On the emergence of the Quanta Prime sequence
This paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications. The study uncovers profound connections between Quanta Prime numbers and essential sequences in number theory and cryptography. The investigation...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-12-01
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| Series: | Arab Journal of Basic and Applied Sciences |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/25765299.2024.2445377 |
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| author | Moustafa Ibrahim |
| author_facet | Moustafa Ibrahim |
| author_sort | Moustafa Ibrahim |
| collection | DOAJ |
| description | This paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications. The study uncovers profound connections between Quanta Prime numbers and essential sequences in number theory and cryptography. The investigation highlights the sequence’s contribution to the emergence of new primes and its embodiment of core mathematical constructs, including Mersenne numbers, Fermat numbers, Lucas numbers, Fibonacci numbers, the Chebyshev sequence, and the Dickson sequence. The comprehensive analysis emphasizes the sequence’s intrinsic relevance to the Lucas-Lehmer primality test. This research positions the Quanta Prime sequence as a pivotal tool in cryptographic applications, offering novel representations of critical mathematical structures. Additionally, a new result linking the Quanta Prime sequence to the Harmonic series is introduced, hinting at potential progress in understanding the Riemann Hypothesis. |
| format | Article |
| id | doaj-art-4f3d455ca4114eb3a244f5b55dad0ccc |
| institution | Kabale University |
| issn | 2576-5299 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Arab Journal of Basic and Applied Sciences |
| spelling | doaj-art-4f3d455ca4114eb3a244f5b55dad0ccc2025-01-07T14:31:27ZengTaylor & Francis GroupArab Journal of Basic and Applied Sciences2576-52992025-12-0132112010.1080/25765299.2024.2445377On the emergence of the Quanta Prime sequenceMoustafa Ibrahim0Department of Mathematics, University of Bahrain, Zallaq, Kingdom of BahrainThis paper presents the Quanta Prime Sequence (QPS) and its foundational theorem, showcasing a unique class of polynomials with substantial implications. The study uncovers profound connections between Quanta Prime numbers and essential sequences in number theory and cryptography. The investigation highlights the sequence’s contribution to the emergence of new primes and its embodiment of core mathematical constructs, including Mersenne numbers, Fermat numbers, Lucas numbers, Fibonacci numbers, the Chebyshev sequence, and the Dickson sequence. The comprehensive analysis emphasizes the sequence’s intrinsic relevance to the Lucas-Lehmer primality test. This research positions the Quanta Prime sequence as a pivotal tool in cryptographic applications, offering novel representations of critical mathematical structures. Additionally, a new result linking the Quanta Prime sequence to the Harmonic series is introduced, hinting at potential progress in understanding the Riemann Hypothesis.https://www.tandfonline.com/doi/10.1080/25765299.2024.2445377Quanta Prime SequenceHarmonic numbersnumber theoryMersenne primesLucas-Lehmer primality testCryptography |
| spellingShingle | Moustafa Ibrahim On the emergence of the Quanta Prime sequence Arab Journal of Basic and Applied Sciences Quanta Prime Sequence Harmonic numbers number theory Mersenne primes Lucas-Lehmer primality test Cryptography |
| title | On the emergence of the Quanta Prime sequence |
| title_full | On the emergence of the Quanta Prime sequence |
| title_fullStr | On the emergence of the Quanta Prime sequence |
| title_full_unstemmed | On the emergence of the Quanta Prime sequence |
| title_short | On the emergence of the Quanta Prime sequence |
| title_sort | on the emergence of the quanta prime sequence |
| topic | Quanta Prime Sequence Harmonic numbers number theory Mersenne primes Lucas-Lehmer primality test Cryptography |
| url | https://www.tandfonline.com/doi/10.1080/25765299.2024.2445377 |
| work_keys_str_mv | AT moustafaibrahim ontheemergenceofthequantaprimesequence |