find-primes 2.2.1

A module to find primes and factors of big numbers.

Find Primes is a library to find all kinds of primes and factors of big numbers.

Install

Stable Version:

pip install -U find-primes

Beta Version:

pip install --pre -U find-primes

Find all primes below a number

Example: Find all primes below 100.

from find_primes import all_primes
print(all_primes(100, 'list'))

Check if a number is a prime

Example: Check if 189765 is a prime.

from find_primes import is_prime
print(is_prime(189765))

Factor a big number

Example: Factor 2776889953055853600532696901.

from find_primes import factor_mpqs
print(factor_mpqs(2776889953055853600532696901))

The CLI Tool

Usage:

find_primes.py --help

Twin Primes

A twin prime is a prime number that is either 2 less or 2 more than another prime number.

Example: Find all twin primes below 1000.

from find_primes import find_twins
print(find_twins(1000))

Palindrome Primes

A palindrome prime is a prime number that is also a palindrome number.

Example: Find all palindrome primes below 1000.

from find_primes import find_palindromes
print(find_palindromes(1000))

Example: Find all palindrome primes below 1000 in base 2.

from find_primes import find_palindromes_base_2
print(find_palindromes(8200)) #return in base 10

Emirps

An emirp is a prime number that results in a different prime when its decimal digits are reversed.

Example: Find all emirps below 1000.

from find_primes import find_reverses
print(find_reverses(1000))

Primes in Arithmetic Progression

Primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression.

Example: Find all primes in arithmetic progression below 1000.

from find_primes import find_arithmetic_prime_progressions
print(find_arithmetic_prime_progressions(100))

Mersenne Primes

A mersenne prime is a prime number that is one less than a power of two.

Example: Find all mersenne primes below 600000.

from find_primes import find_mersenne
print(find_mersenne(600000))

Double Mersenne Primes

A double mersenne prime is a double mersenne number that is prime.

Example: Find all double mersenne primes below 130.

from find_primes import find_double_mersennes
print(find_double_mersennes(130))

Fermat Pseudoprimes

A fermat pseudoprime is a pseudoprime that satisfies fermat's little theorem.

Example: Find all fermat pseudoprimes below 1000.

from find_primes import find_fermat_pseudoprimes
print(find_fermat_pseudoprimes(1000))

Balence Primes

A balence prime is a prime number which is equal to the arithmetic mean of the nearest primes above and below.

Example: Find all balence primes below 1000.

from find_primes import find_balences
print(find_balences(1000))

Carol Primes

A carol prime is a carol number that is prime.

Example: Find all carol primes below 4000.

from find_primes import find_carols
print(find_carols(4000))

Fibonacci Primes

A fibonacci prime is a fibonacci number that is prime.

Example: Find all fibonacci primes below 1000.

from find_primes import find_fibonaccis
print(find_fibonaccis(1000))

Truncatable Primes

A left-truncatable prime is a prime number which remains prime when the leading digit is successively removed.

Example: Find all left-truncatable primes below 140.

from find_primes import find_truncates
print(find_truncates(140, LEFT))

A right-truncatable prime is a prime number which remains prime when the last digit is successively removed.

Example: Find all right-truncatable primes below 295.

from find_primes import find_truncates
print(find_truncates(295, RIGHT))

A left-and-right-truncatable prime is a prime number which remains prime when the leading and last digits are simultaneously successively removed.

Example: Find all left-and-right-truncatable primes below 3800.

from find_primes import find_truncates
print(find_truncates(3800, BOTH))

Cuban Primes

A cuban prime is a prime number that is a solution to a specific equation involving third powers of x and y.

Example: Find all cuban primes below 440.

from find_primes import find_cubans
print(find_cubans(440))

Center Polygonal Primes

A centered triangular prime is a prime number and a centered figurate number that represents a triangle with a dot in the center and all other dots surrounding the center in successive triangular layers.

Example: Find all centered triangular primes below 1000.

from find_primes import find_center_polygons
print(find_center_polygons(1000, TRIANGLE))

A centered square prime is a prime number and a centered figurate number that represents a square with a dot in the center and all other dots surrounding the center in successive square layers.

Example: Find all centered square primes below 1000.

from find_primes import find_center_polygons
print(find_center_polygons(1000, SQUARE))

A centered pentagonal prime is a prime number and a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers.

Example: Find all centered pentagonal primes below 1000.

from find_primes import find_center_polygons
print(find_center_polygons(1000, PENTAGON))

A centered hexagonal prime is a prime number and a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center in successive hexagonal layers.

Example: Find all centered hexagonal primes below 1000.

from find_primes import find_center_polygons
print(find_center_polygons(1000, HEXAGON))

A centered heptagonal number is a prime number and a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center in successive heptagonal layers.

Example: Find all centered heptagon primes below 1000.

from find_primes import find_center_polygons
print(find_center_polygons(1000, HEPTAGON))

Wieferich Primes

A wieferich prime is a prime p that divides .

Example: Find all wieferich primes below 4000.

from find_primes import find_wieferiches
print(find_wieferiches(3515))

Wilson Primes

A wilson prime is a prime p that divides .

Example: Find all wilson primes below 565.

from find_primes import find_wilsons
print(find_wilsons(565))

Happy Primes

A happy prime is a prime that is a happy number.

Example: Find all happy primes in base 10 below 195.

from find_primes import find_happys
print(find_happys(195))

Pierpont Primes

A Pierpont prime is a prime of the form .

Example: Find all pierpont primes below 770.

from find_primes import find_pierponts
print(find_pierponts(770))

Leyland Primes

A leyland prime is a leyland number that is a prime.

Example: Find all leyland primes below 33000.

from find_primes import find_leylands
print(find_leylands(33000))

Leyland Primes of a Second Kind

A leyland prime of a second kind is a leyland number of a second kind that is a prime.

Example: Find all leyland primes of a second kind below 58050.

from find_primes import find_leylands_second_kind
print(find_leylands_second_kind(58050))

Woodall Primes

A woodall prime is a woodall number that is a prime.

Example: Find all woodall primes below 400.

from find_primes import find_woodalls
print(find_woodalls(400))

Unique Primes

A unique prime is a prime that there is no other prime q such that the period length of the decimal expansion of its reciprocal, 1 / p, is equal to the period length of the reciprocal of q, 1 / q.

Notice: You must install mpmath to find unique primes.

Example: Find all unique primes below 105.

from find_primes import find_uniques
print(find_uniques(105))

Friedman Primes

A friedman prime is a friedman number that is a prime.

Example: Find all friedman primes below 128.

from find_primes import find_friedmans
print(find_friedmans(128))

MPQS Method

The Multiple Polynomial Quadratic Sieve (MPQS) method is a factorization method.

Example: Factor a big number.

from find_primes import factor_mpqs
print(factor_mpqs(277688995305593400532696901))

SIQS Method

The Self-initializing Quadratic Sieve (SIQS) method is a factorization method based on the Multiple Polynomial Quadratic Sieve (MPQS) method.

Example: Factor a big number.

from find_primes import factor_siqs
print(factor_siqs(3458280484189))

Lenstra Elliptic-curve Method

The Lenstra Elliptic-curve method is a factorization method.

Example: Factor a big number.

from find_primes import factor_lenstra
print(factor_lenstra(2854159729781))

Pollard p - 1 Method

The Pollard p - 1 method is a factorization method.

Example: Factor a big number.

from find_primes import factor_pollardpm1
print(factor_pollardpm1(2854159729781))

Williams p + 1 Method

The Williams p + 1 Method is a factorization method.

Example: Factor a big number.

from find_primes import factor_williamspp1
print(factor_williamspp1(2854159729781))