Digitally Restricted Sets and the Goldbach Conjecture
Year: 2025
Type: article
Abstract: 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 $|\mathcal {A}\cap \{1,\ldots ,X\}|^{1-\delta }$ .
Author: JAMES CUMBERBATCH
Institution: Purdue University West Lafayette
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,550
OpenAlex ID: W4407094672