Efficient Simple Tests For Primality

  • Fayez Fok Al Adeh President of the Syrian Cosmological Society P.O.Box , 13187, Damascus, Syria
Keywords: Algorithm, Composite; Generating Function; Greatest Common Divisor; Prime; Quotient; Remainder; Solving Polynomial Equation; Square.

Abstract

The tests form a general method to decide whether a given positive odd integer is composite or prime. The tests are based on the divisibility properties of the sum of two squared positive integers. The algorithms comprising the tests are polynomial- time algorithms.

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References

[ 1 ] Aigner, Martin; Ziegler, Gunter M. (2002)

"Proofs from The Book" ,New York ; Springer – Verlag.

[ 2 ] Ribenboim, Paulo (1988) "The Book of Prime Number Records " , New York; Sprintger.

[ 3 ] Wilf, Herbert S . (1994) " Generatingfunctionology", London; Academic Press.

[ 4 ] Dickson, Leonard Eugene (1922) " First Course in The Theory of Equations " , New York; John Wiley.

[ 5 ] Schroeder, M.R.(1986) " Number Theory in Science and Communication ", New York ; Springer – Verlag.

[ 6 ] Rader, Robert J.(1978) " Advanced Software Design Techniques" , Princeton; Petrocelli Books,Inc.

[ 7 ] Koblitz,Neal (1987) " A Course in Number Theory and Cryptography ", New York ; Springer – Verlag.

[ 8 ] Guy, Richard K.(1994) " Unsolved Problems in Number Theory" , New York ; Springer – Verlag.

Published
2017-09-19
How to Cite
Al Adeh, F. (2017). Efficient Simple Tests For Primality. Journal of Progressive Research in Mathematics, 12(3), 1957-1980. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1239
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Articles