![]() 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. A "list" of known primes would have to be recorded. 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". We cross out every number which is a multiple of 2 except 2. Step 2: We start from the first number 2 in the list. We leave the number 1 because all prime numbers are more than 1. ![]() 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. Step 1: First create a list of numbers from 2 to 100 as shown above. ![]() 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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