{"title":"计算机作为新颖的数学现实。哥德巴赫问题","authors":"N. Vavilov","doi":"10.32603/2071-2340-2021-4-5-71","DOIUrl":null,"url":null,"abstract":"In this part I pursue the discussion of the role of computers in additive number theroy. Here I sketch the definitive solution of the ternary = odd Goldbach problem, not in one of its XX century asymptotric reformulations, but in its original XVII century form. Namely, that every odd number n > 5 is a sum n = p1 + p2 + p3 of three positive rational primes. A solution of this problem was only completed by Harald Helfgott in 2013–2014 and there is no chance that it could be obtained without the use of computers. Apart from that, I discuss the status of the binary = even Goldbach problem, partial results towards its solution, as well as some further related proiblems.","PeriodicalId":319537,"journal":{"name":"Computer Tools in Education","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Computers as Novel Mathematical Reality. IV. Goldbach Problem\",\"authors\":\"N. Vavilov\",\"doi\":\"10.32603/2071-2340-2021-4-5-71\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this part I pursue the discussion of the role of computers in additive number theroy. Here I sketch the definitive solution of the ternary = odd Goldbach problem, not in one of its XX century asymptotric reformulations, but in its original XVII century form. Namely, that every odd number n > 5 is a sum n = p1 + p2 + p3 of three positive rational primes. A solution of this problem was only completed by Harald Helfgott in 2013–2014 and there is no chance that it could be obtained without the use of computers. Apart from that, I discuss the status of the binary = even Goldbach problem, partial results towards its solution, as well as some further related proiblems.\",\"PeriodicalId\":319537,\"journal\":{\"name\":\"Computer Tools in Education\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computer Tools in Education\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32603/2071-2340-2021-4-5-71\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Tools in Education","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32603/2071-2340-2021-4-5-71","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Computers as Novel Mathematical Reality. IV. Goldbach Problem
In this part I pursue the discussion of the role of computers in additive number theroy. Here I sketch the definitive solution of the ternary = odd Goldbach problem, not in one of its XX century asymptotric reformulations, but in its original XVII century form. Namely, that every odd number n > 5 is a sum n = p1 + p2 + p3 of three positive rational primes. A solution of this problem was only completed by Harald Helfgott in 2013–2014 and there is no chance that it could be obtained without the use of computers. Apart from that, I discuss the status of the binary = even Goldbach problem, partial results towards its solution, as well as some further related proiblems.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
