Re: [PrimeNumbers] n^n+ (n+1)^(n+1)
- Hi, Mark,
An interesting expression.
Let np ( n ) = n^n + (n+1)^(n+1) .
I confirm that n = 1, 2, and 3 are the only known primes of this form.
If n mod 6 = 4,
then 3 and ( n^2 + n + 1 ) / 3 (twice) are divisors.
If n = 415 , then np ( n ) has only 2 prime factors
and one of them is 29 .
You might want to look at posts on this subject to NMBRTHRY, e.g.,
Also, you might want to try to fill in the gap left by the reply of
Ismael Jimenez Calvo in explaining the production of the interesting
There are some sequences in the On-line Encyclopedia. E.g.,
- --- In email@example.com,
"djbroadhurst" <d.broadhurst@> wrote:
> primes p inThis is now a conjecture-free OEIS sequence:
> for which (x+1)^p-x^p-1 and x^x+(x+1)^(x+1)
> are never simultaneously divisible by p^2.