Solution to @TechSparx's special math challenge!

solve.pl

is_prime(X) :-
    findall(
    Y,
    (between(1,X,Y), divisible(X,Y)),
    F),
    (F=[1,X];F=[X,1]).

divisible(X,Y) :-
    0 is X rem Y.

% first 25 prime numbers.
test_is_prime() :-
    findall(X,(between(1,100,X),is_prime(X)),L),
    L=[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97].

/*
    let matrix =

    |A B|
    |C D|

    then,

    determinate = A*D-B*C
*/
determinant(A,B,C,D,Result) :-
    Result is A*D-B*C.

determinant_is_prime(A,B,C,D) :-
    determinant(A,B,C,D,Result),
    Result > 0,
    is_prime(Result).

/*
    Q:
        How many 2x2 matrices with all integer elements between 0 and 11 (inclusive) are there, such that the determinant is a (positive) prime number? Remember: 1 is not prime!
        See: https://twitter.com/TechSparx/status/1089448076308299776
    A:
        2019
*/

solution(Result, Count) :-
    findall(
        (A,B,C,D),
        (
            between(0,11,A),
            between(0,11,B),
            between(0,11,C),
            between(0,11,D),
            determinant_is_prime(A,B,C,D)
        ),
        Result
    ),
    length(Result,Count).