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

1923/01/01 by G. H. Hardy, J. E. Littlewood · 31 citations
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Arithmetic #Combinatorics #Expression (computer science) #History and Theory of Mathematics #Mathematics

paper · pdf · doi:10.1007/bf02403921

openalex publication_date 1923/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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'. ~

Citations

• Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes
• Asymptotic Formulaae in Combinatory Analysis

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• THE JUMPING CHAMPION CONJECTURE
• Statistical properties of the zeros of zeta functions-beyond the Riemann case
• Analog of the Skewes number for twin primes
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