prime_1000thprime_diff_eq_9000.pl

#! /usr/bin/perl

# Is there a prime wich after the 1000th prime is exactley bigger by
# 8000 / 9000 / 10000?
# 1000th_prime - prime == 8000 / 9000 / 10000;

use strict;
use warnings;

sub prime($) {
  my $number = shift;
  return 1 if ($number == 2);

  my $d = 2;
  my $sqrt = sqrt($number);

  while (1) {
    return 0 if ($number % $d == 0);

    if ($d < $sqrt) {
      $d++;
    } else {
      return 1;
    }
  }
}

my @res;
for (my $diff = 8000; $diff <= 10000; $diff += 1000) {
    # find a prime, call it 1st
    my $first = 1;

    OUTER: while (1) {
      $first += 2;
      next unless prime($first);

      # find the 1000th prime ($next) to the 1st prime
      my $last = $first;
      my $next = 0;

      while (1) {
        $last += 2;
        next unless prime($last);
        $next++;

        # check the 1000th prime
        if ($next == 1000) {
          printf("%-40s", "1000th prim after $first = $last");
          my $difference = $last - $first;

          # if it fit, search is over :)
          if ($difference == $diff) {
            print "I FOUND IT! " x 3 . "\n";
            push(@res, "$diff == $first-$last ($next.)\n");
            last OUTER;
          }
          # if it's too big, search is over
          elsif ($difference > $diff) {
            print "difference is too big    $difference\n";
            last OUTER;
          }
          # if it's too small, get a bigger 1st prime!
          else {
            print "difference is too small  $difference\n";
            last
          }
       }
    }
  }
}

print "\n" x 2 . join('',@res);