in reply to Re: Factors
in thread Vampire Numbers
The Quadratic Sieve has running time
O(e^(sqrt(1.125ln(n)ln(ln(n)))))
But with certain improvements (such as using Wiedemann's Gaussian Elimination algorithm over GF(2)), it's running time is given by
O(e^(sqrt(ln(n)ln(ln(n)))))
The Number Field Sieve is better for numbers over 100-digits and has running time
O(e^(1.9223((ln(n))^1/3(ln(ln(n))))^2/3))
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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