## VERSION

Version 0.58## SYNOPSIS

The functionality is basically identical to Math::Prime::Util, as this module is just the Pure Perl implementation. This documentation will only note differences.

# Normally you would just import the functions you are using.

# Nothing is exported by default.

use Math::Prime::Util ':all';

## DESCRIPTION

Pure Perl implementations of prime number utilities that are normally handled with XS or GMP. Having the Perl implementations (1) provides examples, (2) allows the functions to run even if XS isn't available, and (3) gives big number support if Math::Prime::Util::GMP isn't available. This is a subset of Math::Prime::Util's functionality.All routines should work with native integers or multi-precision numbers. To enable big numbers, use bigint or bignum:

use bigint; say prime_count_approx(1000000000000000000000000)' # says 18435599767347543283712

This is still experimental, and some functions will be very slow. The Math::Prime::Util::GMP module has much faster versions of many of these functions. Alternately, Math::Pari has a lot of these types of functions.

## FUNCTIONS

## euler_phi

Takes a*single*integer input and returns the Euler totient.

## euler_phi_range

Takes two values defining a range`"low"`to

`"high"`and returns an array with the totient of each value in the range, inclusive.

## moebius

Takes a*single*integer input and returns the Moebius function.

## moebius_range

Takes two values defining a range`"low"`to

`"high"`and returns an array with the Moebius function of each value in the range, inclusive.

## LIMITATIONS

The SQUFOF and Fermat factoring algorithms are not implemented yet.
Some of the prime methods use more memory than they should, as the segmented
sieve is not properly used in `"primes"` and `"prime_count"`.

## PERFORMANCE

Performance compared to the XS/C code is quite poor for many operations. Some operations that are relatively close for small and medium-size values:

next_prime / prev_prime is_prime / is_prob_prime is_strong_pseudoprime ExponentialIntegral / LogarithmicIntegral / RiemannR primearray

Operations that are slower include:

primes random_prime / random_ndigit_prime factor / factor_exp / divisors nth_prime prime_count is_aks_prime

Performance improvement in this code is still possible. The prime sieve is over 2x faster than anything I was able to find online, but it is still has room for improvement.

Math::Prime::Util::GMP offers `"C+XS+GMP"` support for most of the important
functions, and will be vastly faster for most operations. If you install that
module, Math::Prime::Util will load it automatically, meaning you should
not have to think about what code is actually being used (C, GMP, or Perl).

Memory use will generally be higher for the PP code, and in some cases **much**
higher. Some of this may be addressed in a later release.

For small values (e.g. primes and prime counts under 10M) most of this will not matter.

## AUTHORS

Dana Jacobsen <[email protected]>## COPYRIGHT

Copyright 2012-2016 by Dana Jacobsen <[email protected]>This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.