Thanks for the article.

"it may make more sense to call it a disproof by counterexample".

Actually no, it is a counter example, not a disproof. With a counter example, I can always say that the conjecture is valid, except for N counter examples.

One thing is to provide a counterexample, one thing is to provide a full proof that the conjecture is not valid (Eg provide a way to create a non finite sequence of counter-examples).

I know, this reasoning doesn't seem fair. But actually evolving better this naively exposed concept, we can end up in the "almost everywhere" concept: https://en.wikipedia.org/wiki/Almost_everywhere

or https://en.wikipedia.org/wiki/Almost_surely

In a very few words: some properties can be true excluding a set that is "irrelevant" to the domain set of the conjecture.

In the original example, to disproof the conjecture formally, you need to provide a logic to create a non finite sequence of counterexamples. Or at least I suppose so... I am assuming that a finite set of counterexamples is a measure 0 subset of Natural numbers. But I cannot prove it.