\(P({N}_{x})=\prod _{ i=1 }^{ { P }_{ N }<{ N }_{ x }<{ P }_{ N+1 } }{ \frac { { P }_{ i }-1 }{ { P }_{ i } } } \), when \({ P }_{ N }={ N }_{ x }\) the associated probability is 1.
as \({N}_{x}\) increases leaving out all prime numbers is a good indication of the distribution of numbers around the primes. The probability graph of \({N}_{x}\) seemed to have an asymptote at around \(P({N}_{x}\))=0.0412 for \({N}_{x}\) large.
This graph was generated from a list of primes up to and including 821641. The initial sharp drop down the y-axis is due to new discoveries of small primes that rule out many higher numbers as candidate for primes. The graph seem to have an asymptote, but is actually decreasing very slowly. There are simply not enough small numbers to go around, especially small prime numbers. This then is the distribution of primes.
