Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes

G. H. Hardy, J. E. Littlewood

Type: Article

Publication Date: 1923-01-01

Citations: 891

DOI: https://doi.org/10.1007/bf02403921

Abstract

z.I.It was asserted by GOLDBACH, in a letter to "EuLER dated 7 June, 1742 , that every even number 2m is the sum o/two odd primes, ai~d this propos ition has generally been described as 'Goldbach's Theorem'.There is no reasonable doubt that the theorem is correct, and that the number of representations is large when m is large; but all attempts to obtain a proof have been completely unsuccessful.Indeed it has never been shown that every number (or every large number, any number, that is to say, from a certain point onwards) is the sum of xo primes, or of i oooooo; and the problem was quite recently classified as among those 'beim gegenwiirtigen Stande der Wissensehaft unangreifbar'.~In this memoir we attack the problem with the aid of our new transcendental method in 'additiver Zahlentheorie'.~ We do not solve it: we do not

Locations

Acta Mathematica - View - PDF
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