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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.
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3 is a prime number, which means it can only be multiplied by itself or by 1. 1x3 =3, or 3x1 is 3. The number 3 adds to be 6 twice; 2 x 3 = 6.
3 is a Prime number, which means it can only be multiplied by itself or by 1. 1x3 =3, or 3x1 is 3. The number 3 adds to be 6 twice; 2 x 3 = 6.
The rule for this sequence appears to be adding consecutive prime numbers. The sequence starts with 3, then adds the next prime number 2 to get 4. It then adds 3 (the next prime number) to 4 to get 7, then 5 to 7 to get 12, and so on. Each number in the sequence is the sum of the previous number and the next prime number in order.