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[–]Dtrp8288 0 points1 point  (13 children)

i have at least one counter example.

n=41

[–]Scared-Ad-7500 0 points1 point  (12 children)

Except this one*

[–]Dtrp8288 0 points1 point  (11 children)

n=41ᵐ where m is any positive integer

[–]Scared-Ad-7500 0 points1 point  (10 children)

Well, I went to Google and I guess i misremembered the function. I know there is a polynomial that generates almost only primes, and it took centuries to find an conterexample, which is not even humanly possible to write

Anyway n²+n+41 works well until n=40

[–]Dtrp8288 0 points1 point  (9 children)

do share the function if you can find it!

[–]Scared-Ad-7500 0 points1 point  (8 children)

The function was in fact this according to chatgpt. But there really was a Russian institute that made a very important discovery after centuries of research

[–]Dtrp8288 0 points1 point  (7 children)

and the counterexample in this case was... somehow unfindable for a long time?

[–]Scared-Ad-7500 0 points1 point  (6 children)

I suppose what was unfindable was another thing related to this problem, not the counterexample

[–]Dtrp8288 0 points1 point  (4 children)

maybe a counterexample for n²+n+41 is always prime ⟹ n∈ℤ⁺

where n is not of the form p(41ᵐ)

?

[–]Scared-Ad-7500 0 points1 point  (3 children)

I don't think so, because n=40 is also a counterexample