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1、AdvancesinTheoreticalandAppliedMathematics,ISSN0793-4554,Vol.8,№1,2013,pp.17-26ThereareInfinitelyManySetsofN-OddPrimeNumbersandPairsofConsecutiveOddPrimeNumbersZhangTianshuNanhaiwestoilcorporation,ChinaoffshorePetroleum,Zhanjiangcity,Guangdongprovince,P.R.China.Email:tianshu_zhang507@aliyun.comAbstr
2、actLetusconsiderpositiveoddnumberswhichshareaprimefactor>>>1asakind,thenthepositivedirectionalhalflineofthenumberaxisconsistsofinfinitemanyequivalentlinesegmentsonsamepermutationofχχχkinds’oddpointsplusoddpointsamongsttheχχχkinds’oddpoints,whereχχχ≥1.Wewillprovetogetherthatthereareinfinitelymanysets
3、ofn-oddprimenumbersandpairsofconsecutiveoddprimenumbersbythemathematicalinductionwithaidofsuchequivalentlinesegmentsandoddpointsthereof,inthisarticle.KeywordsSetsofn-oddprimenumbers,Pairsofconsecutiveoddprimenumbers,Mathematicalinduction,Oddpoints,Positivedirectionalhalflineofthenumberaxis,RLSS№1~№χ
4、,Setsof•µ(•s)+b(◦s)•,Pairsof•υ(◦s)•,Thecoexistingtheorem,№1RLS№1~№χ,Setof♠µ(♠s)+b(◦s)♠,Pairof♠υ(◦s)♠.BasicConceptsSupposen>1,andκ1<κ2<...<κn-1aren-1naturalnumbers,andJχ,Jχ+κ1,Jχ+κ2,Jχ+κ3,...Jχ+κn-1arealloddprimenumbers,thenwecall(Jχ,Jχ+κ1,Jχ+κ2,Jχ+κ3,...Jχ+κn-1)asetofn-oddprimenumbers.Thereuponwecon
5、jecturethatforanypositiveoddprimenumberJp,ifanumberofresidue’sclasseswhichnintegers0,κ1,...κn-1dividerespectivelyby1modulusJpislessthanJp,thenthereareinfinitelymanysetsofn-oddprimenumberswhichdifferorderlybyκ1,κ2-κ1,κ3-κ2,...andκn-1-κn-2.Wetermtheconjectureasn-oddprimenumbers’conjecture.Forexample,w
6、henn≥2,andκ1=2,itcontainstwinprimenumbers’conjecture.Inaddition,itcontains3-oddprimenumbers’conjecturewhenn≥3,κ1=2andκ2=6.Andsoonandsoforth…Evidently,ifmodulusJp≥Jχ+κn-1,theneachoddprimenumberofsuchasetofoddnumbersbelongsinaresidueclass,thusnumbernofn-oddprimenumbersislessthanJp.IfmodulusJp≤Jχ,thenn
7、umbernofn-oddprimenumbersmaybegreaterthanJp.Forexample,asetof16-oddprimenumbers(13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73)formodulusJ4(i.e.11),ithas16oddprimenumbersof10residue’sclassesbecause17
