%Source: https://sites.google.com/site/prologsite/prolog-problems %query:goldbach_list(g,g). % 2.06 (*) A list of Goldbach compositions. % Given a range of integers by its lower and upper limit, % print a list of all even numbers and their Goldbach composition. % goldbach_list(A,B) :- print a list of the Goldbach composition % of all even numbers N in the range A <= N <= B % (integer,integer) (+,+) goldbach_list(A,B) :- goldbach_list(A,B,2). % goldbach_list(A,B,L) :- perform goldbach_list(A,B), but suppress % all output when the first prime number is less than the limit L. goldbach_list(A,B,L) :- A =< 4, !, g_list(4,B,L). goldbach_list(A,B,L) :- A1 is ((A+1) // 2) * 2, g_list(A1,B,L). g_list(A,B,_) :- A > B, !. g_list(A,B,L) :- goldbach(A,[P,Q]), A2 is A + 2, g_list(A2,B,L). goldbach(4,[2,2]) :- !. goldbach(N,L) :- N mod 2 =:= 0, N > 4, goldbach(N,L,3). goldbach(N,[P,Q],P) :- Q is N - P, is_prime(Q), !. goldbach(N,L,P) :- P < N, next_prime(P,P1), goldbach(N,L,P1). next_prime(P,P1) :- P1 is P + 2, is_prime(P1), !. next_prime(P,P1) :- P2 is P + 2, next_prime(P2,P1). is_prime(2). is_prime(3). is_prime(P) :- integer(P), P > 3, P mod 2 =\= 0, \+ has_factor(P,3). % Define integer for termination analysis. integer(_). % has_factor(N,L) :- N has an odd factor F >= L. % (integer, integer) (+,+) has_factor(N,L) :- N mod L =:= 0. has_factor(N,L) :- L * L < N, L2 is L + 2, has_factor(N,L2).
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