All integers can be represented as:
Now, first we try to find the statements for which this is seemingly prime:
It's immediately clear that this is divisible by 6.
This has no immediate factors, MAY be prime.
It is immediately clear that it is divisible by two.
It is immediately clear that it is divisible by three.
Immediately clear that it is divisible by two.
It has no immediate factors. MAY be prime.
The only candidates for primacy are:
Therefore, all integers that are candidates for primacy are:
Since it has already been proven that there are infinitely many primes, then there are also infinitely many primes represented by each:
Thus, there are infinitely many primes represented by
I know it may not be as good as you need. But you can use it to build your own proof if you would like.