primes(Limit, Ps) :- integers(2, Limit, Is), sift(Is, Ps).

integers(Low, High, [Low | Rest]) :-
   Low =< High, 
   M is Low + 1, 
   integers(M, High, Rest).

integers(Low, High, []) :-
   Low > High.

sift([], []).

sift([I | Is], [I | Ps]) :- 
   remove(I, Is, New), 
   sift(New, Ps).

remove(P, [], []).

remove(P, [I | Is], [I | Nis]) :-
   \+ (0 is I mod P),
   remove(P, Is, Nis).

remove(P, [I | Is], Nis) :-
   0 is I mod P,
   remove(P, Is, Nis).