Assuming a zero-free region for Dirichlet L-functions, almost all even integers with a missing digit in intervals of length x^{2/3+epsilon} are sums of two primes.
Discorrelation bet ween primes in short intervals and polynomial phases
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Goldbach's Problem in short intervals for numbers with a missing digit
Assuming a zero-free region for Dirichlet L-functions, almost all even integers with a missing digit in intervals of length x^{2/3+epsilon} are sums of two primes.