primelibpy 2.2

This library can be used in cryptoanalysis and some compatitive exams. It cover many different types of prime number and three factorization algorithems. This library also helps to generate random spacific type of prime number with desire digits. To use this library you mast have python 3.x

Python Prime Library

This is the official documentation of the python prime library.

• Generate Specific types of Prime numbers between the given range

• Generate Random Prime number

• Factorization of the given number

---

Installation!

Use pip3 if you are using python version 3+ else follow the same steps as mentioned below:

1. If you don’t have pip then follow the below procedure else go to step 2.

• For window Users

  • Download get-pip to a folder on your computer.

  • Put that file on Desktop

  • Open cmd and run the following commands:

  $ cd Desktop

  $ python get-pip.py

• For Mac Users

  • Install python

  $ brew install python

  • Run the following command:

  $ python get-pip.py

• For Linux Users

  • Run the following commands for python(version > 2.0):

    $ sudo apt-get install python-pip

    $ sudo pacman -S python2-pip

    $ sudo yum upgrade python-setuptools

    $ sudo yum install python-pip python-wheel

    $ sudo dnf upgrade python-setuptools

    $ sudo dnf install python-pip python-wheel

    $ sudo zypper install python-pip python-setuptools python-wheel

  • Run the following commands for python(version > 3.0):

    $ sudo apt-get install python3-pip

    $ sudo pacman -S python-pip

    $ sudo yum install python3 python3-wheel

    $ sudo dnf install python3 python3-wheel

    $ sudo zypper install python3-pip python3-setuptools python3-wheel

• For Raspberry Users

  • Run the following commands for python(version > 2.0):

    $ sudo apt-get install python-pip

  • Run the following commands for python(version > 2.0):

    $ sudo apt-get install python3-pip

2. Import gmpy2 file

   • This package is required to install primelibpy library

   • Run the following command

     $ pip install gmpy2==2.1.0a2

3. Now, install the prime python library using the below command.

   • Run the following command

     $ pip install primelibpy

4. How to use Library

   • Inside of your python IDE(Python file)

     from primelibpy import Prime as p

   • Now, using p all functions can be used in code e.g.

     balancedNumberList = p.getBalancedPrime(2,100,2)

---

Functions Description

• Prime Functions

  In all the prime numbers Start_Limit and End_Limit are the range of prime numbers the user wants to print inclusively.

Balanced Prime

Syntex: getBalancedPrime(startLimit,endLimit,balancedMode)

Return Type: list

Description: Balanced_Mode is how number which decide a balanced limit for prime.

Circular Prime

Syntex: getCircularPrime(startLimit,endLimit)

Return Type: list

Cousin Prime

Syntex: getCousinPrime(startLimit,endLimit)

Return Type: list

Description: Cousin prime are in pair so return list is have list inside it e.g.[ [1,2], [2,3] ]

Double Mersenne Prime

Syntex: getDoubleMersennePrime(startLimit,endLimit)

Return Type: list

Factorial Prime

Syntex: getFactorialPrime(startLimit,endLimit)

Return Type: list

Good Prime

Syntex: getGoodPrime(startLimit,endLimit)

Return Type: list

Mersenne Prime

Syntex: getMersennePrime(startLimit,endLimit)

Return Type: list

Palindromic Prime

Syntex: getPalindromicPrime(startLimit,endLimit)

Return Type: list

Permutable Prime

Syntex: getPermutablePrime(startLimit,endLimit)

Return Type: list

Primorial Prime

Syntex: getPrimorialPrime(startLimit,endLimit)

Return Type: list

Fermat Pseudo Prime

Syntex: getFermatPseudoPrime(startLimit,endLimit,baseNumber)

Return Type: list

Description: Base_number helps to generate a composite the number and the second argument is the Total number of Pseudo primes

Pythagorean Prime

Syntex: getPythagoreanPrime(startLimit,endLimit)

Return Type: list

Reversible Prime

Syntex: getReversiblePrime(startLimit,endLimit)

Return Type: list

Semi Prime

Syntex: getSemiPrime(startLimit,endLimit)

Return Type: list

Sophie Germain Prime

Syntex: getSophieGermainPrime(startLimit,endLimit)

Return Type: list

Twin Prime

Syntex: getTwinPrime(startLimit,endLimit)

Return Type: list

Description: Twin prime are in pair so return list is have list inside it e.g.[ [1,2], [2,3] ]

Wagstaff Prime

Syntex: getWagstaffPrime(startLimit,endLimit)

Return Type: list

Wieferich Prime

Syntex: getWieferichPrime(startLimit,endLimit)

Return Type: list

Wilson Prime

Syntex: getWilsonPrime(startLimit,endLimit)

Return Type: list

Left Truncatable Prime

Syntex: getLeftTruncatablePrime(startLimit,endLimit)

Return Type: list

Right Truncatable Prime

Syntex: getRightTruncatablePrime(startLimit,endLimit)

Return Type: list

Truncatable Prime

Syntex: getTruncatablePrime(startLimit,endLimit)

Return Type: list

Gaussian Prime

Syntex: checkGaussianPrime(realPart,imaginaryPart)

Return Type: None

Note: This will print whether the number is gaussian or not

---

Random Prime Generation

Random Prime generation function has three arguments and it requires little knowledge of above all functions.

The first argument is the type of prime number. Note that name of prime followed by Prime. The name of the prime type has to be in the capital.

e.g. PrimorialPrime

The second argument is the number of digits of random numbers.

The third argument is only mandatory for balanced prime numbers.

Syntex: getRandomPrime(primeType,totalDigits,mode=0)

Return Type: integer

Example:

import Prime as p

randomPrimorial = p.getRandomPrime("PrimorialPrime",3)

---

Factorization

This Section is related to Number factorization. Use Semi-Prime where it is indicated.

Traditional Way for Factorization

Syntex: getFactorTraditional(semiPrimeNumber)

Return Type: list

Note: This function will work all kinds of numbers but I’ll suggest using Semi prime number because This function returns the Factor of input number except 1 and the number itself.

Fermat Theorem for Factorization

Syntex: getFactorFermatTheorem(semiPrimeNumber)

Return Type: tuple

Note: This is only for composite numbers that have only two prime factors except for the number itself e.g. 33 have two prime factors 3 and 11.

Pollard Rho Factorization

Syntex: getFactorPollardRho(semiPrimeNumber)

Return Type: integer

Note: This will return any one factor of the given number because this algorithm works on random numbers.

General Factorization

Syntex: getAllFactors(compositeNumber)

Return Type: list

Note: This will return a list of all prime factors.

License

MIT

Free Software, Hell Yeah!