Dissertation/Thesis
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
| Τίτλος: | 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 |
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| Συγγραφείς: | Polak, Robert |
| Στοιχεία εκδότη: | Zenodo |
| Έτος έκδοσης: | 2025 |
| Συλλογή: | Zenodo |
| Θεματικοί όροι: | primality testing, Euler's criterion, pseudoprimes, Miller–Rabin, Mersenne primes, number theory, gmpy2 |
| Περιγραφή: | 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). |
| Τύπος εγγράφου: | Thesis |
| Γλώσσα: | English |
| Relation: | https://zenodo.org/records/17064974; oai:zenodo.org:17064974; https://doi.org/10.5281/zenodo.17064974 |
| DOI: | 10.5281/zenodo.17064974 |
| Διαθεσιμότητα: | https://doi.org/10.5281/zenodo.17064974 https://zenodo.org/records/17064974 |
| Rights: | Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode ; Copyright @2025 Ing. Robert Polak |
| Αριθμός Καταχώρησης: | edsbas.D7A4BA7C |
| Βάση Δεδομένων: | BASE |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://doi.org/10.5281/zenodo.17064974# Name: EDS - BASE (ns324271) Category: fullText Text: View record from BASE |
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| Items | – Name: Title Label: Title Group: Ti Data: 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 – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Polak%2C+Robert%22">Polak, Robert</searchLink> – Name: Publisher Label: Publisher Information Group: PubInfo Data: Zenodo – Name: DatePubCY Label: Publication Year Group: Date Data: 2025 – Name: Subset Label: Collection Group: HoldingsInfo Data: Zenodo – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22primality+testing%22">primality testing</searchLink><br /><searchLink fieldCode="DE" term="%22Euler's+criterion%22">Euler's criterion</searchLink><br /><searchLink fieldCode="DE" term="%22pseudoprimes%22">pseudoprimes</searchLink><br /><searchLink fieldCode="DE" term="%22Miller–Rabin%22">Miller–Rabin</searchLink><br /><searchLink fieldCode="DE" term="%22Mersenne+primes%22">Mersenne primes</searchLink><br /><searchLink fieldCode="DE" term="%22number+theory%22">number theory</searchLink><br /><searchLink fieldCode="DE" term="%22gmpy2%22">gmpy2</searchLink> – Name: Abstract Label: Description Group: Ab Data: 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). – Name: TypeDocument Label: Document Type Group: TypDoc Data: Thesis – Name: Language Label: Language Group: Lang Data: English – Name: NoteTitleSource Label: Relation Group: SrcInfo Data: https://zenodo.org/records/17064974; oai:zenodo.org:17064974; https://doi.org/10.5281/zenodo.17064974 – Name: DOI Label: DOI Group: ID Data: 10.5281/zenodo.17064974 – Name: URL Label: Availability Group: URL Data: https://doi.org/10.5281/zenodo.17064974<br />https://zenodo.org/records/17064974 – Name: Copyright Label: Rights Group: Cpyrght Data: Creative Commons Attribution 4.0 International ; cc-by-4.0 ; https://creativecommons.org/licenses/by/4.0/legalcode ; Copyright @2025 Ing. Robert Polak – Name: AN Label: Accession Number Group: ID Data: edsbas.D7A4BA7C |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.D7A4BA7C |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.5281/zenodo.17064974 Languages: – Text: English Subjects: – SubjectFull: primality testing Type: general – SubjectFull: Euler's criterion Type: general – SubjectFull: pseudoprimes Type: general – SubjectFull: Miller–Rabin Type: general – SubjectFull: Mersenne primes Type: general – SubjectFull: number theory Type: general – SubjectFull: gmpy2 Type: general Titles: – TitleFull: 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 Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Polak, Robert IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2025 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa |
| ResultId | 1 |