To allow for maximum performance, module prime_lgc provides unsafe public (not exported) predicates that user code can call directly instead of calling the safe predicates exported by module prime.

For info on the implementation, see library(nan_numerics_prime).

NOTE: Predicates in this module are unsafe, i.e. do not validate input arguments and are not steadfast.

author

- Julio P. Di Egidio

version

- 1.2.5-beta

See also

- library(nan_numerics_prime)

copyright

- 2016 Julio P. Di Egidio

license

- GNU GPLv3

To be done

- Integrate isqrt function from GMP?

 test_(+N:posint) is semidet

True if N is a prime number.

 div_(+N:posint, -P:prime) is semidet

True if N is a composite number with P its smallest prime divisor.

 div_rev_(+N:posint, -P:prime) is semidet

True if N is a composite number with P its greatest prime divisor.

 fact_(+N:posint, -PFs:list(pfact)) is det

PFs is the list of all prime factors of N in ascending order of the prime divisors.

Elements of PFs are of the form P^F with P the prime divisor and F the corresponding power.

If N is equal to 1 or if N is a prime number, PFs is [N^1].

 gen_(+Inf:posint, -P:prime) is multi

 gen_(+Inf:posint, +Sup:posint, -P:prime) is nondet

Generates in ascending order all prime numbers P greater than or equal to Inf, and less than or equal to Sup in the variant with arity 3. Fails if the prime to the left of Sup is less than the prime to the right of Inf.

 gen_p_(+L:prime, -P:prime) is multi

 gen_p_(+L:prime, +H:prime, -P:prime) is nondet

Generates in ascending order all prime numbers P starting from L, and up to H in the variant with arity 3. Fails if H is less than L.

 gen_rev_(+Sup:prime, -P:prime) is nondet

 gen_rev_(+Inf:posint, +Sup:posint, -P:prime) is nondet

Generates in descending order all prime numbers P less than or equal to Sup, and greater than or equal to Inf in the variant with arity 3. Fails if Sup is equal to 1 or if the prime to the left of Sup is less than the prime to the right of Inf.

 gen_rev_p_(+H:prime, -P:prime) is multi

 gen_rev_p_(+L:prime, +H:prime, -P:prime) is nondet

Generates in descending order all prime numbers P starting from H, and down to L in the variant with arity 3. Fails if H is less than L.

 next_(+N:posint, -P:prime) is det

P is the smallest prime number greater than N.

 next_p_(+P0:prime, -P:prime) is det

P is the smallest prime number greater than P0.

 prev_(+N:posint, -P:prime) is semidet

P is the greatest prime number less than N. Fails if N is less than or equal to 2.

 prev_p_(+P0:prime, -P:prime) is semidet

P is the greatest prime number less than P0. Fails if P is equal to 2.

 right_(+N:posint, -P:prime) is det

P is the smallest prime number greater than or equal to N.

 left_(+N:posint, -P:prime) is semidet

P is the greatest prime number less than or equal to N. Fails if N is equal to 1.