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229
Task/Giuga-numbers/Free-Pascal/giuga-numbers-1.pas
Normal file
229
Task/Giuga-numbers/Free-Pascal/giuga-numbers-1.pas
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program Giuga;
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{$IFDEF FPC}
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{$MODE DELPHI} {$OPTIMIZATION ON,ALL} {$COPERATORS ON}
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{$ELSE}
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{$APPTYPE CONSOLE}
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{$ENDIF}
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uses
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sysutils
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{$IFDEF WINDOWS},Windows{$ENDIF}
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;
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//######################################################################
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//prime decomposition only squarefree and multiple of 6
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type
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tprimeFac = packed record
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pfpotPrimIdx : array[0..9] of Uint64;
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pfMaxIdx : Uint32;
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end;
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tpPrimeFac = ^tprimeFac;
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tPrimes = array[0..65535] of Uint32;
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var
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{$ALIGN 8}
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SmallPrimes: tPrimes;
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{$ALIGN 32}
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procedure InitSmallPrimes;
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//get primes. #0..65535.Sieving only odd numbers
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const
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MAXLIMIT = (821641-1) shr 1;
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var
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pr : array[0..MAXLIMIT] of byte;
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p,j,d,flipflop :NativeUInt;
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Begin
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SmallPrimes[0] := 2;
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fillchar(pr[0],SizeOf(pr),#0);
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p := 0;
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repeat
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repeat
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p +=1
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until pr[p]= 0;
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j := (p+1)*p*2;
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if j>MAXLIMIT then
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BREAK;
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d := 2*p+1;
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repeat
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pr[j] := 1;
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j += d;
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until j>MAXLIMIT;
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until false;
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SmallPrimes[1] := 3;
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SmallPrimes[2] := 5;
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j := 3;
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d := 7;
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flipflop := (2+1)-1;//7+2*2,11+2*1,13,17,19,23
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p := 3;
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repeat
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if pr[p] = 0 then
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begin
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SmallPrimes[j] := d;
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inc(j);
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end;
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d += 2*flipflop;
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p+=flipflop;
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flipflop := 3-flipflop;
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until (p > MAXLIMIT) OR (j>High(SmallPrimes));
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end;
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function OutPots(pD:tpPrimeFac;n:NativeInt):Ansistring;
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var
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s: String[31];
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chk,p: NativeInt;
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Begin
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str(n,s);
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result := s+' :';
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with pd^ do
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begin
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chk := 1;
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For n := 0 to pfMaxIdx-1 do
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Begin
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if n>0 then
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result += '*';
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p := pfpotPrimIdx[n];
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chk *= p;
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str(p,s);
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result += s;
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end;
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str(chk,s);
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result += '_chk_'+s+'<';
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end;
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end;
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function IsSquarefreeDecomp6(var res:tPrimeFac;n:Uint64):boolean;inline;
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//factorize only not prime/semiprime and squarefree n= n div 6
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var
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pr,i,q,idx :NativeUInt;
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Begin
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with res do
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Begin
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Idx := 2;
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q := n DIV 5;
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if n = 5*q then
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Begin
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pfpotPrimIdx[2] := 5;
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n := q;
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q := q div 5;
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if q*5=n then
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EXIT(false);
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inc(Idx);
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end;
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q := n DIV 7;
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if n = 7*q then
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Begin
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pfpotPrimIdx[Idx] := 7;
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n := q;
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q := q div 7;
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if q*7=n then
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EXIT(false);
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inc(Idx);
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end;
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q := n DIV 11;
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if n = 11*q then
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Begin
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pfpotPrimIdx[Idx] := 11;
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n := q;
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q := q div 11;
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if q*11=n then
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EXIT(false);
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inc(Idx);
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end;
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if Idx < 3 then
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Exit(false);
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i := 5;
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while i < High(SmallPrimes) do
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begin
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pr := SmallPrimes[i];
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q := n DIV pr;
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//if n < pr*pr
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if pr > q then
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BREAK;
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if n = pr*q then
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Begin
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pfpotPrimIdx[Idx] := pr;
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n := q;
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q := n div pr;
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if pr*q = n then
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EXIT(false);
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inc(Idx);
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end;
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inc(i);
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end;
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if n <> 1 then
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begin
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pfpotPrimIdx[Idx] := n;
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inc(Idx);
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end;
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pfMaxIdx := idx;
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end;
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exit(true);
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end;
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function ChkGiuga(n:Uint64;pPrimeDecomp :tpPrimeFac):boolean;inline;
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var
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p : Uint64;
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idx: NativeInt;
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begin
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with pPrimeDecomp^ do
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Begin
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idx := pfMaxIdx-1;
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repeat
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p := pfpotPrimIdx[idx];
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result := (((n DIV p)-1)MOD p) = 0;
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if not(result) then
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EXIT;
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dec(idx);
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until idx<0;
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end;
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end;
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const
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LMT = 24423128562;//2214408306;//
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var
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PrimeDecomp :tPrimeFac;
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T0:Int64;
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n,n6 : UInt64;
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cnt:Uint32;
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Begin
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InitSmallPrimes;
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T0 := GetTickCount64;
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with PrimeDecomp do
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begin
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pfpotPrimIdx[0]:= 2;
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pfpotPrimIdx[1]:= 3;
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end;
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n := 0;
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n6 := 0;
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cnt := 0;
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repeat
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//only multibles of 6
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inc(n,6);
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inc(n6);
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//no square factor of 2
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if n AND 3 = 0 then
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continue;
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//no square factor of 3
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if n MOD 9 = 0 then
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continue;
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if IsSquarefreeDecomp6(PrimeDecomp,n6)then
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if ChkGiuga(n,@PrimeDecomp) then
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begin
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inc(cnt);
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writeln(cnt:3,'..',OutPots(@PrimeDecomp,n),' ',(GettickCount64-T0)/1000:6:3,' s');
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end;
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until n >= LMT;
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T0 := GetTickCount64-T0;
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writeln('Found ',cnt);
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writeln('Tested til ',n,' runtime ',T0/1000:0:3,' s');
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writeln;
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writeln(OutPots(@PrimeDecomp,n));
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end.
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198
Task/Giuga-numbers/Free-Pascal/giuga-numbers-2.pas
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198
Task/Giuga-numbers/Free-Pascal/giuga-numbers-2.pas
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@ -0,0 +1,198 @@
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program Giuga;
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{
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30 = 2 * 3 * 5.
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858 = 2 * 3 * 11 * 13.
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1722 = 2 * 3 * 7 * 41.
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66198 = 2 * 3 * 11 * 17 * 59.
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2214408306 = 2 * 3 * 11 * 23 * 31 * 47057.
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24423128562 = 2 * 3 * 7 * 43 * 3041 * 4447.
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432749205173838 = 2 * 3 * 7 * 59 * 163 * 1381 * 775807.
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14737133470010574 = 2 * 3 * 7 * 71 * 103 * 67213 * 713863.
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550843391309130318 = 2 * 3 * 7 * 71 * 103 * 61559 * 29133437.
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244197000982499715087866346 = 2 * 3 * 11 * 23 * 31 * 47137 * 28282147 * 3892535183.
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554079914617070801288578559178 = 2 * 3 * 11 * 23 * 31 * 47059 * 2259696349 * 110725121051.
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1910667181420507984555759916338506 = 2 * 3 * 7 * 43 * 1831 * 138683 * 2861051 * 1456230512169437. }
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{$IFDEF FPC}
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{$MODE DELPHI} {$OPTIMIZATION ON,ALL} {$COPERATORS ON}
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{$ELSE}
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{$APPTYPE CONSOLE}
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{$ENDIF}
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uses
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sysutils
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{$IFDEF WINDOWS},Windows{$ENDIF}
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;
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const
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LMT =14737133470010574;// 432749205173838;//24423128562;//2214408306;
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type
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tFac = packed record
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fMul :Uint64;
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fPrime,
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fPrimIdx,
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fprimMaxIdx,dummy :Uint32;
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dummy2: Uint64;
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end;
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tFacs = array[0..15] of tFac;
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tPrimes = array[0..62157] of Uint32;//775807 see factor of 432749205173838
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// tPrimes = array[0..4875{14379}] of Uint32;//sqrt 24423128562
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// tPrimes = array[0..1807414] of Uint32;//29133437
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// tPrimes = array[0..50847533] of Uint32;// 1e9
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// tPrimes = array[0..5761454] of Uint32;//1e8
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var
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SmallPrimes: tPrimes;
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T0 : Int64;
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cnt:Uint32;
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procedure InitSmallPrimes;
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//get primes. #0..65535.Sieving only odd numbers
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const
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//MAXLIMIT = (trunc(sqrt(LMT)+1)-1) shr 1+4;
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MAXLIMIT = 775807 DIV 2+1;//(trunc(sqrt(LMT)+1)-1) shr 1+4;
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var
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pr : array of byte;
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pPr :pByte;
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p,j,d,flipflop :NativeUInt;
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Begin
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SmallPrimes[0] := 2;
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setlength(pr,MAXLIMIT);
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pPr := @pr[0];
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p := 0;
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repeat
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repeat
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p +=1
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until pPr[p]= 0;
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j := (p+1)*p*2;
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if j>MAXLIMIT then
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BREAK;
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d := 2*p+1;
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repeat
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pPr[j] := 1;
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j += d;
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until j>MAXLIMIT;
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until false;
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SmallPrimes[1] := 3;
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SmallPrimes[2] := 5;
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j := 3;
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d := 7;
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flipflop := (2+1)-1;//7+2*2,11+2*1,13,17,19,23
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p := 3;
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repeat
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if pPr[p] = 0 then
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begin
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SmallPrimes[j] := d;
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inc(j);
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end;
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d += 2*flipflop;
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p+=flipflop;
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flipflop := 3-flipflop;
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until (p > MAXLIMIT) OR (j>High(SmallPrimes));
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setlength(pr,0);
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end;
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procedure OutFac(var F:tFacs;maxIdx:Uint32);
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var
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i : integer;
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begin
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write(cnt:3,' ');
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For i := 0 to maxIdx do
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write(F[i].fPrime,'*');
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write(#8,' = ',F[maxIdx].fMul);
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writeln(' ',(GetTickCount64-T0)/1000:10:3,' s');
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//readln;
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end;
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function ChkGiuga(var F:tFacs;MaxIdx:Uint32):boolean;inline;
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var
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n : Uint64;
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idx: NativeInt;
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p : Uint32;
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begin
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n := F[MaxIdx].fMul;
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idx := MaxIdx;
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repeat
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p := F[idx].fPrime;
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result := (((n DIV p)-1)MOD p) = 0;
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if not(result) then
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EXIT;
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dec(idx);
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until idx<0;
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inc(cnt);
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end;
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procedure InsertNextPrimeFac(var F:tFacs;idx:Uint32);
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var
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Mul : Uint64;
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i,p : uint32;
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begin
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with F[idx-1] do
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begin
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Mul := fMul;
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i := fPrimIdx;
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end;
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while i<High(SmallPrimes) do
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begin
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inc(i);
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with F[idx] do
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begin
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if i >fprimMaxIdx then
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BREAK;
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p := SmallPrimes[i];
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if p*Mul>LMT then
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BREAK;
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fMul := p*Mul;
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fPrime := p;
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fPrimIdx := i;
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IF (Mul-1) MOD p = 0 then
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IF ChkGiuga(F,idx) then
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OutFac(F,idx);
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end;
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// max 6 factors //for lmt 24e9 need 7 factors
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if idx <5 then
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InsertNextPrimeFac(F,idx+1);
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end;
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end;
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var
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{$ALIGN 32}
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Facs : tFacs;
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i : integer;
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Begin
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InitSmallPrimes;
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T0 := GetTickCount64;
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with Facs[0] do
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begin
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fMul := 2;fPrime := 2;fPrimIdx:= 0;
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end;
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with Facs[1] do
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begin
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fMul := 2*3;fPrime := 3;fPrimIdx:= 1;
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end;
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i := 2;
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//search the indices of mx found factor
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while SmallPrimes[i] < 11 do inc(i); Facs[2].fprimMaxIdx := i;
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while SmallPrimes[i] < 71 do inc(i); Facs[3].fprimMaxIdx := i;
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while SmallPrimes[i] < 3041 do inc(i); Facs[4].fprimMaxIdx := i;
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while SmallPrimes[i] < 67213 do inc(i); Facs[5].fprimMaxIdx := i;
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while SmallPrimes[i] < 775807 do inc(i); Facs[6].fprimMaxIdx := i;
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{
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writeln('Found ',cnt,' in ',(GetTickCount64-T0)/1000:10:3,' s');
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//start with 2*3*7
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with Facs[2] do
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begin
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fMul := 2*3*7;fPrime := 7;fPrimIdx:= 3;
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end;
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InsertNextPrimeFac(Facs,3);
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//start with 2*3*11
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writeln('Found ',cnt,' in ',(GetTickCount64-T0)/1000:10:3,' s');
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with Facs[2] do
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begin
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fMul := 2*3*11;fPrime := 11;fPrimIdx:= 4;
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end;
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InsertNextPrimeFac(Facs,3);
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}
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InsertNextPrimeFac(Facs,2);
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writeln('Found ',cnt,' in ',(GetTickCount64-T0)/1000:10:3,' s');
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writeln;
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end.
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