Math::Prime::Util::PrimeArray(3)

NAME
Math::Prime::Util::PrimeArray - A tied array for primes

VERSION
Version 0.74

SYNOPSIS
  # Use package and create a tied variable
  use Math::Prime::Util::PrimeArray;
  tie my @primes, 'Math::Prime::Util::PrimeArray';

  # or all in one (allowed: @primes, @prime, @pr, @p):
  use Math::Prime::Util::PrimeArray '@primes';

  # Use in a loop by index:
  for my $n (0..9) {
    print "prime $n = $primes[$n]\n";
  }

  # Use in a loop over array:
  for my $p (@primes) {
    last if $p > 1000;   # stop sometime
    print "$p\n";
  }

  # Use via array slice:
  print join(",", @primes[0..49]), "\n";

  # Use via each:
  use 5.012;
  while( my($index,$value) = each @primes ) {
    last if $value > 1000;   # stop sometime
    print "The ${index}th prime is $value\n";
  }

  # Use with shift:
  while ((my $p = shift @primes) < 1000) {
    print "$p\n";
  }

DESCRIPTION
An array that acts like the infinite set of primes. This may be more convenient than using Math::Prime::Util directly, and in some cases it can be faster than calling "next_prime" and "prev_prime".

If the access pattern is ascending or descending, then a window is sieved and results returned from the window as needed. If the access pattern is random, then "nth_prime" is used.

Shifting acts like the array is losing elements at the front, so after two shifts, "$primes[0] == 5". Unshift will move the internal shift index back one, unless given an argument which is the number to move back. It will not shift past the beginning, so "unshift @primes, ~0" is a useful way to reset from any shifts.

Example:

  say shift @primes;     # 2
  say shift @primes;     # 3
  say shift @primes;     # 5
  say $primes[0];        # 7
  unshift @primes;       #     back up one
  say $primes[0];        # 5
  unshift @primes, 2;    #     back up two
  say $primes[0];        # 2

If you want sequential primes with low memory, I recommend using "forprimes" in Math::Prime::Util. It is much faster, as the tied array functionality in Perl is not high performance. It isn't as flexible as the prime array, but it is a very common pattern.

If you prefer an iterator pattern, I would recommend using "prime_iterator" in Math::Prime::Util. It will be a bit faster than using this tied array, but of course you don't get random access. If you find yourself using the "shift" operation, consider the iterator.

LIMITATIONS
The size of the array will always be shown as 2147483647 (IV32 max), even in a 64-bit environment where primes through "2^64" are available.

Perl will mask all array arguments to 32-bit, making "2^32-1" the maximum prime through the standard array interface. It will silently wrap after that. The only way around this is using the object interface:

    use Math::Prime::Util::PrimeArray;
    my $o = tie my @primes, 'Math::Prime::Util::PrimeArray';
    say $o->FETCH(2**36);

Here we store the object returned by tie, allowing us to call its FETCH method directly. This is actually faster than using the array.

Some people find the idea of shifting a prime array abhorrent, as after two shifts, "the second prime is 7?!". If this bothers you, do not use "shift" on the tied array.

PERFORMANCE
Performance of tied arrays increased substantially (40% faster) between Perl v5.18 and 5.24. It is recommended to use a new-ish Perl.

  sumprimes:      sum_primes(nth_prime(100_000))
  MPU forprimes:  forprimes { $sum += $_ } nth_prime(100_000);
  MPU iterator:   my $it = prime_iterator; $sum += $it->() for 1..100000;
  MPU array:      $sum = vecsum( @{primes(nth_prime(100_000))} );
  MPUPA:          tie my @prime, ...; $sum += $prime[$_] for 0..99999;
  MPUPA-FETCH:    my $o=tie my @pr, ...; $sum += $o->FETCH($_) for 0..99999;
  MNSP:           my $seq = Math::NumSeq::Primes->new;
                  $sum += ($seq->next)[1] for 1..100000;
  MPTA:           tie my @prime, ...; $sum += $prime[$_] for 0..99999;
  List::Gen       $sum = primes->take(100000)->sum

Memory use is comparing the delta between just loading the module and running the test. M1 Macbook, Perl 5.42.0, Math::NumSeq v75, Math::Prime::TiedArray v0.04 with "extend_step 1000", List::Gen 0.979.

Summing the first 0.1M primes via walking the array (milliseconds):

       .05      56k    Math::Prime::Util      sumprimes
      1.7       56k    Math::Prime::Util      forprimes
      1.6      4 MB    Math::Prime::Util      sum big array
     12          0     Math::Prime::Util      prime_iterator
     31        3 MB    MPU::PrimeArray        using FETCH
     41        3 MB    MPU::PrimeArray        array
     63        6 MB    List::Gen              sequence
     51        950k    Math::NumSeq::Primes   sequence iterator
   2367ms     78 MB    Math::Prime::TiedArray (extend 1k)

Summing the first 1M primes via walking the array (seconds):

      .0003    268k    Math::Prime::Util      sumprimes
      .018     268k    Math::Prime::Util      forprimes
      .015    41 MB    Math::Prime::Util      sum big array
     0.11        0     Math::Prime::Util      prime_iterator
     0.3       644k    MPU::PrimeArray        using FETCH
     0.4       644k    MPU::PrimeArray        array
     0.8      57 MB    List::Gen              sequence
     4.3      3179k    Math::NumSeq::Primes   sequence iterator
    35.9s    722 MB    Math::Prime::TiedArray (extend 1k)

Summing the first 10M primes via walking the array (seconds):

     0.0015    432k    Math::Prime::Util      sumprimes
     0.19      432k    Math::Prime::Util      forprimes
     0.16    394 MB    Math::Prime::Util      sum big array
     1.2         0     Math::Prime::Util      prime_iterator
     3.0       772k    MPU::PrimeArray        using FETCH
     4.0       772k    MPU::PrimeArray        array
     8.3s    652 MB    List::Gen              sequence
   577       22.8MB    Math::NumSeq::Primes   sequence iterator
           >5000 MB    Math::Prime::TiedArray (extend 1k)

Math::Prime::Util offers four obvious solutions: the "sum_primes" function, summing a big generated array, an iterator, and the "forprimes" construct. The big array is fast but uses a lot of memory, forcing the user to start programming segments. Using the iterator avoids all the memory use, but isn't as fast. The "forprimes" construct is both fast and low memory, but it isn't quite as flexible as the iterator.

Math::NumSeq::Primes offers an iterator alternative, and works quite well as long as you don't need lots of primes. It does not support random access. It has reasonable performance for the first few hundred thousand, but each successive value takes much longer to generate, and once past 1 million it isn't very practical. Internally it is sieving all primes up to "n" every time it makes a new segment which is why it slows down so much.

List::Gen includes a built-in prime sequence. Version 0.975 will use this module for primes if it can, which is shown in the above numbers. It is the odd module out in this comparison, as primes aren't a core feature. Without this module, it is very slow.

Math::Prime::TiedArray is remarkably impractical for anything other than tiny numbers.

SEE ALSO
This module uses Math::Prime::Util to do all the work. If you're doing anything but retrieving primes, you should examine that module to see if it has functionality you can use directly, as it may be a lot faster or easier.

Similar functionality can be had from Math::NumSeq and Math::Prime::TiedArray.

AUTHORS
Dana Jacobsen <dana@acm.org>

COPYRIGHT
Copyright 2012-2026 by Dana Jacobsen <dana@acm.org>

This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.