The Baillie-PSW primality test is an arithmetic test aiming to determine wether a given number is prime or not. It lies in the category of probabilistic in contrast to deterministic ones. It relies on a base 2 Miller-Rabin test combined with a strong lucas test.
Note that its reliability has been proven with base 2 Miller-Rabin but in theory, "any" base could work, they just haven't been formally proven. No composite number under 10k digits can pass this test.
Here you may find three different implementations of the BPSW test: one in python, one in C and the other also in C but using bignums for real cryptographic purposes (the python one being way too slow). It uses the openssl Bignum library.
For more informations, check my conference on the subject: https://www.youtube.com/watch?v=MMX7LeDe9GQ (exclusively in french) and my slides at: https://www.lse.epita.fr/data/lt/2022-04-05/lt-2022-04-05-martin-grenouilloux-carmichael.pdf