# 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:

$\pi(\sqrt{2P-3})=\pi(j_{m})$.

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

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