primality.erl

-module(primality).
-export([primality/1]).

%% @doc test the primality number using the Sieve of Eratosthenes.
-spec(primality(number()) -> boolean()).
primality(Nmbr) ->
	List = lists:reverse(generate_integer_list(Nmbr, [Nmbr])),
	Enumerated = enumarate(lists:last(List), [lists:nth(1, List)]),
	Marked = lists:filter(fun(Elem) -> Elem =/= false end, Enumerated),

	Number = lists:member(Marked, Nmbr),
	Number.

%% @doc generate a list of integer betwenn 2 and Nmbr
-spec(generate_integer_list(number(), list()) -> list()).
generate_integer_list(Nmbr, List) ->
	Last = lists:last(List),
	Number = Nmbr-1,

	if
		Last > 2 -> generate_integer_list(Number, lists:append(List, [Number]));
		Last == 2 -> List
	end.

%% @doc generate a list of multiples of 2
-spec(enumarate(number(), list()) -> list()).
enumarate(Limit, List) ->
	Last = lists:last(List),

	Number = if
			Last =/= false; Last rem 2 == 0 -> false;
			Last =/= false; Last div 3 == 0 -> false;
			Last -> Last
	end,

	NotFalseList = lists:filter(fun(Elem) -> Elem =/= false end, List),
	NotFalse = lists:last(NotFalseList),

	erlang:display(NotFalse),
	erlang:display(Number),
	erlang:display(Last),
	
	if
		Last == false -> enumarate(Limit, lists:append(List, [NotFalse+2]));
		Last =< Limit -> enumarate(Limit, lists:append(List, [list_to_integer(Number)+1]));
		Last > Limit -> List
	end.