The Quadratic Sieve has running time
But with certain improvements (such as using Wiedemann's Gaussian Elimination algorithm over GF(2)), it's running time is given by
The Number Field Sieve is better for numbers over 100-digits and has running time
Excuse my notation (but TeX would be overkill).
Note: O(stuff) means the magnitude of the running time is < A * stuff for some constant A and all values of n.
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