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


Aebi, Ch. and G. Cairns. C"atalan numbers, primes, and twin primes." Elem. Math. 63 (2008): 153-164.

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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