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The first proof is basically just begging the question.

It says that having infinitely many composite numbers must mean infinitely many factors, and thus infinitely many primes.

But we can construct infinite sets of numbers from finite prime factors easily. [2] and the powers of 2.

Which might be a good starting point to teach someone Euclid's proof that there are infinite primes, but ChatGPT didn't get all the way there.



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