The Sieve of Eratosthenes is an elegant algorithm for finding all of theprime numbers up to some limit n. The basic idea is to first create a listof numbers from 2 to n. The first number is removed from the list, andannounced as a prime number, and all multiples of this number up to nare removed from the list. This process continues until the list is empty.For example, if we wished to find all the primes up to 10, the listwould originally contain 2, 3, 4, 5, 6, 7, 8, 9, 10. The 2 is removedand announced to be prime. Then 4, 6, 8, and 10 are removed, sincethey are multiples of 2. That leaves 3, 5, 7, 9. Repeating the process,3 is announced as prime and removed, and 9 is removed because it is amultiple of 3. That leaves 5 and 7. The algorithm continues by announcingthat 5 is prime and removing it from the list. Finally, 7 is announced andremoved, and we're done.Write a program that prompts a user for n and then uses the sievealgorithm to find all the primes less than or equal to n.
The Sieve of Eratosthenes is an elegant
prime numbers up to some limit n. The basic idea is to first create a list
of numbers from 2 to n. The first number is removed from the list, and
announced as a prime number, and all multiples of this number up to n
are removed from the list. This process continues until the list is empty.
For example, if we wished to find all the primes up to 10, the list
would originally contain 2, 3, 4, 5, 6, 7, 8, 9, 10. The 2 is removed
and announced to be prime. Then 4, 6, 8, and 10 are removed, since
they are multiples of 2. That leaves 3, 5, 7, 9. Repeating the process,
3 is announced as prime and removed, and 9 is removed because it is a
multiple of 3. That leaves 5 and 7. The algorithm continues by announcing
that 5 is prime and removing it from the list. Finally, 7 is announced and
removed, and we're done.
Write a program that prompts a user for n and then uses the sieve
algorithm to find all the primes less than or equal to n.
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