A possible way to tackle the twin prime conjecture

Assume that there are only a finite number m=2N of twin primes greater than 4 sorted in increasing order and let’s denote them j_{1}=5, j_{2}=7,\cdots, j_{m-1},j_{m}.

Let’s now formulate the following Prim conjecture:

There exists a primorial P greater than 2j_{m} such that both j_{m-1} and j_{m} are primality radii of P.

If true, this would entail that there are at least m+2 twin primes greater than 4 and not m. Hence the infiniteness of twin primes.

I postulate that P can be expressed as a function of m by solving the following equation:


This is just the very beginning of a sketch of proof which obviously needs further investigations.


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