Data commit

Task/Twin-primes/Delphi/twin-primes.delphi

@@ -0,0 +1,119 @@
+program Primes;
+
+{$APPTYPE CONSOLE}
+
+{$R *.res}
+
+uses
+  System.SysUtils;
+
+function IsPrime(a: UInt64): Boolean;
+var
+  d: UInt64;
+begin
+  if (a < 2) then
+    exit(False);
+
+  if (a mod 2) = 0 then
+    exit(a = 2);
+
+  if (a mod 3) = 0 then
+    exit(a = 3);
+
+  d := 5;
+
+  while (d * d <= a) do
+  begin
+    if (a mod d = 0) then
+      Exit(false);
+    inc(d, 2);
+
+    if (a mod d = 0) then
+      Exit(false);
+    inc(d, 4);
+  end;
+
+  Result := True;
+end;
+
+
+function Sieve(limit: UInt64): TArray<Boolean>;
+var
+  p, p2, i: UInt64;
+begin
+  inc(limit);
+  SetLength(Result, limit);
+  FillChar(Result[2], sizeof(Boolean) * limit - 2, 0); // all false except 1,2
+  FillChar(Result[0], sizeof(Boolean) * 2, 1); // 1,2 are true
+
+  p := 3;
+  while true do
+  begin
+    p2 := p * p;
+    if p2 >= limit then
+      break;
+
+    i := p2;
+    while i < limit do
+    begin
+      Result[i] := true;
+      inc(i, 2 * p);
+    end;
+
+    while true do
+    begin
+      inc(p, 2);
+      if not Result[p] then
+        Break;
+    end;
+  end;
+end;
+
+function Commatize(const n: UInt64): string;
+var
+  str: string;
+  digits: Integer;
+  i: Integer;
+begin
+  Result := '';
+  str := n.ToString;
+  digits := str.Length;
+
+  for i := 1 to digits do
+  begin
+    if ((i > 1) and (((i - 1) mod 3) = (digits mod 3))) then
+      Result := Result + ',';
+    Result := Result + str[i];
+  end;
+end;
+
+var
+  limit, start, twins: UInt64;
+  c: TArray<Boolean>;
+  i, j: UInt64;
+
+begin
+
+  c := Sieve(Trunc(1e9 - 1));
+  limit := 10;
+  start := 3;
+  twins := 0;
+  for i := 1 to 9 do
+  begin
+    j := start;
+    while j < limit do
+    begin
+      if (not c[j]) and (not c[j - 2]) then
+        inc(twins);
+      inc(j, 2);
+    end;
+    Writeln(Format('Under %14s there are %10s pairs of twin primes.', [commatize
+      (limit), commatize(twins)]));
+
+    start := limit + 1;
+    limit := 10 * limit;
+  end;
+
+  readln;
+
+end.