Generation and Distribution of Prime Numbers Using a Modified Lagrange Polynomial
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866929212202418176 |
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| author | Sivaraman, Dileep Pillai, Branesh M. Suthakorn, Jackrit Ongwattanakul, Songpol |
| author_facet | Sivaraman, Dileep Pillai, Branesh M. Suthakorn, Jackrit Ongwattanakul, Songpol |
| contents | A modified Lagrange Polynomial is introduced for polynomial extrapolation, which can be used to estimate the equally spaced values of a polynomial function. As an example of its application, this article presents a prime-generating algorithm based on a 1-degree polynomial that can generate prime numbers from consecutive primes. The algorithm is based on the condition that infinitely many prime numbers exist that satisfy the equation $Π_{n} =2Π_{n-1} - Π_{n-2} \pm 2 \ \ \forall \ Π_{n} >7$. where $Π_{n-1}$ and $Π_{n-2}$ are the consecutive primes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_08582 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generation and Distribution of Prime Numbers Using a Modified Lagrange Polynomial Sivaraman, Dileep Pillai, Branesh M. Suthakorn, Jackrit Ongwattanakul, Songpol General Mathematics A modified Lagrange Polynomial is introduced for polynomial extrapolation, which can be used to estimate the equally spaced values of a polynomial function. As an example of its application, this article presents a prime-generating algorithm based on a 1-degree polynomial that can generate prime numbers from consecutive primes. The algorithm is based on the condition that infinitely many prime numbers exist that satisfy the equation $Π_{n} =2Π_{n-1} - Π_{n-2} \pm 2 \ \ \forall \ Π_{n} >7$. where $Π_{n-1}$ and $Π_{n-2}$ are the consecutive primes. |
| title | Generation and Distribution of Prime Numbers Using a Modified Lagrange Polynomial |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2401.08582 |