> I have discovered an extension to the Sieve of Eratosthenes that not only > finds the primes, but also finds the prime > factorization of the composites in canonical form. The algorithm requires no > explicit multiplication or division, only > loops and increments, the same as the "Sieve". > > Is such an algorithm already known? I have never been able to find a > reference to such an algorithm. I realize that the > algorithm probably does not have any practical application. But I think such > an algorithm would be of interest to the > study of the "Fundamental Theorem of Arithmetic" since it is so simple, just > as the "Sieve" is. > > I just want to know if it is something new, which I can't imagine it is. But > I cannot find a reference to it.
In Davis Moews and Paul C. Moews, A search for aliquot cycles below 10^10, Math. Comp., 57 (1991), 849-855 you can see that this method is used to factorize a range of numbers and calculate the sigma function of them. Jan _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
