The Prime Number Theorem (PNT for short) says that the average gap between two consecutive primes of size is . Defining the quantity as , where is the -th typical primality radius of , one can expect to get closer to as increases for a given .
Let’s define the « gap-variance » of , denoted by , as follows:
where is the total number of typical primality radii of .
From the observation above, one can write
As, whenever is -central, one has , one gets for such :
Hence, , so that it’s very likely that the strong form of Cramer’s conjecture, namely , is true.