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  • 1 Department of Mathematics, China University of Mining and Technology Beijing 100083, P. R. China
  • | 2 School of Applied Science, Beijing Information Science and Technology University Beijing 100192, P. R. China
  • | 3 School of Mathematical Sciences, University of Chinese Academy of Sciences Beijing 100049, P. R. China
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Let N be a sufficiently large integer. In this paper, it is proved that, with at most O(N 119/270+ s) exceptions, all even positive integers up to N can be represented in the form p12+p22+p33+p43+p56+p66,

where p 1 , p 2 , p 3 , p 4 , p 5 , p 6 are prime numbers.

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