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Prime Digit Sum

 Published on Saturday, 27th May 2023, 05:00 pm and solved by 1274
Difficulty: Level 7 [18%]

Problem 845

Let $D(n)$ be the $n$-th positive integer that has the sum of its digits a prime.
For example, $D(61) = 157$ and $D(10^8) = 403539364$.

Find $D(10^{16})$.



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