If we know the index [n] of given Prime Number P[n] in the set of Prime numbers, then P[n] + 1 is the number of all positive integers in the set with n Prime numbers.

It implies that ratio [tex]n/(P[n] + 1)[/tex] gives the part (in percentage) of Prime numbers in this set.

Function [tex]f(n, P) = n/(P[n] + 1)[/tex]\infty, where n = 1,2,3,...\rightarrow\infty and P[n] the Prime Number, converges to 0.05……

Example:

n = 4, P[4] = 7 \Rightarrow0.5

n = 46, P[46] = 199 \Rightarrow 0.23

n = 1053, P[1053] = 8423 \Rightarrow 0.125

n = 21944, P[21944] = 248779 \Rightarrow 0.088206447

n = 41191865, P[41191865] = 800934961 \Rightarrow 0.051429725

n = 50409172, P[50409172] = 990919439 \Rightarrow 0.05087111

n = 50848100, P[50848100] = 1000011601 \Rightarrow 0.05084751

Looks like around 5% of positive integers are Prime Numbers!?