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> calculating ever-larger prime numbers, they get further apart

iirc that's not completely true. It may be in practice for bitcoin as a currency, but I remember reading that there's a limit to the distance between two primes, no matter how large they become.



Actually, false. There are no primes between n! + 1 and n! + n + 1 for all n, so arbitrarily large gaps between consecutive primes do exist.




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