Consider again,
\({\prod _{ 1 }^{ { N }_{ x }}{ (\frac { 1 }{ 2 } )(\frac { 2 }{ 3 } )(\frac { 4 }{ 5 } )(\frac { 6 }{ 7 } )...\frac{{P}_{N}-1}{{P}_{N}}}}\)
This term can be evaluated for all \({N}_{x}\) but the summation of its product with \({N}_{x}\) is not. It is possible to evaluate \(E[{N}_{x}]\) for a bounded set but not for all primes. The proof that there are infinite numbers of primes suggests that the tail of the Probability \({N}_{x}\)of being Prime graph is never zero. And as \({N}_{x}\) tends towards infinity, the term
\(\frac{{N}_{x}-1}{{N}_{x}}=1-\frac{1}{{N}_{x}}\) is divergent with respect to \(\int { (1-\frac { 1 }{ { N }_{ x } } ) } d{ N }_{ x }\).
