6. Nikita writes down numbers one after another according to the following rule: first, he writes down three natural numbers. Then he repeats the same procedure: he adds the last three numbers and appends the resulting sum at the end. Can Nikita write down 9 prime numbers in a row, acting this way?


Solution. This is possible, and in a unique way:

$$
5,3,3,11,17,31,59,107,197 .
$$