No. It's the product of 73 and 137. (Both of those are primes.)
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10001
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 number "10001" is the number 17 in binary (base two). 24 + 20 = 16 + 1 = 17
10001
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