Assume that there are only a finite number of twin primes greater than sorted in increasing order and let’s denote them .
Let’s now formulate the following Prim conjecture:
There exists a primorial greater than such that both and are primality radii of .
If true, this would entail that there are at least twin primes greater than and not . Hence the infiniteness of twin primes.
I postulate that can be expressed as a function of by solving the following equation:
This is just the very beginning of a sketch of proof which obviously needs further investigations.