Note the problem is asking you to do the process of the Sieve of Eratosthenes to find prime numbers up to $199$.

The Sieve of Eratosthenes allows you to find all prime numbers smaller than a given number. Remember that it is enough to remove all multiples of prime numbers smaller than the square root of the number. All other prime numbers would not remove any additional numbers from the Sieve.

So, to find the largest prime that will remove composite numbers from the list is the same as to find what is the largest prime so that its square is less than $199$.