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Parallel numerical verification of the σ_odd problem  October 6, 2018
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primes.hpp File Reference

Functions to access to tables of precaculated prime numbers and offsets to iterate on possible prime numbers. More...

#include "divisors.hpp"
#include "primes__inline.hpp"
Include dependency graph for primes.hpp:

Go to the source code of this file.

Namespaces

 sigmaodd
 A lot of functions and stuffs to deal the sigma_odd problem and related stuffs.
 

Typedefs

typedef uint32_t sigmaodd::prime_type
 Type for prime number, particularly for the table of primes. More...
 

Functions

std::vector< FactorExp > sigmaodd::factorize (nat_type n)
 Return a list of prime factors with their exponents. More...
 
nat_type sigmaodd::factorization_to_n (std::vector< FactorExp > prime_exps)
 Return the number corresponding to the factorization. More...
 
nat_type sigmaodd::factorization_to_nu (std::vector< FactorExp > prime_exps)
 Return the number of all divisors of the number corresponding to the factorization. More...
 
nat_type sigmaodd::factorization_to_nu_odd (std::vector< FactorExp > prime_exps)
 Return the number of odd divisors of the number corresponding to the factorization. More...
 
nat_type sigmaodd::factorization_to_sigma (std::vector< FactorExp > prime_exps)
 Return the sum of all divisors of the number corresponding to the factorization. More...
 
nat_type sigmaodd::factorization_to_sigma_odd (std::vector< FactorExp > prime_exps)
 Return the sum of odd divisors of the number corresponding to the factorization. More...
 
bool sigmaodd::is_prime (nat_type n)
 Return true iff n is a prime number. More...
 
bool sigmaodd::is_prime_in_odd_primes_table (nat_type n)
 Return true iff n is a prime number present in the precalculated table. More...
 
prime_type sigmaodd::odd_primes_table_by_index (unsigned int i)
 Return the (i + 1)th odd prime number from the precalculated table. More...
 
prime_type sigmaodd::odd_primes_table_last ()
 Return the last odd prime number in the precalculated table. More...
 
constexpr unsigned int sigmaodd::odd_primes_table_nb ()
 Return the number of odd prime numbers in the precalculated table. More...
 
const prime_typesigmaodd::odd_primes_table_ptr ()
 Return a pointer to the first number in the precalculated table. More...
 
bool sigmaodd::read_primes_table ()
 Read the binary file prime_filename to fill the table with all primes < 2^28. This table must be read from the binary file big_data/prime28.bin. More...
 

Variables

constexpr unsigned int sigmaodd::array_odd_primes_nb_ = 14630843u - 1
 Number of odd prime numbers in the table array_odd_primes_. More...
 

Detailed Description

Functions to access to tables of precaculated prime numbers and offsets to iterate on possible prime numbers.

(January 5, 2018) By default a table of all primes < 2^28 is used. This table must be read from the binary file big_data/prime28.bin.

If the macro PRIME16 is defined then a little table of all primes < 2^16 is used. This table is automatically included by the compilation.

If the macro PRIME16 is defined then there are also a table of offset to iterate on possible primes.

GPLv3 — Copyright (C) 2017, 2018 Olivier Pirson http://www.opimedia.be/

Definition in file primes.hpp.