You wouldn't use a list to determine if x is prime. And nobody records large lists of known primes because it is pointless. If nobody recorded that x is prime then I cannot do this). (Given a list of known primes, I can determine whether x is prime or not by checking that it would be in the list if it was prime due to the list size, and then checking whether it is on the list. A number x that has at some point be determined to be a prime is not a "known prime" if it is not recorded. It works in the browser and is powered by alien technology from the future. It lets you generate as many primes as you need, starting from any value. A "list" of known primes would have to be recorded. Last updated 1 week ago I often have to generate a sequence of prime numbers so I created this simple utility that does it for me. If $n$ is composite, it will almost certainly (again, a slippery term) return "COMPOSITE", but there's a small probability $(\frac$ on a large hard drive for say $500, which would pay for some of the cost creating the list. The Miller-Rabin primality test is an algorithm that takes a number $n$, and a "certainty" parameter $m$, and (in layman's terms) if $n$ is prime, it will return "PRIME". Moreover, it's fairly easy to come up with large primes, and it's fairly easy to "guarantee" (guarantee being a slippery term), that a given large number is prime. This may be a somewhat unsatisfying answer, but no-one's really keeping a complete list of known primes (to the best of my knowledge).
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