I found this problem on a discussion board for beginning programmers. It feels like a Project Euler problem, but I looked and didn’t find it there:

The smallest pair of consecutive natural numbers that each have two distinct prime factors are 14 = 2 * 7 and 15 = 3 * 5. The smallest triplet of consecutive natural numbers that each have three distinct prime factors are 644 = 2^2 * 7 * 23, 645 = 3 * 5 * 43 and 646 = 2 * 17 * 19. What is the smallest set of four consecutive natural numbers that each have four distinct prime factors?

Your task is to write a program that finds the set of four natural numbers. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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