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LICENSE

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+Copyright (c) 2021 JamesJ
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

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+[![Downloads](https://static.pepy.tech/personalized-badge/find-primes?period=total&units=international_system&left_color=lightgrey&right_color=yellowgreen&left_text=Downloads)](https://pepy.tech/project/find-primes)
+
+Find Primes is a library to find all kinds of primes and factors of big numbers.
+
+**Install**
+
+Stable Version:
+```shell
+pip install -U find-primes
+```
+Beta Version:
+```shell
+pip install --pre -U find-primes
+```
+
+**[Twin Primes](https://en.wikipedia.org/wiki/Twin_prime)**
+
+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.
+```python
+from find_primes import find_twins
+print(find_twins(1000))
+```
+
+**[Palindrome Primes](https://en.wikipedia.org/wiki/Palindromic_prime)**
+
+A palindrome prime is a prime number that is also a palindrome number.
+
+Example: Find all palindrome primes below 1000.
+```python
+from find_primes import find_palindromes
+print(find_palindromes(1000))
+```
+
+Example: Find all palindrome primes below 1000 in base 2.
+```python
+from find_primes import find_palindromes_base_2
+print(find_palindromes(8200)) #return in base 10
+```
+
+**[Emirps](https://en.wikipedia.org/wiki/Emirp)**
+
+An emirp is a prime number that results in a different prime when its decimal digits are reversed.
+
+Example: Find all emirps below 1000.
+```python
+from find_primes import find_reverses
+print(find_reverses(1000))
+```
+
+**[Primes in Arithmetic Progression](https://en.wikipedia.org/wiki/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.
+```python
+from find_primes import find_arithmetic_prime_progressions
+print(find_arithmetic_prime_progressions(100))
+```
+
+**[Mersenne Primes](https://en.wikipedia.org/wiki/Mersenne_prime)**
+
+A mersenne prime is a prime number that is one less than a power of two.
+
+Example: Find all mersenne primes below 600000.
+```python
+from find_primes import find_mersenne
+print(find_mersenne(600000))
+```
+
+**[Double Mersenne Primes](https://en.wikipedia.org/wiki/Double_Mersenne_number#Double_Mersenne_primes)**
+
+A double mersenne prime is a double mersenne number that is prime.
+
+Example: Find all double mersenne primes below 130.
+```python
+from find_primes import find_double_mersennes
+print(find_double_mersennes(130))
+```
+
+**[Fermat Pseudoprimes](https://en.wikipedia.org/wiki/Fermat_pseudoprime)**
+
+A fermat pseudoprime is a pseudoprime that satisfies fermat's little theorem.
+
+Example: Find all fermat pseudoprimes below 1000.
+```python
+from find_primes import find_fermat_pseudoprimes
+print(find_fermat_pseudoprimes(1000))
+```
+
+**[Balence Primes](https://en.wikipedia.org/wiki/Balanced_prime)**
+
+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.
+```python
+from find_primes import find_balences
+print(find_balences(1000))
+```
+
+**[Carol Primes](https://en.wikipedia.org/wiki/Carol_number#Primes_and_modular_relations)**
+
+A carol prime is a carol number that is prime.
+
+Example: Find all carol primes below 4000.
+```python
+from find_primes import find_carols
+print(find_carols(4000))
+```
+
+**[Fibonacci Primes](https://en.wikipedia.org/wiki/Fibonacci_prime)**
+
+A fibonacci prime is a fibonacci number that is prime.
+
+Example: Find all fibonacci primes below 1000.
+```python
+from find_primes import find_fibonaccis
+print(find_fibonaccis(1000))
+```
+
+**[Truncatable Primes](https://en.wikipedia.org/wiki/Truncatable_prime)**
+
+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.
+```python
+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.
+```python
+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.
+```python
+from find_primes import find_truncates
+print(find_truncates(3800, BOTH))
+```
+
+**[Cuban Primes](https://en.wikipedia.org/wiki/Cuban_prime)**
+
+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.
+```python
+from find_primes import find_cubans
+print(find_cubans(440))
+```
+
+**[Center Polygonal Primes](https://en.wikipedia.org/wiki/Centered_polygonal_number)**
+
+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.
+```python
+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.
+```python
+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.
+```python
+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.
+```python
+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.
+```python
+from find_primes import find_center_polygons
+print(find_center_polygons(1000, HEPTAGON))
+```
+
+**[Wieferich Primes](https://en.wikipedia.org/wiki/Wieferich_prime)**
+
+A wieferich prime is a prime p that <img src="https://latex.vimsky.com/test.image.latex.php?fmt=png&val=%255Cdpi%257B150%257D%2520%255Clarge%2520p%2520%255E%257B2%257D&dl=0" width = "13.5" height = "15"> divides <img src="https://latex.vimsky.com/test.image.latex.php?fmt=png&val=%255Cdpi%257B150%257D%2520%255Clarge%25202%255E%257Bp-1%257D-1&dl=0" height = "15">.
+
+Example: Find all wieferich primes below 4000.
+```python
+from find_primes import find_wieferiches
+print(find_wieferiches(3515))
+```
+
+**[Wilson Primes](https://en.wikipedia.org/wiki/Wilson_prime)**
+
+A wilson prime is a prime p that <img src="https://latex.vimsky.com/test.image.latex.php?fmt=png&val=%255Cdpi%257B150%257D%2520%255Clarge%2520p%2520%255E%257B2%257D&dl=0" width = "13.5" height = "15"> divides <img src="https://latex.vimsky.com/test.image.latex.php?fmt=png&val=%255Cdpi%257B150%257D%2520%255Clarge%2520%2528p-1%2529%2521%26plus%3B1&dl=0" width = "80" height = "15">.
+
+Example: Find all wilson primes below 565.
+```python
+from find_primes import find_wilsons
+print(find_wilsons(565))
+```
+
+**[Happy Primes](https://en.wikipedia.org/wiki/Happy_number#Happy_primes)**
+
+A happy prime is a prime that is a happy number.
+
+Example: Find all happy primes in base 10 below 195.
+```python
+from find_primes import find_happys
+print(find_happys(195))
+```
+
+**[Pierpont Primes](https://en.wikipedia.org/wiki/Pierpont_prime)**
+
+A Pierpont prime is a prime of the form <img src="https://latex.vimsky.com/test.image.latex.php?fmt=png&val=%255Cdpi%257B150%257D%2520%255Clarge%25202%257B%255Eu%257D%255Ccdot3%257B%255Ev%257D%26plus%3B1&dl=0" width = "80" height = "15">.
+
+Example: Find all pierpont primes below 770.
+```python
+from find_primes import find_pierponts
+print(find_pierponts(770))
+```
+
+**[Leyland Primes](https://en.wikipedia.org/wiki/Leyland_number#Leyland_primes)**
+
+A leyland prime is a leyland number that is a prime.
+
+Example: Find all leyland primes below 33000.
+```python
+from find_primes import find_leylands
+print(find_leylands(33000))
+```
+
+**[Leyland Primes of a Second Kind](https://en.wikipedia.org/wiki/Leyland_number#Leyland_number_of_the_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.
+```python
+from find_primes import find_leylands_second_kind
+print(find_leylands_second_kind(58050))
+```
+
+**[MPQS Method](https://www.rieselprime.de/ziki/Multiple_polynomial_quadratic_sieve)**
+
+The Multiple Polynomial Quadratic Sieve (MPQS) method is a factorization method.
+
+Example: Factor a big number.
+```python
+from find_primes import factor_mpqs
+print(factor_mpqs(2776889953055853600532696901))
+```
+
+**[SIQS Method](https://www.rieselprime.de/ziki/Self-initializing_quadratic_sieve)**
+
+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.
+```python
+from find_primes import factor_siqs
+print(factor_siqs(3458280484189))
+```
+
+**[Lenstra Elliptic-curve Method](https://en.wikipedia.org/wiki/Lenstra_elliptic-curve_factorization)**
+
+The Lenstra Elliptic-curve method is a factorization method.
+
+Example: Factor a big number.
+```python
+from find_primes import factor_lenstra
+print(factor_lenstra(2854159729781))
+```
+
+**[Pollard p - 1 Method](https://en.wikipedia.org/wiki/Pollard%27s_p_%E2%88%92_1_algorithm)**
+
+The Pollard p - 1 method is a factorization method.
+
+Example: Factor a big number.
+```python
+from find_primes import factor_pollardpm1
+print(factor_pollardpm1(2854159729781))
+```
+
+**[Williams p + 1 Method](https://en.wikipedia.org/wiki/Williams%27s_p_%2B_1_algorithm)**
+
+The Williams p + 1 Method is a factorization method.
+
+Example: Factor a big number.
+```python
+from find_primes import factor_williamspp1
+print(factor_williamspp1(2854159729781))
+```