%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Generating the set of all the prime numbers smaller
%%% than a given integer N
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Last revision: August 2002 (G.Rossi)
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%%% primes(N,S): 
%%% true if S is the set of all the prime numbers smaller than N

primes(N,S) :- 
     M is N - 1 &
     S = {X : X in int(2,M) & labeling(X) & is_prime(X)}!.
is_prime(X) :-
     Y is X -1 & 
     forall(Z in int(2,Y), non_div(Z,X)).

non_div(A,B) :- 
     Rmdr is (B mod A) & Rmdr neq 0.


% Sample goal:
%
% {log}=> primes(15,S).
% S = {2,3,5,7,11,13}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% start predicate
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start :- 
   nl &
   write('Generating the set of all the prime numbers smaller ') & nl &
   write('than a given integer N ') & nl & nl &
   write('Give the goal primes(N,S): ') & nl &
   write('S is the set of all the prime numbers smaller than N').

%:-start.