LatMRG::Primes< Int > Class Template Reference

This class provides methods to search for integers \(m\) that are prime, for which the integer \(r = (m^k-1)/(m-1)\) is also prime for a given \(k\), and possibly for which \((m-1)/2\) is also prime. More...

#include <latmrg/Primes.h>

Public Member Functions
	Primes ()
	Constructor. More...
	~Primes ()
	Destructor. More...
void	find (int e, int s, bool facto, std::ostream &fout)
	Finds \(s\) prime integers \(m<2^e\) that are closest to \(2^e\). More...
void	find (int k, int e, int s, bool safe, bool facto, std::ostream &fout)
	Finds \(s\) prime integers \(m<2^e\) that are closest to \(2^e\), such that \(m\) and \(r = (m^k-1)/(m-1)\) are prime. More...
void	find (int k, int e, long c1, long c2, bool safe, bool facto, std::ostream &fout)
	Finds all integers \(m\), in \(2^e + c_1 \le m \le2^e + c_2\), such that \(m\) and \(r = (m^k-1)/(m-1)\) are prime. More...

Public Attributes
bool	print_time = true
	Used by the main executable to compare the examples. More...

Private Member Functions
void	find (int k, int e, int s, const Int &S1, const Int &S2, bool safe, bool facto, std::ostream &fout)
	This is the general purpose function used by this program. More...
void	nextM (Int &m)
void	writeFooter (std::ostream &fout)
	Writes the CPU time of the find to the stream fout. More...
void	writeHeader (int k, int e, long c1, long c2, bool safe, bool facto, std::ostream &fout)
	Writes the parameters of the find to the stream fout. More...

Private Attributes
Chrono	timer

Detailed Description

template<typename Int>
class LatMRG::Primes< Int >

This class provides methods to search for integers \(m\) that are prime, for which the integer \(r = (m^k-1)/(m-1)\) is also prime for a given \(k\), and possibly for which \((m-1)/2\) is also prime.

This class solely uses probabilistic primality tests, but does it a lot of times.

Todo:

Could probably switch to a deterministic test because it is possible to do everything this class does with efficient deterministic tests for integers < 2^64 see https://math.stackexchange.com/questions/2481148/primality-testing-for-64-bit-numbers

Constructor & Destructor Documentation

Primes()

template<typename Int >

LatMRG::Primes< Int >::Primes

(

)

Constructor.

~Primes()

template<typename Int >

LatMRG::Primes< Int >::~Primes

(

)

Destructor.

Member Function Documentation

find() [1/4]

template<typename Int >

void LatMRG::Primes< Int >::find	(	int	e,
		int	s,
		bool	facto,
		std::ostream &	fout
	)

Finds \(s\) prime integers \(m<2^e\) that are closest to \(2^e\).

If facto is true, then \(m-1\) is factorized in its prime factors. The results are printed on stream fout.

find() [2/4]

template<typename Int >

void LatMRG::Primes< Int >::find	(	int	k,
		int	e,
		int	s,
		bool	safe,
		bool	facto,
		std::ostream &	fout
	)

Finds \(s\) prime integers \(m<2^e\) that are closest to \(2^e\), such that \(m\) and \(r = (m^k-1)/(m-1)\) are prime.

If safe is true, \((m-1)/2\) is also required to be prime. The results are printed on stream fout. If facto is true, then \(m-1\) is factorized in its prime factors. If \(k=1\), \(r\) is considered to be prime.

find() [3/4]

template<typename Int >

void LatMRG::Primes< Int >::find	(	int	k,
		int	e,
		long	c1,
		long	c2,
		bool	safe,
		bool	facto,
		std::ostream &	fout
	)

Finds all integers \(m\), in \(2^e + c_1 \le m \le2^e + c_2\), such that \(m\) and \(r = (m^k-1)/(m-1)\) are prime.

If safe is true, \((m-1)/2\) is also required to be prime. The results are printed on stream fout. If facto is true, then \(m-1\) is factorized in prime factors. If \(k=1\), \(r\) is considered to be prime.

find() [4/4]

template<typename Int >

void LatMRG::Primes< Int >::find ( int  k, int  e, int  s, const Int &  S1, const Int &  S2, bool  safe, bool  facto, std::ostream &  fout  )

private

This is the general purpose function used by this program.

This method searches for s prime integers between S1 and S2.

nextM()

template<typename Int >

void LatMRG::Primes< Int >::nextM ( Int &  m )

inlineprivate

writeFooter()

template<typename Int >

void LatMRG::Primes< Int >::writeFooter ( std::ostream &  fout )

private

Writes the CPU time of the find to the stream fout.

writeHeader()

template<typename Int >

void LatMRG::Primes< Int >::writeHeader ( int  k, int  e, long  c1, long  c2, bool  safe, bool  facto, std::ostream &  fout  )

private

Writes the parameters of the find to the stream fout.

Member Data Documentation

print_time

template<typename Int >

bool LatMRG::Primes< Int >::print_time = true

Used by the main executable to compare the examples.

timer

template<typename Int >

Chrono LatMRG::Primes< Int >::timer

private

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The documentation for this class was generated from the following file:

• include/latmrg/Primes.h