Touting my own horn a bit, I have a constructive* proof [0] of the infinitude of prime numbers from first principles: there is no dependence on mathlib so I build all the concepts from scratch. I have been thinking about turning it into a literate code document.
*The only axiom I cannot avoid is propositional extensionality (which is kind of unavoidable in any non-toy proof in Lean).
*The only axiom I cannot avoid is propositional extensionality (which is kind of unavoidable in any non-toy proof in Lean).
[0] https://github.com/ykonstant1/InfinitePrimes