/* 

  Primes (cp version) in Picat.

  Calculating primes using cp. 
  Note: Picat has an efficient check for primes as built-in (prime/1).

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.


main => go.

go ?=>
  N = 1000,

  Primes = new_list(N),
  Primes :: 0..1,

  NumPrimes #= sum(Primes),

  foreach(I in 2..N)
    is_prime(I,Primes[I])
  end,

  Vars = Primes ++ [NumPrimes],
  solve(Vars),
  println(primes=[I : I in 1..N, Primes[I] == 1]),
  println(numPrimes=NumPrimes),
  
  nl.

go => true.


is_prime(X,B) =>
   X #> 1,
   fd_max(X) = Max,
   Len = 1+ceiling(sqrt(Max)),
   B :: 0..1,
   % Have to hard code for 2 and 3
   (X #= 2 #\/ X #= 3 #\/
    sum([X mod I #> 0 : I in 2..1+ceiling(sqrt(Max))]) #= Len-1
   ) #<=> B#=1.