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This question already has an answer here:

Some mathematical patterns stay true for a set of integers $1..n$ only to break at $n+1$.

What are some nontrivial examples where $n$ is ``large''?

As an example $x^2+x+41$ is prime for $x=1..40$, but not at $41$.

I am particularly looking for examples other than prime producing polynomials. Especially examples suitable for an introductory class.

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marked as duplicate by Travis Willse, Matthew Towers, Robert Israel number-theory Nov 26 '18 at 14:26

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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It's not number theory, but I've always found the Borwein integrals to be fascinating.

https://en.wikipedia.org/wiki/Borwein_integral

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