A module for number theory in Perl. This includes prime sieving,
primality tests, primality proofs, integer factoring, counts /
bounds / approximations for primes, nth primes, and twin primes,
random prime generation, and much more.
This module is the fastest on CPAN for almost all operations it
supports. This includes Math::Prime::XS, Math::Prime::FastSieve,
Math::Factor::XS, Math::Prime::TiedArray, Math::Big::Factors,
Math::Factoring, and Math::Primality (when the GMP module is
available). For numbers in the 10-20 digit range, it is often orders
of magnitude faster. Typically it is faster than Math::Pari for
64-bit operations.
All operations support both Perl UV's (32-bit or 64-bit) and bignums.
If you want high performance with big numbers (larger than Perl's
native 32-bit or 64-bit size), you should install Math::Prime::Util::GMP
and Math::BigInt::GMP. This will be a recurring theme throughout
this documentation -- while all bignum operations are supported in
pure Perl, most methods will be much slower than the C+GMP alternative.
The module is thread-safe and allows concurrency between Perl threads
while still sharing a prime cache. It is not itself multi-threaded.
See the Limitations section if you are using Win32 and threads in
your program. Also note that Math::Pari is not thread-safe (and
will crash as soon as it is loaded in threads), so if you use
Math::BigInt::Pari rather than Math::BigInt::GMP or the default
backend, things will go pear-shaped.
Two scripts are also included and installed by default:
* primes.pl displays primes between start and end values or
expressions, with many options for filtering (e.g.
twin, safe, circular, good, lucky, etc.). Use --help
to see all the options.
* factor.pl operates similar to the GNU factor program.
It supports bigint and expression inputs.
Original from henning@ with adjustments by me
OK sthen@
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