{"title":"Infinite partial sumsets in the primes","authors":"","doi":"10.1007/s11854-023-0323-y","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We show that there exist infinite sets <em>A</em> = (<em>a</em><sub>1</sub>, <em>a</em><sub>2</sub>, …} and <em>B</em> = {<em>b</em><sub>1</sub>, <em>b</em><sub>2</sub>, …} of natural numbers such that <em>a</em><sub><em>i</em></sub> + <em>b</em><sub><em>j</em></sub> is prime whenever 1 ≤ <em>i</em> < <em>j</em>.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal d'Analyse Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11854-023-0323-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We show that there exist infinite sets A = (a1, a2, …} and B = {b1, b2, …} of natural numbers such that ai + bj is prime whenever 1 ≤ i < j.
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