{"title":"Class numbers, Ono invariants and some interesting primes","authors":"Alexandru Gica","doi":"10.1016/j.indag.2024.06.003","DOIUrl":null,"url":null,"abstract":"Our aim is to find all the prime numbers such that has at most two different prime factors, for all the odd integers such that . We solve entirely the cases , using the knowledge of the quadratic imaginary number fields with class numbers 4, 1 and 2 respectively. The case is not completely solved. Taking into account a result of Stéphane Louboutin, we prove that there is at most one value besides our list. Assuming a Restricted Riemann Hypothesis, the list is complete. In the last section of the paper we give a short sketch for the general problem: find all odd integers such that has at most two different prime factors, for all the odd integers such that .","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1016/j.indag.2024.06.003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Our aim is to find all the prime numbers such that has at most two different prime factors, for all the odd integers such that . We solve entirely the cases , using the knowledge of the quadratic imaginary number fields with class numbers 4, 1 and 2 respectively. The case is not completely solved. Taking into account a result of Stéphane Louboutin, we prove that there is at most one value besides our list. Assuming a Restricted Riemann Hypothesis, the list is complete. In the last section of the paper we give a short sketch for the general problem: find all odd integers such that has at most two different prime factors, for all the odd integers such that .