Calculating the largest known prime in Ruby

Looking to impress your Ruby friends by calculating the largest known prime, 2 ** 136_279_841-1?

On Ruby 3.4.0-preview2 and earlier, 2 ** 136_279_841-1 logs a warning and returns Infinity 😔:

2 ** 136_279_841-1
# warning: in a**b, b may be too big
# => Infinity

Thanks to @mametter, Ruby 3.4 will handle this calculation just fine! See Do not round a**b to infinity.

Knowing this, you excitedly use your ruby manager of choice to pull down ruby master:

rvm install ruby-head

You run ruby -e "puts 2 ** 136_279_841-1", and your excitement is slowly eroded. An hour into calculating, you terminate the command in frustration 😫.

Is @mametter a liar?!

As it turns out, there is critically important library you need for accelerating “Bignum” calculations: GMP, the GNU Multiple Precision Arithmetic Library. It’s even specifically mentioned in the CRuby guide to building ruby.

Without it, you can kiss your largest prime calculating dreams goodbye 👋.

You reinstall ruby head, making sure gmp is available

brew install gmp
rvm reinstall ruby-head --with-gmp-dir=$(brew --prefix gmp)

With a bit of hope in your heart, you try again:

ruby -e "puts 2 ** 136_279_841-1"

Success! @mametter was telling the truth!

Within around 5 seconds, your terminal is filled with a beautiful output of 41,024,320 digits. Your Ruby friends cheer and carry you off on their shoulders.

This was all inspired by Matz’s keynote at RubyConf 2024 - where he mentioned that Ruby 3.4 can now calculate the largest known prime. For fun, I tried it on my mac and just let it keep running - 2 hours later, it was still running! I’d never heard of GMP, but now I know!