10-4. Initially, a natural number was displayed on the calculator screen. Each time, Olya added a natural number to the current number \( n \) on the calculator screen, which \( n \) did not divide. For example, if the screen showed the number 10, Olya could add 7 to get 17.

Olya repeated this operation five times, and the number 200 appeared on the screen. What is the largest initial number for which this could have happened?
Answer: 189.

Solution. Estimation. Note that Olya increased the number on the screen by at least 2 each time, because any number is divisible by 1. If Olya added two five times, the initial number would have been 190, and it would not have been possible to add two to it. Therefore, Olya must have added a number greater than two at least once. Consequently, she increased the number by at least 11 in total, from which $n \leqslant 189$.

Estimation. For $n=189$, this is possible: $200=189+2+2+2+2+3$.