A Novel Algorithmic Approach using Little Theorem of Fermat For Generating Primes and Poulet Numbers in Order

Authors

Abd Elhakeem Abd Elnaby, Department of Mathematics, Faculty of Science, Damietta University, New Damietta, EgyptFollow
A. H. El-Baz, Department of Computer Science, Faculty of Computers and Artificial Intelligence, Damietta University, New Damietta, EgyptFollow

Abstract

Computer encryption are based mostly on primes, which are also vital for communications. The aim of this paper is to present a new explicit strategy for creating all primes and Poulet numbers in order up to a certain number by using the Fermats little theorem. For this purpose, we construct a set C of odd composite numbers and transform Fermats little theorem from primality test of a number to a generating set Q of odd primes and Poulet numbers. The set Q is sieved to separate the odd primes and the Poulet numbers. By this method, we can obtain all primes and Poulet numbers in order up to a certain number. Also, we obtain a closed form expression which precisely gives the number of primes up to a specific number. The pseudo-code of the proposed method is presented.

Recommended Citation

Elhakeem Abd Elnaby, Abd and H. El-Baz, A. (2022) "A Novel Algorithmic Approach using Little Theorem of Fermat For Generating Primes and Poulet Numbers in Order," Information Sciences Letters: Vol. 11 : Iss. 4 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol11/iss4/30