## Task A-1.4.

On a board, the numbers $1,2,3, \ldots, 2021$ are written. Is it possible to erase the numbers one by one until only one number remains, such that after each erasure, the sum of all remaining numbers is a composite number?
## Solution.

It is possible.

Notice that the sum of the first $n$ natural numbers $1+2+\cdots+n=\frac{n(n+1)}{2}$ is a composite number for all $n \geqslant 3$.

We delete the numbers from the largest to the smallest. First, we will delete the largest number 2021, and then continue deleting all the way down to the number 5 (including it).

The remaining numbers are 1, 2, 3, and 4. Notice that the condition of the problem will be satisfied if we first delete the number 1, then 3, followed by 2, and finally the number 4 remains.