I tried to forward the following computation using a new function

that has characterists similar to Li(x).

pi(1,000,000) ~ 78,561.2

pi(2,000,000) ~ 148,937.8

pi(3,000,000) ~ 216,805.5

pi(4,000,000) ~ 283,142.1

and to top it off... the formula isn't hokey looking.

N = x

Q = N - N/ln(N)

R = ln(Q)

S = R/3

T = sqrt(N)/R

pi(x) = N/R + N/(R^2) + N/(R^3)+... N/(R^S) + T

Interesting? Bill