sub primep_div {
 my $cand = 0 + $_[0];
 my($p, $sqr);
 1 < $cand && $cand == int($cand) or
  die "error: invalid number to primep_div: $cand";
  $cand < $greatest_prime_squared or
  die "error: number too large in primep_div: $cand";
 $sqr = sqrt($cand) + 0.5;
 for $p (@primes) {
  $p <= $sqr or
   return 1;
  0 == $cand % $p and
   return $p == $cand;
 }
 die "internal error: shouldn't fall through here";
}