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DIGITALLY RESTRICTED SETS AND THE GOLDBACH CONJECTURE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 04 February 2025, pp. 1-9
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- Article
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We show that for any set D of at least two digits in a given base b, almost all even integers taking digits only in D when written in base b satisfy the Goldbach conjecture. More formally, if
$\mathcal {A}$ is the set of numbers whose digits base b are exclusively from D, almost all elements of 
$\mathcal {A}$ satisfy the Goldbach conjecture. Moreover, the number of even integers in 
$\mathcal {A}$ which are less than X and not representable as the sum of two primes is less than 
$|\mathcal {A}\cap \{1,\ldots ,X\}|^{1-\delta }$.
