關于Romanov定理中的常數.pdf

1、南京師范大學碩士學位論文關于Romanov定理中的常數姓名：孫學功申請學位級別：碩士專業(yè)：基礎數學指導教師：陳永高2003.5.1AbstractLeta22，a∈Z，A=PakIpisaprimeandkisaninteger，A(z)=#nln≤z，n∈ARomanovprovedthatthereexistsaconstantC0suchthatA(x)≥CXforallsufficientlylargeXInthispaper，

2、weinvestigatetheconstantinRomanov’StheoremWenotethattheconstantiseffectivecomputable，andgiveaneffectiveconstantTheoremlLetc=古，c，=孕H(1；)(30394898512119178109logn，l’12119178logIog(38807930000log口))logo，thenA(x)≥∞forallsuff

3、icientlylargeXChoosingn=2inTheoremlwegivethefollowingresultfortheintegersoftheformP2^Theorem2Letc=器罰l5豫，thenA掃)≥c￡forallsufficientlylargexLetr(N)=襻(p，k)lN=P2‘，pisaprime，kisapositiveintegerRomanov’Stheoremmeansthatapositi

4、veproportionofthenaturalnumberscanberepresentedintheformofp2tForthisproblem。thefollowingbetterresultisgivenTheorem3Letd=4896292003thenthereexistsaconstantc0suchthat∑1≥∞lSr(N)SdtNzforallsufficientlylargexKeyWords：Romanov’