大偶数表为一个素数与一个殆素数

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1、E40E4BmVol.40,No.419977AACTAMATHEMATICASINICAJuly,1997mittnwtpk&
(8_O5n8210097)S51(85F?d!8210003)LH3#GN28-'!4#G+J>.*(POBE<(LH3#G"FQ8M[1–3]R/K-'!4#G(*7DI=(60uylGoldbach#G:@CB#G%A*7?,)$B9Dirichlet*7MR(1991)s

2、11N,11Ps

3、

4、O156.4OntheRepresentationofaLargeEvenIntegerastheSumofaPrimeandanAlmostPrime:ThePrimeBelongstoaFixedArithmeticSequenceShanZun(DepartmentofMathematics,NanjingNormalUniversity,Nanjing210097,China)KanJiahai(NanjingInstituteofPostsandTelecommunications,Nanjing210

5、003,China)AbstractYu’sConjectureimpliesGoldbach’sConjecture.ForYu’sConjecturewithanyfixedpositiveintegermodulus,weshowhereresultswhichareasstrongasthosetheoremsof[1–3]aboutGoldbach’sConjecture.KeywordsTheGoldbachconjecture,Thetwinprimesconjecture,Chen’stheorem

6、,Sievemethods,Arithmeticsequence,Dirichlet’stheorem1991MRSubjectClassification11N,11PChineseLibraryClassificationO156.41zv[N
,S3?22

7、N1973[1]::%UL4'a8Goldbach?_5H−2#{p:p0.67CNNlnN

8、.(I)fYSC1995-11-14,WSC1996-11-04,hSC1996-11-19626l401990[2,3]:2L4':#{p:pCNNlnN(lnlnN),r≥3.(II)(r−2)!4(II)#>0.77−2r−2#{p:pCNNlnN(lnlnN),r≥3.(III)(r−2)!-

9、'HHMIrH?L4HH?L4^9),K(I)(II)(III)Y?skpD
%@j}XpMc6ZA"k(?K[a,bKJkϕEulerlk?^"f3?%zHcq}3WalnN,F#{p:pCNNlnN(lnlnN),r≥2.(r−2)!ϕ(a)p−2p

10、a,p
Ncq}4WalnN,F#{p:p

11、),(a,b)=1,(N−b,a)=1,p+Pr=N}0.771p−1−2r−2>CNNlnN(lnlnN),r≥2.(r−2)!ϕ(a)p−2p

12、a,p
N*H3,4Cj'(I)(II)(III)."T)M(KN%(i)kk−1*a=2,b=1.(ii)*a=2(k≥2),bgmodaNxy>N2ZAa
(iii)*a=Eskp0,bgmodaNx9b≡N(p0),Dy>

13、)?uwub`YH3,4(I)(II)(III)?ar8DirichletHskH?a2h[A6JkzAd={a:a∈A,d

14、a}.)

15、A

16、AY>skPskz[

17、A

18、∼XIKjAP0b?d,ω(d)(A1)

19、Ad

20、=dX+rd,ω(d)xlk0≤ω(p)