I regret to inform you that you have made the wrong decision. There are actually infinitely many prime numbers. The intuitive reason for believing that there are infinitely many primes is simply that there is no good reason for it not be so. There is no plausible barrier that one can erect and say, with certainty, "Beyond here, primes dare not venture."
Of course, that intuitive justification is a far cry from the certainty of a formal mathematical proof of the existence of infinitely many primes, and it's not even a good informal explanation of how you might come up with such a proof.
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