What is a property that looks like it holds for all natural numbers but it turns out it doesn't?

Asked Mar 13 '21 at 13:05

Active Mar 13 '21 at 13:05

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I want to find a simple example of a property that looks like it holds for all $n \in \mathbb{N}$, but that does not. I remember reading about one that got in hold for centuries before someone found out a ridiculously big value of $n$ for which the property didn't hold, but I don't remember what the property was.

I'd like if the example property was easy to explain and didn't demand many concepts outside basic knowledge of the natural numbers.

Anything like that?

asked Mar 13 '21 at 13:05

karlabos

1,257

Well, a very basic one is that $n^2+n+41$ is prime, but you don't have to go far to disprove it. – Rushabh Mehta Mar 13 '21 at 13:08
Just read about this. For example purposes, n=40 is pretty big, so it works. thanks! – karlabos Mar 13 '21 at 13:17
I believe you mean $n=41$. – Rushabh Mehta Mar 13 '21 at 13:24

What is a property that looks like it holds for all natural numbers but it turns out it doesn't?

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