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+--- Forum: General Software Library (/forum-13.html)
+--- Thread: (49G) Prime Counting Programme (/thread-4465.html)
(49G) Prime Counting Programme - Gerald H - 08-02-2015 08:55 AM
For integer input the programme returns the number of prime numbers up to & including the input.
eg For input
5
the programme returns
3.
Maximum input is 1680, higher values produce an error.
Code:
::
CK1&Dispatch
BINT1
::
::
%ABS
COERCEDUP
BINT2
#<case
DROPZERO
DUP
BINT4
#<case
#1-
DUP
# 690
#>
caseSIZEERR
'
::
BINT1
#=casedrop
::
#1+
#2/
;
2DUP
#1-
2GETEVAL
ROT
1GETLAM
4PICK
NTHCOMPDROP
#/
SWAPDROP
ROT
#1-
2GETEVAL
#-
;
{
BINT2
BINT3
BINT5
BINT7
BINT11
BINT13
2REAL
BINT19
BINT23
BINT29
BINT31
BINT37
BINT41
}
FPTR2 ^2LAMBIND
DUP
UNCOERCE
%SQRT
%IP
COERCE
1GETLAM
SWAP'
#>
POSCOMP
#1-DUP
#1-UNROT
2GETEVAL
ABND
#+
;
UNCOERCE
;
;RE: HP 49G: Prime Counting Programme - Gerald H - 08-03-2015 03:22 PM
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
%%-
%%/
%%>%
;
;