Test and find prime numbers
Project description
Pseudoprimes
Test and find prime numbers.
>>> import pseudoprimes
>>> pseudoprimes.is_prime(11)
True
>>> pseudoprimes.is_prime(1022117) # 1009*1013
False
>>> pseudoprimes.get_prime(128) # 128-bit prime
181872728983755108091298489166590324849
>>> pseudoprimes.next_prime(3)
5
>>> pseudoprimes.prev_prime(100)
97
Installation
pip install pseudoprimes
Probabilistic or deterministic?
The used Miller–Rabin primality test^1 is deterministic until ~3.3 * 10^24[^2] (or ~1.37 * 2^81). Numbers larger than that are tested using a probabilistic Baillie–PSW primality test[^3]. While there are no known composite numbers that pass the test, it's believed they exist.
[^2]: The exact number is 3,317,044,064,679,887,385,961,981 https://oeis.org/A014233 [^3]: https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test
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