<?php

  // This program displays the number of centuries (blocks of 100 integers
  //  starting at a mutiple of 100) between two limits containing various numbers
  //  of primes. The limits are set in variable $LO and $HI towards the top.

  // The program depends on primes-1M-1.1M.txt, a list of all the primes, in
  //  order, between 1,000,000 and 1,100,000, one prime per line. So must have:

  //  $LO >= 1,000,000
  //  $HI <= 1,100,000

  // Note pi(1.1M) - pi(1M) = 7216, so there are 7216 primes in the file and
  //  then the array the primes are loaded into from the file.

  // See C. F. Gauss, Werke, Vol 2, 2nd ed (1876), pp. 438-443
  // https://books.google.com/books?id=BTun-k0U128C&pg=PA438#v=onepage&q&f=false

  //------------------------------------------------------------------------

  // Load array from file of primes
  $primes = file("primes-1M-1.1M.txt");

  // For all the primes beween  1,000,000 and 1,100,000.
  //$LO = 1000000;
  //$HI = 1100000;

  // For the myriad (block of 10,000) above 1,000,000.
  $LO = 1000000;
  $HI = 1010000;

  // The 7216 primes between 1M and 1.1M now loaded into array $primes[].

  // $bucket[$k] will hold the number of centuries with $k primes.
  $buckets = array();

  // 50 is the absolute maximum number of primes in a century.
  $MAX_BUCKETS = 50;

  // Init all buckets to zero.
  for ($i = 0; $i < $MAX_BUCKETS; $i++)
    $buckets[] = 0;

  $lim = $LO + 100;
  $k = 0;

  // Go through primes calculating how many are in each century,
  //  increment $buckets array accordingly.
  foreach ($primes as $prime)
  {
    // Ignore primes out of range.
    if ($prime < $LO)
      continue;
    if ($prime > $HI)
      break;
    if ($prime < $lim)
    {
      $k++;
    }
    else
    {
      $buckets[$k]++;
      $k = 1;
      $lim += 100;
    } // else
  } // foreach

  // Get the last block.
  $buckets[$k]++;

  // Delete buckets at the end that still contain 0.
  $j = $MAX_BUCKETS - 1;
  do
  {
    if ($buckets[$j] == 0)
      unset($buckets[$j]);
    $j--;
  } while ($buckets[$j] == 0);

  print_r($buckets);

?>