Much faster solution

[arguiot]

Proposing an incredibly fast solution for checking if a number is prime or not.
Currently working fine until Number.MAX_SAFE_INTEGER.

This was inspired by the code I have written for https://github.com/arguiot/TheoremJS. I already told you about this in #1

[arguiot]

Simple comparisons:

• v2: all tests were done in 27s
• my version: all tests were done in 14ms

And it's not a probabilistic test.

[lukeed]

This is great, thank you~! I did see your original comment in #1 – I just wanted to mess around and implement AKS since I didn't see an implementation anywhere. PS, I know it's slow 😄

Is this a known algorithm / theorem? Or it a brute force method you've come up with?

I pushed a change to this PR with a refactored version. It's 50B smaller (gzip) and is actually significantly faster, too. It's the same logic, but you were checking against (and reassigning) the out value repeatedly & unnecessarily, as you totally could have aborted the loop early.

While the primes bench is a little bit slower, I'd personally much prefer to trade a 100k loss on rare occasion for 9-14M gain the majority of the time 🎉

Here are the benchmarks of your original PR against the refactor. I've also included Theorem, if that's okay! The number sets are taken from the tests.

# Primes
theorem  x  64,608 ops/sec ±4.40% (93 runs sampled)
before   x 932,150 ops/sec ±0.50% (94 runs sampled)
after    x 853,139 ops/sec ±0.28% (97 runs sampled)

# Not Primes
theorem  x    234,204 ops/sec ±0.24% (98 runs sampled)
before   x  4,391,996 ops/sec ±0.28% (97 runs sampled)
after    x 18,300,594 ops/sec ±0.26% (97 runs sampled)

# Carmichael Numbers
theorem  x    57,118 ops/sec ±0.30% (95 runs sampled)
before   x    73,004 ops/sec ±0.40% (93 runs sampled)
after    x 9,271,695 ops/sec ±0.53% (90 runs sampled)

[arguiot]

Great! TheoremJS should be slower as it uses the BigNumber API for all the computations.

It's an algorithm I came with, but it's based on Eratosthenes' sieve.

[lukeed]

Yeah, I saw that. Totally makes sense.

Thanks! The name was escaping me, I was thinking it began with an S___ 🙃

[lukeed]

Hey @arguiot, I switched approaches again~! If you check out the latest README, you can find benchmarks of the new approach.

[arguiot]

@lukeed great 👍. I saw that in arguiot.js you called me Arthur Goi, But my name is Arthur Guiot 🙃. Otherwise, I really like this method.

[lukeed]

Oh shoot, sorry! I was distracted. 🙈