Abstract
In this chapter, we shall prove one of the most famous results in additive prime number theory: Chen’s theorem that every sufficiently large even integer can be written as the sum of an odd prime and a number that is either prime or the product of two primes.
Is it even true that every even n is the sum of 2 primes? To show this seems to transcend our present mathematical powers.... The prime numbers remain very elusive fellows. H. Weyl [142]
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes
Chen [10, 11] announced his theorem in 1966 but did not publish the proof until 1973, apparently because of difficulties arising from the Cultural Revolution in China. An account of Chen’s original proof appears in Halberstam and Richert’s Sieve Methods [44]. The proof in this chapter is based on unpublished notes and lectures of Henryk Iwaniec [67]. The argument uses standard results from multiplicative number theory (Dirichlet characters, the large sieve, and the Siegel-Walfisz and Bombieri-Vinogradov theorems), all of which can be found in Davenport [19]. Other good references for these results are the monographs of Montgomery [83] and Bombieri [3]. For bilinear form inequalities, see Bombieri, Friedlander, and Iwaniec [4].
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media New York
About this chapter
Cite this chapter
Nathanson, M.B. (1996). Chen’s theorem. In: Additive Number Theory. Graduate Texts in Mathematics, vol 164. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3845-2_10
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3845-2_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2848-1
Online ISBN: 978-1-4757-3845-2
eBook Packages: Springer Book Archive