Goldbach Number

A Goldbach number is a positive integer that is the sum of two odd primes (Li 1999). Let E(x) (the "exceptional set of Goldbach numbers") denote the number of even numbers not exceeding x which cannot be written as a sum of two odd primes. Then the Goldbach conjecture is equivalent to proving that E(x)=2 for every x>=4. Li (1999) proved that for sufficiently large x,


See also

Goldbach Conjecture, Goldbach Partition

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Chen, J. R. "The Exceptional Set of Goldbach Numbers (II)." Sci. Sinica 26, 714-731, 1983.Chen, J. R. and Liu, J. "The Exceptional Set of Goldbach Numbers (III)." Chinese Quart. J. Math. 4, 1-15, 1989.Chen, J. R. and Pan, C. "The Exceptional Set of Goldbach Numbers." Sci. Sinica 23, 416-430, 1980.Li, H. "The Exceptional Set of Goldbach Numbers." Quart. J. Math. Oxford 50, 471-482, 1999.Montgomery, H. L. and Vaughan, R. C. "The Exceptional Set of Goldbach's Problem." Acta. Arith. 27, 353-370, 1975.

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Goldbach Number

Cite this as:

Weisstein, Eric W. "Goldbach Number." From MathWorld--A Wolfram Web Resource.

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