On the K-th extension of the Sieve of eratosthenes
The Sieve of Eratosthenes has been recently extended by excluding the multiples of 2, 3, and 5 from the initial set, and finding the additive rules that give the positions of the multiples of the remaining primes. We generalize these results. For a given k we let the initial set Sk consists of natur...
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| Format: | Article |
| Language: | English |
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Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171295000688 |
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| _version_ | 1832554214724730880 |
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| author | Antonio R. Quesada |
| author_facet | Antonio R. Quesada |
| author_sort | Antonio R. Quesada |
| collection | DOAJ |
| description | The Sieve of Eratosthenes has been recently extended by excluding the multiples
of 2, 3, and 5 from the initial set, and finding the additive rules that give the positions of the
multiples of the remaining primes. We generalize these results. For a given k we let the initial
set Sk consists of natural numbers relatively prime to the first k primes, and find the rules
governing the positions of the multiples of the remaining elements. |
| format | Article |
| id | doaj-art-42161dab25a44a04bd3a692e886a8d1e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-42161dab25a44a04bd3a692e886a8d1e2025-02-03T05:52:04ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118353954410.1155/S0161171295000688On the K-th extension of the Sieve of eratosthenesAntonio R. Quesada0Department of Mathematical Sciences, The University of Akron, Akron 44325-4002, OH, USAThe Sieve of Eratosthenes has been recently extended by excluding the multiples of 2, 3, and 5 from the initial set, and finding the additive rules that give the positions of the multiples of the remaining primes. We generalize these results. For a given k we let the initial set Sk consists of natural numbers relatively prime to the first k primes, and find the rules governing the positions of the multiples of the remaining elements.http://dx.doi.org/10.1155/S0161171295000688prime numberssievetables of primesalgorithms. |
| spellingShingle | Antonio R. Quesada On the K-th extension of the Sieve of eratosthenes International Journal of Mathematics and Mathematical Sciences prime numbers sieve tables of primes algorithms. |
| title | On the K-th extension of the Sieve of eratosthenes |
| title_full | On the K-th extension of the Sieve of eratosthenes |
| title_fullStr | On the K-th extension of the Sieve of eratosthenes |
| title_full_unstemmed | On the K-th extension of the Sieve of eratosthenes |
| title_short | On the K-th extension of the Sieve of eratosthenes |
| title_sort | on the k th extension of the sieve of eratosthenes |
| topic | prime numbers sieve tables of primes algorithms. |
| url | http://dx.doi.org/10.1155/S0161171295000688 |
| work_keys_str_mv | AT antoniorquesada onthekthextensionofthesieveoferatosthenes |