%query: prime(i). /* from Giesl, Thiemann, Schneider-Kamp, Falke, 2004 */ div(X,Y,Z) :- quot(X,Y,Y,Z). quot(0,s(Y),s(Z),0). quot(s(X),s(Y),Z,U) :- quot(X,Y,Z,U). quot(X,0,s(Z),s(U)) :- quot(X,s(Z),s(Z),U). prime(s(s(X))) :- pr(s(s(X)),s(X)). pr(X,s(0)). pr(X,s(s(Y))) :- not_divides(s(s(Y)),X), pr(X,s(Y)). not_divides(Y,X) :- div(X,Y,U), times(U,Y,Z), neq(X, Z). neq(s(X),0). neq(0,s(X)). neq(s(X),s(Y)) :- neq(X,Y). times(0,Y,0). times(s(X),Y,Z) :- times(X,Y,U), add(U,Y,Z). add(X,0,X). add(0,X,X). add(s(X),Y,s(Z)) :- add(X,Y,Z). %generate(0,0). %generate(X,s(Y)) :- X >= 0, Z is X-1, generate(Z,Y). %primenumber(X) :- generate(X,Y), prime(Y).
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