-11
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23
111111
The smallest prime number, of course, is 2. The smallest prime number whose digits add up to 2 is, of course, 2. The next-smallest is 11. It is left as an exercise for the reader to determine whether the other numbers whose digits add up to 2 (e.g. 101, 1001, 10001) are prime.
The smallest two-digit prime number whose digits themselves are prime is 23. Both 2 and 3 are prime numbers, and together they form the prime number 23.
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