Integer factorization and twin primes verification algorithms

Abstract

In this paper two algorithms based on the the divisibility properties of binomial expressions are introduced. The mathematical foundation lies in the connection that exists between binomial expressions and the number of carries that result in the sum in different bases, of the variables that form the binomial expression. The first one decomposes an integer into its prime factorization, while the second one answers if given two twin integers whether they are twin primes or not by just verifying one condition. The proposed procedures have the inconvenience of requiring the knowledge of the primes up to some fix number however, by a slight modification of the first algorithm this can be overcome. The mathematical approach applied is novice, and both algorithms are new. Mathematics Subject Classification: 11Y05, 11Y11, 11Y16