Is this a prime?

For every natural number $n$ , ${ 3 }^{ n-1 }$ is an odd number.

For every natural number $k$ , ${ 7 }^{ k-1 }$ is an odd number.

An odd number plus an odd number is always an even number.

There is only one even prime number: $2$ . $2$ as sum of two natural numbers can only be expressed by $1+1$ .

So ${ 3 }^{ n-1 }=1$ Thus: $n=1$ .

And ${ 7 }^{ k-1 }=1$ Thus: $k=1$ .

As you can see, there exists only one pair of $\left( n; k \right)$ : $\boxed { \left( 1;1 \right) }$