Factoring into coprimes in essentially linear time

  title={Factoring into coprimes in essentially linear time},
  author={Daniel J. Bernstein},
  journal={J. Algorithms},
Let Sbe a finite set of positive integers. A “coprime base for S” means a set P of positive integers such that (1) each element of P is coprime to every other element of P and (2) each element of S is a product of powers of elements of P. There is a natural coprime base for S. This paper introduces an algorithm that computes the natural coprime base for S in essentially linear time. The best previous result was a quadratic-time algorithm of Bach, Driscoll, and Shallit. This pap er lso shows how… CONTINUE READING
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