# powmod($a, $f, $m) calculates $a**$f % $m,
# precondition: 1 < $m, 0 < $f, $a are integers representable as a perl integer
sub powmod {
 my($a, $f, $m) = @_;
 my $r = 1;
 for (;;) {
  0 != ($f & 1) and
   $r = mulmod($r, $a, $m);
  $f >>= 1;
  0 == $f and
   last;
  $a = mulmod($a, $a, $m);
 }
 $r;
}

}


{
# simple factoring

my @primes;
{
 my($n, $p, $sqrp);
 NLOOP: for $n (2 .. 100_100) {
  $sqrp = sqrt($n) + 0.5;
  for $p (@primes) {
   $sqrp < $p and last; 
   0 == $n % $p and next NLOOP;
  }
  push @primes, $n
 } 
}
my $greatest_prime_squared = $primes[-1]**2;