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Linnik's theorem on Goldbach numbers in short intervals

Published online by Cambridge University Press:  18 May 2009

D. A. Goldston
D. A. Goldston
Affiliation:
Department of Mathematics and Computer ScienceSan Jose State UniversitySan Jose, CA 95192USA
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The Goldbach conjecture states that every even number larger than 2 can be written as the sum of two primes. We shall therefore call an even number a Goldbach number if it can be written as the sum of two primes in at least one way. It has been known for a long time that almost all even numbers are Goldbach numbers. In fact, Montgomery and Vaughan [14] have shown that if E(N) denotes the number of even numbers less than or equal to N which are not Goldbach numbers, then there exists an absolute constant δ>0 such that

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 3 , September 1990 , pp. 285 - 297
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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