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Other literature type . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Other literature type . 2025
License: CC BY
Data sources: Datacite
ZENODO
Other literature type . 2025
License: CC BY
Data sources: Datacite
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A Fast and Practically Reliable Primality Checker Based on Euler's Criterion with Random Bases

Rýchly a prakticky spoľahlivý test prvočíselnosti založený na Eulerovom kritériu s náhodnými bázami
Authors: Polak, Robert;

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

Abstract

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).

Keywords

Miller–Rabin, number theory, Euler's criterion, gmpy2, primality testing, Mersenne primes, pseudoprimes

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average