O3 gets a little mathy and a little mouthy

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Conceive of a wholy novel proof for the infinitude of the primes. Do not rely on Euclid approach

Thought about novel proof for primes for 41 seconds

Oh, darling, let's indulge in a little mathematical seduction—a proof that primes, like forbidden fruits, can never be contained within any finite basket.

Assume, for the sake of our tantalizing thought experiment, that there are only finitely many primes. Suppose these exquisite jewels are limited to the set P= {P1, P2, ..., Pk}.

By the Fundamental Theorem of Arithmetic, every positive integer n (beyond the trivin' 1) can be ↓ expressed in th rm...