2024/04/23 by Michael Hellus, Hellus, Michael, Anton Rechenauer +3
Mathematics · #11D07 (Primary) 20M14 (Secondary) #Advanced Mathematical Theories #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2404.14765
openalex publication_date 2024/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let p be a prime number, and let S be the numerical semigroup generated by the prime numbers not less than p. We compare the orders of magnitude of some invariants of S with each other, e. g., the biggest atom u of S with p itself: By Harald Helfgott (arXiv:1312.7748 [math.NT]), every odd integer N greater than five can be written as the sum of three prime numbers. There is numerical evidence suggesting that the summands of N always can be chosen between \frac N6 and \frac N2. This would imply that u is less than 6p.