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Primes with Restricted-Digit Differences
Fix a base $b\ge2$ and a digit set $\mathcal{D}\subset\{0,1,\dots,b-1\}$, and let $\mathcal C_k$ be the set of integers in $[0,b^k)$ whose $k$ base-$b$ digits all lie in $\mathcal D$. We study prime pairs and three-term arithmetic progressions in primes whose difference, or common difference, belong
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