<?pas
// BigInteger: Arbitrary-precision math and number theory

// 1. Calculating a large Factorial
function Factorial(n: Integer): BigInteger;
begin
  var r := BigInteger(1);
  for var i := 2 to n do
    r := r * i;
  Result := r;
end;

var f100 := Factorial(100);
PrintLn('100! = ' + f100.ToString);
PrintLn('Length: ' + IntToStr(f100.ToString.Length) + ' digits');
PrintLn('');

// 2. Primality testing with large numbers
// M31 = 2^31 - 1
var m31 := (BigInteger(1) shl 31) - 1;
PrintLn('M31 (2^31 - 1) = ' + m31.ToString);
if m31.IsPrime then
  PrintLn('M31 is prime.');

// M61 = 2^61 - 1
var m61 := (BigInteger(1) shl 61) - 1;
PrintLn('M61 (2^61 - 1) = ' + m61.ToString);
if m61.IsPrime then
  PrintLn('M61 is prime.');

// 3. Modular Exponentiation
// Calculate (7^123) mod 100
var v7 := BigInteger(7);
var e123 := BigInteger(123);
var m100 := BigInteger(100);
var res := v7.ModPow(e123, m100);
PrintLn('');
PrintLn('(7^123) mod 100 = ' + res.ToString);
?>