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.