1. Find all natural numbers such that if you add their smallest divisor greater than one to them, the result is 30.
Answer: $25 ; 27 ; 28$.

Solution. The smallest divisor greater than one is a prime number. If each of the addends is divisible by it, then the sum is also divisible. The number 30 has three prime factors: $2,3,5$. Possible options for the desired numbers: $30-2=28,30-3=27,30-5=25$. Checking shows that all these numbers fit.

Criteria. Any correct solution: 7 points.

Correct answer without explaining why other numbers do not fit: 3 points.

Presence of each number in the answer: 1 point.