## Task 3 - 270913

Someone wants to answer the question of whether 1987 is a prime number. Among his calculation aids (number table, calculator), he also has a prime number table; however, it only contains the prime numbers below 100.

How can the investigation be conducted (without further aids); what answer does it yield?
If it can be shown that 1987 is not divisible by any prime number \( p \) for which \( p \leq \sqrt{1987} \), then 1987 is proven to be a prime number.

Since \( \sqrt{1987} < 44 \), it suffices to show that 1987 is not divisible by any of the numbers \( 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 \). These statements can indeed be confirmed by calculation (for example, one can use a calculator to verify that none of the 14 numbers 1987 : 2, 1987 : 3, ..., 1987 : 43 is an integer).

Thus, it is proven that 1987 is a prime number.