PERMUTABLE PRIME NUMBERS and CIRCULAR PRIME NUMBERS DECOMPOSITIONS FOR MERSENNES EXPONENTS
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2026
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| _version_ | 1866901155816144896 |
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| author | Martin, Doina |
| author_facet | Martin, Doina |
| contents | <p>We present a novel representation system for integers based on families of permutable primes. We demonstrate that any integer can be expressed in the form:</p> <p> </p> <p>$$N = k \times A + \sum_{i=1}^{n} P_i$$</p> <p> </p> <p>where $A$ is a specially chosen "anchor" permutable prime from a family with digits $\{9,9,9,3,3,1\}$ (or its higher-dimensional extensions), the $P_i$ are permutable primes drawn from a fixed set of families, and $k$ is a positive integer that typically matches the first digits of $N$. This representation reveals deep connections between Mersenne exponents and permutable prime families, with applications to primality testing and number classification</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18794919 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | PERMUTABLE PRIME NUMBERS and CIRCULAR PRIME NUMBERS DECOMPOSITIONS FOR MERSENNES EXPONENTS Martin, Doina Mersenne primes, multi-basis decomposition, decimal geometry, Lucas sequences, circular prime, permutable prime <p>We present a novel representation system for integers based on families of permutable primes. We demonstrate that any integer can be expressed in the form:</p> <p> </p> <p>$$N = k \times A + \sum_{i=1}^{n} P_i$$</p> <p> </p> <p>where $A$ is a specially chosen "anchor" permutable prime from a family with digits $\{9,9,9,3,3,1\}$ (or its higher-dimensional extensions), the $P_i$ are permutable primes drawn from a fixed set of families, and $k$ is a positive integer that typically matches the first digits of $N$. This representation reveals deep connections between Mersenne exponents and permutable prime families, with applications to primality testing and number classification</p> |
| title | PERMUTABLE PRIME NUMBERS and CIRCULAR PRIME NUMBERS DECOMPOSITIONS FOR MERSENNES EXPONENTS |
| topic | Mersenne primes, multi-basis decomposition, decimal geometry, Lucas sequences, circular prime, permutable prime |
| url | https://doi.org/10.5281/zenodo.18794919 |