Primality

Primality helps you easily find, test and work with prime numbers in Python.

primality.is_prime(516349073509121311)
>> True

primality.nth_prime(9999)
>> 104729

primality.prange(10)
>> [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]

primality.between(10,19)
>> [11, 13, 17, 19]

primality.next_prime(3)
>> 5

primality.prev_prime(1000)
>> 997

primality.rand_prime(10, 50, RandomStrategy.RANDOM_LIB)
>> 17

Installation

Use the package manager pip to install Primality.

pip install primality

Implementation

Primality officially supports Python 3.8+.

from primality import primality

Documentation

For usage documentation and examples, please check out our wiki and docs.

Theory

The current version uses the Miller primality test⁽¹⁾ with known strong pseudoprime bases⁽²⁾ to provide deterministic testing for integers between 2 and 2⁶⁴ - 1⁽³⁾. For more details, please read THEORY.md

1. Miller, G. (1976), "Riemann's Hypothesis and Tests for Primality", Journal of Computer and System Sciences.

2. Zhang, Z and Tang, M. (2003), "Finding strong pseudoprimes to several bases. II", Mathematics of Computation.

3. McCraine, J. (1997), "Sequence A014233 (Smallest odd number for which Miller-Rabin primality test on bases <= n-th prime does not reveal compositeness)". The On-Line Encyclopedia of Integer Sequences, OEIS Foundation.

Contributing

Contributions are welcome. Please remember to read CONTRIBUTING.md if it's your first time interacting with this project.