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 test1 is deterministic until ~3.3 * 10^242 (or ~1.37 * 2^81). Numbers larger than that are tested using a probabilistic Baillie–PSW primality test3. While there are no known composite numbers that pass the test, it's believed they exist.
-
https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test#Deterministic_variants ↩
-
The exact number is 3,317,044,064,679,887,385,961,981 https://oeis.org/A014233 ↩
-
https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test ↩
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