Primes of form n^p+1

[hv at crypt.org]

"Pfoertner, Hugo" <Hugo.Pfoertner at muc.mtu.de> wrote:
:<http://mathworld.wolfram.com/Power.html>  says:
:Very few numbers of the form n^p+-1 are prime. 
:... [snip primes of form n^p-1] ...
:The only prime numbers of the form n^p+1 for n<=100 and prime 2<=p<=10
:correspond to p=2 with n = 1, 2, 4, 6, 10, 14, 16, 20, 24, 26, ...
:http://www.research.att.com/projects/OEIS?Anum=A005574
:<http://www.research.att.com/projects/OEIS?Anum=A005574>  
:
:I extended the search to even n<=10000 and prime p<=2099 using PFGW and
:didn't find any further primes of this form. Are there _any_ known other
:examples?

No: n^(2m+1) is divisible by (n+1); n^(2m-1) is divisible by (n-1).
So for n^p +/- 1 we can only have Mersenne primes (2^p - 1) and
n^2 + 1.

Hugo van der Sanden