Congruences characterizing twin primes

Jan Górowski, Adam Łomnicki

Abstract


Inspired by P.A. Clement’s results in [2], we give new necessary and sufficient conditions for two prime numbers to be twin primes.

Keywords


prime number, twin prime pair

Mathematics Subject Classification


11A41, 11A07

References


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Clement, P.A. "Congruences for sets primes." Amer. Math. Monthly 56 (1949): 23-25.

Dence, J.B. and T.P. Dence. "A necessary and sufficient conditions for twin primes." Missouri J. Math. Sci. 7 (1995): 129-131.

Gold, J.F. and D.H. Tucker. "A characterization of twin prime pairs." Proceedings NCUR V.1 (1991): 362-366.

Górowski, J. and A. Łomnicki. "Around the Wilson’s theorem." Ann. Univ. Paedagog.Crac. Stud. Did. Math. Pert. (to appear).

Ribenboim, P. "The little book of big primes." New York: Springer Verlag, 1991.

Sierpiński, W. "Elementary theory of numbers." Second edition. North-Holland Mathematical Library 31. Amsterdam: North-Holland Publishing Co.,; Warsaw: PWN–Polish Scientific Publishers, 1988.

Yan, S.Y. "Number Theory for Computing." Second edition. Berlin: Springer Verlag, 2002.


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