On the Exceptional Set of Goldbach’s Problem in Short Intervals

Denote by EX,X+H] the set of even integers in X,X+H] that are not a sum of two primes (i.e. that are not Goldbach numbers). Here we prove that there exists a (small) positive constant H 3 X ^7/24]+7dH\ge X^{\,{7\over24}+7\delta} we have |E(X,H) | << H^1-d/600\vert E(X,H) \vert \ll H^{1-\delta/600} .