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A Novel Algorithmic Approach using Little Theorem of Fermat For Generating Primes and Poulet Numbers in Order |
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PP: 1325-1328 |
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doi:10.18576/isl/110430
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Author(s) |
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Abd Elhakeem Abd Elnaby,
A. H. El-Baz,
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Abstract |
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| 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.
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