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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Hindawi Limited
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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doaj-42161dab25a44a04bd3a692e886a8d1e2020-11-24T21:57:35ZengHindawi LimitedInternational 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. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Antonio R. Quesada |
| 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. |
| author_facet |
Antonio R. Quesada |
| author_sort |
Antonio R. Quesada |
| title |
On the K-th extension of the Sieve of eratosthenes |
| title_short |
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_sort |
on the k-th extension of the sieve of eratosthenes |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1995-01-01 |
| 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. |
| topic |
prime numbers sieve tables of primes algorithms. |
| url |
http://dx.doi.org/10.1155/S0161171295000688 |
| work_keys_str_mv |
AT antoniorquesada onthekthextensionofthesieveoferatosthenes |
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1725854775623286784 |