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>> No.8420723 [View]
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8420723

>>8420711
That's a research field. The general number sieve is the fast one for large numbers.
https://en.wikipedia.org/wiki/Integer_factorization#Factoring_algorithms

>Is there a way to determine whether or not it's divisible without having to resort to trial division?
If you don't care about what the primes are, just the knowledge IF there are any factors, there are more fast algorithms for that
https://en.wikipedia.org/wiki/Primality_test
https://en.wikipedia.org/wiki/AKS_primality_test

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