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Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by kevinventullo on Saturday June 21, 2025 @02:51AM (#44335182)
As far as I know, the Lucas-Lehrer test used by GIMPS does not actually factor: https://en.m.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primali...
Re:Mathematicians Hunting Prime Numbers Discover Infinite Ne... by Someone on Saturday June 21, 2025 @03:24AM (#44335439)
That works for very few numbers. From that Wikipedia article: “In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers”

That’s fine for GIMPS, which only searches for Mersenne primes, but doesn’t work in general.

https://en.wikipedia.org/wiki/Primality_test#Fast_determinis... mentions several tests that do not require factorization, though.