SMARANDACHE PRIME AND COPRIME FUNCTIONS

                        edited by Emil Burton
                        Babes-Bolyai University
                        Department of Mathematics
                        Cluj-Napoca, Romania


1) SMARANDACHE PRIME FUNCTIONS are defined as follows:

   P : N --> {0, 1}, with
           __
          |
          | 0, if n is prime;
   P(n) = |
          | 1, otherwise.
          |__

   For example P(2) = P(3) = P(5) = P(7) = P(11) = 0, whereas
   P(0) = P(1) = P(4) = P(6) = ... = 1.

   More general:

         k
   P  : N  --> {0, 1}, where k is an integer >= 2, and
    k
                          __
                         |
                         | 0, if n , n , ..., n  are all prime numbers;
   P (n , n , ..., n ) = |        1   2        k
    k  1   2        k    | 1, otherwise.
                         |__



2) SMARANDACHE COPRIME FUNCTIONS are similarly defined:

          k
    C  : N  --> {0, 1}, where k is an integer >= 2, and
     k
                          __
                         |
                         | 0, if n , n , ..., n  are coprime numbers;
    C (n , n , ...,n ) = |        1   2        k
     k  1   2       k    | 1, otherwise.
                         |__



Reference:
  [1] F. Smarandache, "Collected Papers", Vol. II, 200 p., <Functii
      Prime and Coprime>, p. 137, Kishinev University Press,
      Kishinev, 1997.