Data commit

Task/Meissel-Mertens-constant/Delphi/meissel-mertens-constant.delphi

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+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 7 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;