| _version_ | 1866902339318710272 |
|---|---|
| author | Civan, Çınar |
| author_facet | Civan, Çınar |
| contents | <p>Euclid Numbers are a special sequence of numbers defined by taking the product of the first <em>n</em> prime numbers and adding 1. Some Euclid Numbers are prime. These are called Euclid Primes. Not all Euclid Numbers are prime, but the construction guarantees that each new Euclid number is coprime with all previous primes. This idea was first used by Euclid in his proof that there are infinitely many prime numbers.</p> <p>Whether or not Euclid Primes are infinite is still an open problem and requires proof. This dataset was generated using the Miller-Rabin Algorithm and Pollard's Rho Algorithm. The codes used to generate the data are available in <a href="https://github.com/cinarcivan/euclid-primes" target="_blank" rel="noopener">this</a> GitHub repository.</p> <p>The dataset is updated as the number of calculations increases.</p> <p><strong>Found primes (by number of primes used, idx):</strong> 1, 2, 3, 4, 5, 11, 75, 171, 172, 384, 457, 616, 643, 1391, 1613, 2122 <strong><em>(16 integer)</em></strong><br><strong>Numer of primes used (calculated):</strong> 2636</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16934374 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Euclid Primes computed based on the Miller-Rabin Algorithm and Pollard's Rho Algorithm Civan, Çınar math euclid numbers euclid primes primorial primes miller-rabin algorithm pollard's rho algorithm <p>Euclid Numbers are a special sequence of numbers defined by taking the product of the first <em>n</em> prime numbers and adding 1. Some Euclid Numbers are prime. These are called Euclid Primes. Not all Euclid Numbers are prime, but the construction guarantees that each new Euclid number is coprime with all previous primes. This idea was first used by Euclid in his proof that there are infinitely many prime numbers.</p> <p>Whether or not Euclid Primes are infinite is still an open problem and requires proof. This dataset was generated using the Miller-Rabin Algorithm and Pollard's Rho Algorithm. The codes used to generate the data are available in <a href="https://github.com/cinarcivan/euclid-primes" target="_blank" rel="noopener">this</a> GitHub repository.</p> <p>The dataset is updated as the number of calculations increases.</p> <p><strong>Found primes (by number of primes used, idx):</strong> 1, 2, 3, 4, 5, 11, 75, 171, 172, 384, 457, 616, 643, 1391, 1613, 2122 <strong><em>(16 integer)</em></strong><br><strong>Numer of primes used (calculated):</strong> 2636</p> |
| title | Euclid Primes computed based on the Miller-Rabin Algorithm and Pollard's Rho Algorithm |
| topic | math euclid numbers euclid primes primorial primes miller-rabin algorithm pollard's rho algorithm |
| url | https://doi.org/10.5281/zenodo.16934374 |