I struggled a bit on this one to start - mostly because it was a surprisingly deep challenge that more resembled a project. However I sketched abrute force solution in a post yesterday:
Are you familiar with:
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Sieve of Eratosthenes for finding prime numbers?
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Are you familiar with prime factorization?
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Do you realize that the *prime factorization of each number is unique?
Hopefully these hints at the math behind this problem, and solution, help out.