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I was asked to find all the prime numbers in these forms and prove that these are the only prime numbers in these forms. From some basic research on the internet, I suspect it may have been a trick question and that it is conjectured that they are infinite primes in this form.

I am aware there is a unique prime in the form $n^2-1$, $n^3-1$, using the $(n-1)$ factorisation.

Please would you help.

EDIT: this is meant to be a generalisation for any positive integers, n and m.

John Smith
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there is an infinite number of primes of the form $n^1 + 1$

if there was a finite set in the form $n^1 + 1$, then multiplying them all together and adding $1$ would also be of the form $n^1 + 1$ for some new n, and it would be a new prime number, not in the original set - so it could never be true

InsideOut
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Cato
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    The intent is certainly that $m$ is an integer greater than $1$. That OP does not make it explicit is maybe worth a comment, yet not giving an answer based on a loophole. – quid Oct 04 '16 at 12:06
  • @quid - well it's true that I didn't provide an answer to a question if additional info is added by someone else later - the edit to the question seemed to clarify your point though – Cato Dec 29 '16 at 11:24