# Beispiel Primes

Jan Burse, erstellt 15. Sep 2018
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* Prolog code for the arithmetic and list example.
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/**
* Generate a list of integers between Low and High.
*/
integers(Low, High, [Low|Rest]) :-
Low =< High, !,
M is Low+1,
integers(M, High, Rest).
integers(_, _, []).
/**
* Remove all multiples of the given prime from a list.
*/
remove([], _, []).
remove([I|Is], P, Nis) :-
I rem P =:= 0, !,
remove(Is, P, Nis).
remove([I|Is], P, [I|Nis]) :-
remove(Is, P, Nis).
/**
* Detect primes and remove multiples.
*/
sift([I|Is], High, [I|Is]) :-
I*I > High, !.
sift([I|Is], High, [I|Ps]) :-
remove(Is, I, New),
sift(New, High, Ps).
/**
* First create the numbers and then sift.
*/
primes(High, R) :-
integers(2, High, L),
sift(L, High, R).