The Sieve of Eratosthenes Implementation in Python



The Sieve of Eratosthenes is an elegant algorithm for finding all the 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 prime, and all multiples of this number is removed up to n are removed from the list. This process continues until the list is empty.
For example, if you wanted to find all the prime numbers up to 10, the list would contain 2, 3, 4, 5, 6, 7, 8, 9, 10. The 2 is removed and announced to be prime and 4, 6, 8, and 10 are removed since they are multiples of 2. That leaves 3, 5, 7, 9., repeat the process until the list is empty
Write a program that prompts a user for n and then uses the sieve algorithm to find all the prime numbers less than or equal to n
The solution includes python program and screenshot.
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xxxxxx xxxx
xxxxxx xxx
xxx xx_xxxxx(xxxxxx):
Check and return True if number is prime
otherwise return False
for i in range(2, int(math.sqrt(number))):
if number % i == 0:
return False
return True
# xxxxxx x xxxxxxx xxxxxx
xxx = ”
xxx = xxxxx(‘xxxxx x xxxxxxxx xxxxxxx xxxxxx: ‘)
x = xxx(xxx)
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