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Homework help for I-A number theory

 
 
Picture of William Zhang.
Homework help for I-A number theory
by William Zhang. - Saturday, 16 March 2019, 7:06 PM
 

The hint doesn't help me out on question 3.30 since it is such a large number to do sieve of eratosthenes. plz give me another clue to find out the answer. 

 
Picture of David Reynoso
Re: Homework help for I-A number theory
by David Reynoso - Monday, 18 March 2019, 11:53 AM
 

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 $199$.