A Fast and Practically Reliable Primality Checker Based on Euler's Criterion with Random Bases

The paper presents a fast, practically reliable primality checker implemented in Prime_numbers_2025.py. The method combines a strong classical pre-filter (small primes and 6k±1 scan), multiple rounds of Euler’s criterion with randomly selected bases, and parallel evaluation using GMP-backed modular exponentiation. In practice it is faster than common Miller–Rabin implementations in Python, while aggressively suppressing pseudoprimes by randomizing bases and repeating independent rounds. The pipeline scales to very large inputs (e.g., around 2^100000) with minute-level runtimes on commodity hardware. The paper includes algorithm details, pseudocode, and a GUI screenshot; implementation available at GitHub (Prime test GUI).