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The inverse Goldbach problem
Author(s) -
Elsholtz Christian
Publication year - 2001
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014406
Subject(s) - mathematics , goldbach's conjecture , inverse , set (abstract data type) , decomposition , combinatorics , discrete mathematics , number theory , ecology , geometry , computer science , biology , programming language
Improved upper and lower bounds of the counting functions of the conceivable additive decomposition sets of the set of primes are established. Suppose that A + B = S ′ , where, ℝ′ differs from the set of primes in finitely many elements only and| A | , | B | ⩾ 2 . It is shown that the counting functions A ( x ) of ℐ and B ( x ) of ℬ for sufficiently large x , satisfyx 1 / 2( log x )− 5 ≪ A ( x ) ≪ x 1 / 2( log x ) 4 .