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Problem 845

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Prime Digit Sum

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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数字和为质数

记$D(n)$为第$n$个各位数字和为质数的正整数。

例如，$D(61)=157$，$D({10}^8)=403539364$。

求$D({10}^{16})$。

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