Prime Testing

Note that $x^n+1 = (x+1)(x^{n-1}-x^{n-2}+x^{n-3}-...-x+1)$ for odd positive integer $n$ , and hence $x^n+1$ is divisible by $x+1$ . Now $6182^{2816}+1$ $=6182^{256 \times 11}+1$ $=(6182^{256})^{11}+1$ Let $x=6182^{256}$ , we can see that the above expression is equal to $x^{11}+1$ which is divisible by $x+1=6182^{256}+1$ . Hence $6182^{2816}+1$ is not a prime.

The fact that the number is in the form of $A^b$ with $b >1$ means $A$ is a factor which is not equal to $A^b$ which means the number $A^b$ is not prime