Berroov S.L.

A five-digit number is called non-decomposable if it cannot be factored into the product of two three-digit numbers.

What is the maximum number of consecutive non-decomposable five-digit numbers?

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The smallest number that can be represented as the product of two three-digit numbers is $100 \cdot 100=10000$. The next such number is:

$100 \cdot 101=10100$, so the numbers $10001,10002, \ldots, 10099$ - are non-decomposable. Thus, there are 99 consecutive non-decomposable five-digit numbers.

More than 99 non-decomposable numbers cannot occur consecutively: every hundredth five-digit number ends in two zeros, meaning it can be represented as the product of a three-digit number and 100.

## Answer

99 numbers.