Is This Prime

There was an interesting conversation I found on the CodeVision Discord server

Now we have this number, but it’s obviously huge, so we don’t want to calculate all those digits out to determine if it is prime or not. However, it is worth noting that

where $n$ is an integer greater than or equal to $2$. Note the following sequence

$2$ raised to any multiple of $4$ (besides $0$, obviously) results in an integer with a $6$ as the one’s digit. This can be proved with some simple counting… but I’ll leave that up to the reader to do that for themselves.

But why is this important? Well, we can then say

Therefore, $2^{2^{77,232,917}} - 1$ is not prime.