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