Heuristic Running Time
In number theory, there are many integer factoring algorithms that heuristically have expected running time
in o and L-notation. Some examples of those algorithms are the elliptic curve method and the quadratic sieve. Another such algorithm is the class group relations method proposed by Schnorr, Seysen, and Lenstra that is proved under of the Generalized Riemann Hypothesis (GRH).
Read more about this topic: Integer Factorization
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