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A Simple Prime Number Library in Prolog

Nan.Numerics.Primes Nan.Numerics.Primes/Prolog 1.3.0-beta A Simple Prime Number Library in Prolog Copyright 2016-2017 Julio P. Di Egidio Licensed under GNU GPLv3. http://julio.diegidio.name/Projects/Nan.Numerics.Primes/ https://github.com/jp-diegidio/Nan.Numerics.Primes-Prolog/

=|library(nan_numerics_primes)|=

Module =prime= provides predicates to test (positive integer) numbers for primality, find divisors and factor numbers, generate prime numbers in some interval, find consecutive prime numbers, and save/load all prime numbers up to some value to/from a file or stream.

All predicates in module =prime= are safe, i.e. validate input arguments and ensure steadfastness. For maximum performance, user code can directly call the unsafe =public= (not exported) predicates in module =prime_lgc=.

Implements a variant of the Miller-Rabin primality test that is deterministic for numbers up to =3317044064679887385961980=, otherwise it is probabilistic with the number of iterations fixed at =20=.

For better performance, leverages a prime wheel of level =6=, i.e. generated by the first =6= prime numbers, and thread-local memoization of pairs of consecutive prime numbers.

NOTE: Since the primality test in use is probabilistic in general, this library is not suitable for cryptographic applications.

This library was developed and tested with: SWI-Prolog 7.3.25 - http://www.swi-prolog.org/

Usage example:

==
?- pack_install(nan_numerics_primes).
true.

?- use_module(library(nan_numerics_primes)).
true.

?- time(prime_right(1234567891012345678901234567890123456789011111, P)).
% 1,227 inferences, 0.000 CPU in 0.010 seconds (0% CPU, Infinite Lips)
P = 1234567891012345678901234567890123456789011139.
==

To be done: Implement parallel factoring functions. To be done: Implement probabilitic test error estimates? To be done: Implement option for num. of probabilistic iterations? To be done: Implement prime counting/n-th prime functions. To be done: Implement deterministic tests? To be done: Improve compatibility with other Prolog systems.