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Nan.Numerics.Prime/Prolog 1.2.5-beta Nan.Numerics.Prime A simple prime number library Copyright 2016 Julio P. Di Egidio Licensed under GNU GPLv3. http://julio.diegidio.name/Projects/Nan.Numerics.Prime/ https://github.com/jp-diegidio/Nan.Numerics.Prime-Prolog/

`library(nan_numerics_prime)`

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 `4`, i.e. generated by the first `4` consecutive prime numbers, and the 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_prime).
true.

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

?- time(prime_right(1234567891012345678901234567890123456789011111, P)).
% 1,205 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips)
P = 1234567891012345678901234567890123456789011139.

?- time(prime_lgc:right_(1234567891012345678901234567890123456789011111, P)).
% 1,197 inferences, 0.000 CPU in 0.000 seconds (?% CPU, Infinite Lips)
P = 1234567891012345678901234567890123456789011139.```

To be done: Implement prime counting/n-th prime functions. To be done: Implement probabilitic test error estimates? To be done: Implement deterministic tests (elliptic curves)?