- I've started looking at at n^a + (n+1)^b, where a,b <= n+1 .
It generates a reasonable number of primes. I'll be examining for any
patterns in prime generation and will let you know of any earth
But one thing right off that bat which I find somewhat intriguing is
this special case:
n^n + (n+1)^(n+1)
1^1 + 2^2 = 5 (prime)
2^2 + 3^3 = 31 (prime)
3^3 + 4^4 = 283 (prime)
Seems like it could produce a good amount of primes at this rate. But
in what appears to be an odds defying feat, no more primes turn up
for any n up to 500. Perhaps there are no more, for *some* reason.
- --- In firstname.lastname@example.org,
"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.