Lol do you just want the answer?

Hints are fine too, lol

I’ll just give a few (why not), some may be obvious

## 1

The answer must be a product of primes strictly greater than the N-th prime.

## 2

It’s always optimal to have the answer be a product of exactly 2 primes. Let’s say we have a valid number that’s a product of k primes. Then we could divide by k - 2 of those primes and the number would still be valid.

## 3

There’s no reason to use any primes larger than the (N + 1)-th prime, because that prime is the smallest prime that we’re allowed to divide by.

## Answer

Directly following (2) and (3), the answer is the (N + 1)-th prime, squared.

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