{"title":"大偶数表示为正密度集的八个素数之和","authors":"Meng Gao","doi":"10.1016/j.bulsci.2025.103597","DOIUrl":null,"url":null,"abstract":"<div><div>Let <span><math><mi>P</mi></math></span> denote the set of all primes. We have proved that if <em>A</em> is a subset of <span><math><mi>P</mi></math></span>, and the lower density of <em>A</em> in <span><math><mi>P</mi></math></span> is larger than 1/2, then every sufficiently large even integer <em>n</em> can be expressed in the form <span><math><mi>n</mi><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>8</mn></mrow></msub></math></span>, where <span><math><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>8</mn></mrow></msub><mo>∈</mo><mi>A</mi></math></span>. The constant 1/2 in this statement is the best possible.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"201 ","pages":"Article 103597"},"PeriodicalIF":0.9000,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the representation of large even integers as the sum of eight primes from positive density sets\",\"authors\":\"Meng Gao\",\"doi\":\"10.1016/j.bulsci.2025.103597\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Let <span><math><mi>P</mi></math></span> denote the set of all primes. We have proved that if <em>A</em> is a subset of <span><math><mi>P</mi></math></span>, and the lower density of <em>A</em> in <span><math><mi>P</mi></math></span> is larger than 1/2, then every sufficiently large even integer <em>n</em> can be expressed in the form <span><math><mi>n</mi><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><mo>⋯</mo><mo>+</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>8</mn></mrow></msub></math></span>, where <span><math><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>p</mi></mrow><mrow><mn>8</mn></mrow></msub><mo>∈</mo><mi>A</mi></math></span>. The constant 1/2 in this statement is the best possible.</div></div>\",\"PeriodicalId\":55313,\"journal\":{\"name\":\"Bulletin des Sciences Mathematiques\",\"volume\":\"201 \",\"pages\":\"Article 103597\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-02-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin des Sciences Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0007449725000235\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449725000235","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
On the representation of large even integers as the sum of eight primes from positive density sets
Let denote the set of all primes. We have proved that if A is a subset of , and the lower density of A in is larger than 1/2, then every sufficiently large even integer n can be expressed in the form , where . The constant 1/2 in this statement is the best possible.