digit numbers are paired.

Note that if the primes are greater than or equal to seven, then the product is greater than 999.

Then, you can iterate over the options:

2 * 3 * 5 * (7, 11, 13, 17, 19, 23, 29, 31).

2 * 3 * 7 * (11, 13, 17, 19, 23).

2 * 3 * 11 * (13).

2 * 5 * 7 * (11, 13).

It is easy to calculate that the sum of such numbers is 10,524.