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Sep 8, 2016 at 13:23 comment added Steven Landsburg But it's still possible that a) there is an algorithm $A$ for computing the prime factorization of $n+1$ given the prime factorization of $n$, b) $A$ runs faster than any algorithm that does not take as given the prime factorization of $n$, and c) $A$ is too slow, in practice, to find the prime factors of $2^{1048576}+1$. [Or c') $A$ hasn't been discovered yet.]
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Sep 8, 2016 at 6:38 history answered Robert Israel CC BY-SA 3.0