Task B-3.2. Determine all prime numbers less than 2011 whose sum of digits is equal to 2.
Solution. The first prime number that has a digit sum of 2 is the number 2. For other such prime numbers, we conclude as follows:

We look at the last digit. The last digit cannot be 2 or 0, as the number would then be even.

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Therefore, the only possibility is that the number has the first and last digit as 1, and the rest are 0. This gives us the numbers 11, 101, 1001.

It is easy to verify that the numbers 11 and 101 are prime.

However, the number 1001 is not prime. For example, it is divisible by 7.

The solutions are the numbers 2, 11, 101.