A Goldbach number is a positive integer that is the sum of two odd primes (Li 1999). Let (the "exceptional set of Goldbach numbers") denote
the number of even numbers not exceeding which cannot be written as a sum of two odd
primes. Then the Goldbach conjecture is
equivalent to proving that for every . Li (1999) proved that for sufficiently large ,
Chen, J. R. "The Exceptional Set of Goldbach Numbers (II)." Sci. Sinica26, 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. Sinica23,
416-430, 1980.Li, H. "The Exceptional Set of Goldbach Numbers."
Quart. J. Math. Oxford50, 471-482, 1999.Montgomery, H. L.
and Vaughan, R. C. "The Exceptional Set of Goldbach's Problem." Acta.
Arith.27, 353-370, 1975.
(the "exceptional set of Goldbach numbers") denote
the number of even numbers not exceeding 
which cannot be written as a sum of two odd
primes. Then the Goldbach conjecture is
equivalent to proving that 
for every 
. Li (1999) proved that for sufficiently large 
,
