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if (more sophisticatedly) we regard the "conditional" probability that "n" is prime, given that we know all its prime factors exceed "b", as at most "a"ln("b")/ln("n"), then using euler's theorem that the least prime factor of "f""n" exceeds , we would find instead: formula_10although such arguments engender the belief that there are only finitely many fermat primes, one can also produce arguments for the opposite conclusion.
if (more sophisticatedly) we regard the "conditional" probability that "n" is prime, given that we know all its prime factors exceed "b", as at most "a"ln("b")/ln("n"), then using euler's theorem that the least prime factor of "f""n" exceeds , we would find instead: formula_9although such arguments engender the belief that there are only finitely many fermat primes, one can also produce arguments for the opposite conclusion.