I have created various implementations of methods to replace prime? and
prime_division (from the standard lib file prime.rb) based on a class of
mathematical operators I've developed called prime generators (PG).Using
a special form of these PG I term Strictly Prime (SP) prime generators I
have created extremely simple and fast algorithms that can find all the
primes up to some number n, determine the primality of n, or
factorization.

Below are links to the paper which provides the mathematical basis for
the proposed methods with two tables of benchmark results comparing the
performance of the library methods prime? and prime_division with my
proposed methods. I provide test results on 32-bit and 64-bit Linux
systems using 5 reference primes of 17 to 19 digits.

My paper, 'Improved Primality Testing and Factorization in Ruby'
http://www.scribd.com/doc/150217723/Improved-Primality-Testing-and-Factorization-in-Ruby

The code rile 'primeszp.rb' is available in my github repository:
https://gist.github.com/jzakiya/455f2357cdb08f4ee1c4

Attachments:
http://www.ruby-forum.com/attachment/8542/Improved_Primality_Testing_and_Factorization_in_Ruby.pdf
http://www.ruby-forum.com/attachment/8543/primeszp.rb


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