-module(problem3).
-export([solve/0]).
-include_lib("eunit/include/eunit.hrl").

primes(N) when N == 1 ->
    [1];
primes(N) ->
    primes(N, [], 2).

primes(1, Primes, _) -> Primes;
primes(N, Primes, Try) when N rem Try == 0 ->
    primes(N div Try, [Try | Primes], Try);
primes(N, Primes, Try) ->
    primes(N, Primes, Try + 1).

solve() ->
    lists:max(primes(600851475143)).

primes_test_() ->
    [
     ?_assertMatch([1], primes(1)),
     ?_assertMatch([3,2], primes(6)),
     ?_assertMatch([13], primes(13)),
     ?_assertMatch([13,5,3],primes(195))
    ].

solve_test_() ->
    [
     ?_assertMatch(6857,solve())
    ].