Displaying similar documents to “The exceptional set of Goldbach's problem”

Landau’s problems on primes

János Pintz (2009)

Journal de Théorie des Nombres de Bordeaux

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At the 1912 Cambridge International Congress Landau listed four basic problems about primes. These problems were characterised in his speech as “unattackable at the present state of science”. The problems were the following : Are there infinitely many primes of the form n 2 + 1 ? ...

Goldbach numbers represented by polynomials.

Alberto Perelli (1996)

Revista Matemática Iberoamericana

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Let N be a large positive real number. It is well known that almost all even integers in the interval [N, 2N] are Goldbach numbers, i.e. a sum of two primes. The same result also holds for short intervals of the form [N, N+H], see Mikawa [4], Perelli-Pintz [7] and Kaczorowski-Perelli-Pintz [3] for the choice of admissible values of H and the size of the exceptional set in several problems in this direction. One may ask if similar results hold for thinner sequences of integers...