The calculation of p_n and pi_n

A new approach is presented for the calculation of p_n and pi_n which uses the Lambert W function. An approximation is first found and using a calculation technique it makes it possible to have an estimate of these two quantities more precise than those known from Cipolla and Riemann. The calculation of p(n) uses an approximation using the Lambert W function and an estimate based on a logarithmic least square curve (LLS) c_n.