Meissel–Mertens constant: Difference between revisions

=={{header|Delphi}}==

{{works with|Delphi|6.0}}

{{libheader|SysUtils,StdCtrls}}

This program doesn't test the limits of numbers in Delphi. The limit is the processing time. The time to process 10^7 is 3 minutes. The time to process 10^8 is nearly two hours. As a result, process beyond 10^8 is pretty much impossible and a different strategy would be required

<syntaxhighlight lang="Delphi">

function IsPrime(N: int64): boolean;

{Fast, optimised prime test}

var I,Stop: int64;

begin

if (N = 2) or (N=3) then Result:=true

else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false

else

begin

I:=5;

Stop:=Trunc(sqrt(N+0.0));

Result:=False;

while I<=Stop do

begin

if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;

Inc(I,6);

end;

Result:=True;

end;

end;

function GetNextPrime(var Start: integer): integer;

{Get the next prime number after Start}

{Start is passed by "reference," so the

{original variable is incremented}

begin

repeat Inc(Start)

until IsPrime(Start);

Result:=Start;

end;

function MeisselMertens(Depth: integer; Prog: TProgress): extended;

{Calculate MM value up a certain Depth}

var I,P: integer;

const Euler = 0.57721566490153286;

begin

Result:=0;

P:=1;

for I:=1 to Depth do

begin

P:=GetNextPrime(P);

Result:=Result+Ln(1-(1/P)) + (1/P);

if Assigned(Prog) and ((I mod 10000)=0) then

HandleProgress(MulDiv(100,I,Depth));

end;

Result:=Result+Euler;

end;

procedure ShowMeisselMertens(Memo: TMemo; Prog: TProgress);

var I,IT,Digits: integer;

var M,Last: extended;

begin

Memo.Lines.Add('Primes Digits M');

Memo.Lines.Add('-----------------------------------------');

Last:=0;

IT:=1;

{Calculate MM to specified Power of 10}

for I:=1 to 8 do

begin

IT:=IT*10;

M:=MeisselMertens(IT,Prog);

{Calculated Digits of accuracy}

Digits:=Trunc(abs(Log(abs(M-Last))));

Memo.Lines.Add(Format('10^%2d %7d %25.18f',[I,Digits,M]));

Last:=M

end;

end;

</syntaxhighlight>

{{out}}

<pre>

Primes Digits M

-----------------------------------------

10^ 1 0 0.265160104017311294

10^ 2 2 0.261624626172936147

10^ 3 3 0.261503563616850571

10^ 4 5 0.261497594498432488

10^ 5 6 0.261497238454297260

10^ 6 7 0.261497214692305277

10^ 7 8 0.261497212987251183

10^ 8 9 0.261497212858582276

</pre>