What is the bottleneck in this primes related predicate?

Question

So here it is : I'm trying to calculate the sum of all primes below two millions (for this problem), but my program is very slow. I do know that the algorithm in itself is terribly bad and a brute force one, but it seems way slower than it should to me.
Here I limit the search to 20,000 so that the result isn't waited too long.
I don't think that this predicate is difficult to understand but I'll explain it anyway : I calculate the list of all the primes below 20,000 and then sum them. The sum part is fine, the primes part is really slow.

problem_010(R) :-
    p010(3, [], Primes),
    sumlist([2|Primes], R).
p010(20001, Primes, Primes) :- !.
p010(Current, Primes, Result) :-
    (
        prime(Current, Primes)
    ->  append([Primes, [Current]], NewPrimes)
    ;   NewPrimes = Primes
    ),
    NewCurrent is Current + 2,
    p010(NewCurrent, NewPrimes, Result).
prime(_, []) :- !.
prime(N, [Prime|_Primes]) :- 0 is N mod Prime, !, fail.
prime(ToTest, [_|Primes]) :- prime(ToTest, Primes).

I'd like some insight about why it is so slow. Is it a good implementation of the stupid brute force algorithm, or is there some reason that makes Prolog fall?

EDIT : I already found something, by appending new primes instead of letting them in the head of the list, I have primes that occur more often at start so it's ~3 times faster. Still need some insight though :)

Answer 1

First, Prolog does not fail here.

There are very smart ways how to generate prime numbers. But as a cheap start simply accumulate the primes in reversed order! (7.9s -> 2.6s) In this manner the smaller ones are tested sooner. Then, consider to test only against primes up to 141. Larger primes cannot be a factor.

Then, instead of stepping only through numbers not divisible by 2, you might add 3, 5, 7.

There are people writing papers on this "problem". See, for example this paper, although it's a bit of a sophistic discussion what the "genuine" algorithm actually was, 22 centuries ago when the latest release of the abacus was celebrated as Salamis tablets.