function IsPrime(N: Cardinal): Boolean; register;
 // test if N is prime, do some small Strong Pseudo Prime test in certain bounds
 // copyright (c) 2000 Hagen Reddmann, don't remove
asm
  TEST EAX,1  { Odd(N) ?? }
  JNZ @@1
  CMP EAX,2  { N == 2 ?? }
  SETE AL
  RET
@@1: CMP EAX,73  { N JB @@C }
  JE @@E { N == 73 ?? }
  PUSH ESI
  PUSH EDI
  PUSH EBX
  PUSH EBP
  PUSH EAX { save N as Param for @@5 }
  LEA EBP,[EAX - 1] { M == N -1, Exponent }
  MOV ECX,32  { calc remaining Bits of M and shift M' }
  MOV ESI,EBP
@@2: DEC ECX
  SHL  ESI,1
  JNC @@2
  PUSH ECX { save Bits as Param for @@5 }
  PUSH ESI { save M' as Param for @@5 }
  CMP EAX,08A8D7Fh { N = 9080191 ?? }
  JAE @@3
  // now if (N MOV EAX,31
  CALL @@5  { 31^((N-1)(2^s)) mod N }
  JC @@4
  MOV EAX,73  { 73^((N-1)(2^s)) mod N }
  PUSH OFFSET @@4
  JMP @@5
  // now if (N @@3: MOV EAX,2
  CALL @@5
  JC @@4
  MOV EAX,7
  CALL @@5
  JC @@4
  MOV EAX,61
  CALL @@5
@@4: SETNC AL
  ADD ESP,4 * 3
  POP EBP
  POP EBX
  POP EDI
  POP ESI
  RET
// do a Strong Pseudo Prime Test
@@5: MOV EBX,[ESP + 12] { N on stack }
  MOV ECX,[ESP + 8] { remaining Bits }
  MOV ESI,[ESP + 4] { M' }
  MOV EDI,EAX { T = b, temp. Base }
@@6: DEC ECX
  MUL EAX
  DIV  EBX
  MOV EAX,EDX
  SHL  ESI,1
  JNC @@7
  MUL EDI
  DIV  EBX
  AND  ESI,ESI
  MOV EAX,EDX
@@7: JNZ @@6
  CMP EAX,1  { b^((N -1)(2^s)) mod N == 1 mod N ?? }
  JE @@A
@@8: CMP EAX,EBP { b^((N -1)(2^s)) mod N == -1 mod N ?? , EBP = N -1 }
  JE @@A
  DEC ECX { second part to 2^s }
  JNG @@9
  MUL EAX
  DIV  EBX
  CMP EDX,1
  MOV EAX,EDX
  JNE @@8
@@9: STC
@@A: RET
@@B: DB 3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71
@@C: MOV EDX,OFFSET @@B
  MOV ECX,18
@@D: CMP AL,[EDX + ECX]
  JE @@E
  DEC ECX
  JNL @@D
@@E: SETE AL
end;
procedure TForm1.Button1Click(Sender: TObject);
begin
 if IsPrime(3453451) then
  ShowMessage('yes');
end;
{**** Another function ***}
function IsPrime(Prim: Longint): Boolean;
var
 Z: Real;
 Max: LongInt;
 Divisor: LongInt;
begin
 Prime := False;
 if (Prim and 1) = 0 then Exit;
 Z := Sqrt(Prim);
 Max := Trunc(Z) + 1;
 Divisor := 3;
 while Max > Divisor do
 begin
  if (Prim mod Divisor) = 0 then Exit;
  Inc(Divisor, 2);
  if (Prim mod Divisor) = 0 then Exit;
  Inc(Divisor, 4);
 end;
 Prime := True;
end;