(49G) Prime Counting Programme

[Gerald H]

An APPROXIMATE solution to the prime count question is given by Locker-Ernst's formula

p(n) ≈ n / ( H(n) - 3 / 2 )

H(n) the nth harmonic number.

In the programme below the harmonic number function is replaced by the HP 49G function Psi(n) (FPTR 7 11E is the Psi function for long reals), as Psi(n+1)+gamma gives H(n).

Code:


::
  CK1&Dispatch
  BINT1
  ::
    %>%%
    DUP
    %%1+_
    FPTR 7 11E
    %% 9.22784335098467E-1
    %%-
    %%/
    %%>%
  ;
;