| _version_ | 1866902085805539328 |
|---|---|
| author | Kusniec, Charles |
| author_facet | Kusniec, Charles |
| contents | <p><strong>Abstract:</strong><span> This preprint presents an extensive exploration of factorial numbers, particularly focusing on their properties when expressed in various forms such as square minus one numbers, twin prime products, and modular representations. We delve into the nuances of factorial modularity, examining the unique characteristics of sequences like A005563, A082995, A062169, and others from the OEIS database. Our study establishes connections between factorial numbers and twin primes, offering new insights into the Erdős conjecture and Brocard’s problem. Through rigorous analysis of sequences and modular arithmetic, we identify specific cases where factorial expressions exhibit unique properties, contributing to a deeper understanding of factorial numbers in number theory.</span></p> <p><span>Please note that this document is a preprint and has not yet been peer-reviewed. It is intended for discussion and feedback within the scientific community to refine the approaches and conclusions presented.</span></p> <p><strong>Keywords:</strong> <span>Factorial Numbers, Modular Arithmetic, Twin Primes, Erdős Conjecture, Brocard’s Problem, OEIS Sequences, Number Theory, Complementary Divisors, Prime Numbers, Mathematical Sequences.</span></p> <p><strong>2020 Mathematics Subject Classification: </strong><span>11A25 (Factorization; primality), 11B65 (Binomial coefficients; factorials; q-identities), 11Y55 (Calculation of integer sequences), 11A41 (Primes).</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_10507610 |
| institution | Zenodo |
| language | |
| publishDate | 2024 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Erdös Conjecture, Brocard's Problem, and A082995 Question Kusniec, Charles <p><strong>Abstract:</strong><span> This preprint presents an extensive exploration of factorial numbers, particularly focusing on their properties when expressed in various forms such as square minus one numbers, twin prime products, and modular representations. We delve into the nuances of factorial modularity, examining the unique characteristics of sequences like A005563, A082995, A062169, and others from the OEIS database. Our study establishes connections between factorial numbers and twin primes, offering new insights into the Erdős conjecture and Brocard’s problem. Through rigorous analysis of sequences and modular arithmetic, we identify specific cases where factorial expressions exhibit unique properties, contributing to a deeper understanding of factorial numbers in number theory.</span></p> <p><span>Please note that this document is a preprint and has not yet been peer-reviewed. It is intended for discussion and feedback within the scientific community to refine the approaches and conclusions presented.</span></p> <p><strong>Keywords:</strong> <span>Factorial Numbers, Modular Arithmetic, Twin Primes, Erdős Conjecture, Brocard’s Problem, OEIS Sequences, Number Theory, Complementary Divisors, Prime Numbers, Mathematical Sequences.</span></p> <p><strong>2020 Mathematics Subject Classification: </strong><span>11A25 (Factorization; primality), 11B65 (Binomial coefficients; factorials; q-identities), 11Y55 (Calculation of integer sequences), 11A41 (Primes).</span></p> |
| title | Erdös Conjecture, Brocard's Problem, and A082995 Question |
| url | https://doi.org/10.5281/zenodo.10507610 |