Almost prime numbers
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910036579581952 |
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| author | Hakobyan, Tigran |
| author_facet | Hakobyan, Tigran |
| contents | We introduce the concept of an almost prime number generalizing a prime number. It turns out that a composite almost prime number must be a Carmichael number, in case it exists. We prove several properties of almost prime numbers and conjecture the infinitude of composite almost primes. In this regards, the latter seems to hold the potential of shading light onto the infinitude of primes with $ω(p-1)\leq 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_00679 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Almost prime numbers Hakobyan, Tigran Number Theory 11A41, 11A51, 11N80 (Primary) 11C08, 11A07, 11B83 (Secondary) We introduce the concept of an almost prime number generalizing a prime number. It turns out that a composite almost prime number must be a Carmichael number, in case it exists. We prove several properties of almost prime numbers and conjecture the infinitude of composite almost primes. In this regards, the latter seems to hold the potential of shading light onto the infinitude of primes with $ω(p-1)\leq 2$. |
| title | Almost prime numbers |
| topic | Number Theory 11A41, 11A51, 11N80 (Primary) 11C08, 11A07, 11B83 (Secondary) |
| url | https://arxiv.org/abs/2603.00679 |