gistfile1.txt

% computes the prime factorization of N
primeFactorization(N, P) :-
    primeFactorization_prime(N, [N], [], Q),
    P = Q.
primeFactorization_prime(_N, [], P, Q) :-
    Q = P.
primeFactorization_prime(N, [FH |FT], P, Q) :-
    factorization(FH, F_factors),
    pfp_helper([FH|FT], F_factors, N, P, P_prime, F_prime),
    primeFactorization_prime(N, F_prime, P_prime, Q).

% prime factor case
pfp_helper([F_head | F_tail], [], N, P, P_prime, _) :-
    F_head   \= N,     % or else we end up putting N in P if N is prime
    append([F_head], P, P_prime),
    F_prime = F_tail.
pfp_helper([_ | F_tail], F_factors, _N, P, P_prime, F_prime) :-
    F_factors = [_ | _],
    append(F_factors, F_tail, F_prime),
    P_prime = P.