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name-the-biggest-number

The point of this repository is to allow people to submit contenders for the title of biggest number.

The idea of this competition is described by Scott Aaronson here, but generally this is a pretty active area of recreational mathematics and a lot of resources can be found hereabouts.

This repository adds 2 rather large caveats to the process:

  1. The numbers described must be constructive: no Busy Beavers or similar shenanigans! All numbers named must be computable in principle (more on this later).

  2. The numbers submitted must be formally described in the Coq specification system, along with a formal proof that they are larger than the current contender for largest number.

A few base rules:

  • The definition of the number must take no more than 15 seconds to type-check using coqc on a "reasonable" machine.

  • The proof that the number is larger than the current contender should take no more than 1 minute to typecheck, though I might update this as events warrant.

  • No axioms! Libraries may be included if needed, but please try to stick to widely used ones.

  • Submissions are made by making a PR that adds to the file Contender.v, according to the format outlined by that file (your number should be a definition named contender_N, and the proof of soundness contender_(N-1)_lt_contender_N.

  • Hope this doesn't really need to be said, but don't use contender_N as a definition when defining contender_N+1, it's just lazy. Try to defeat the previous contender by a large margin, if you can.

  • No shenanigans! Though I might have an honorable mention category if you can really fool me.

  • Currently the definition and proof should build with Coq version 8.10.2 (thanks to Jakob for "encouraging" this change), but I'll update this on request.