a is a positive integer>1

Let k=a^(a+1)+(a+1)^a

Examples :

k=2^3+3^2=8+9=17 is prime

k=3^4+4^3=145 is composite

If a>2 k is it always composite ?

If yes can we prove it?

Thank you for any comment.

## Always composite?

- Lord_Farin
**Posts:**239**Joined:**Wed Jul 01, 2009 10:43 am**Location:**Netherlands

### Re: Always composite?

k = 80, 342 and 848 yield primes (at least, that's what Mathematica says).

### Re: Always composite?

Thank you very much.Lord_Farin wrote:k = 80, 342 and 848 yield primes (at least, that's what Mathematica says).

You helped me to find the list in Sloane

https://oeis.org/search?q=2%2C80%2C342% ... &go=Search

A073499 as a simple table:

n a(n)

1 1

2 2

3 80

4 342

5 848

6 1194

7 2658

8 4790

9 9376

What is strange is that all are even.

Is that means that if k is odd then there will be no prime of such form?

Thank you.

There is maybe some secret to discover here