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Find all Prime numbers less than or equal to N using the Sieve of Eratosthenes algorithm in Python

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mahmoud2506
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2022-05-19
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What is the Sieve of Eratosthenes?

It is a simple and ancient method for finding all Prime numbers less than or equal to N.

Algorithm to find Prime numbers by Sieve of Eratosthenes

  1. Initially, we will create a boolean array of size equal to the N and mark each position in the array True.
  2. We initialize a variable p as 2. If the variable is prime then mark each multiple of number False in the array and update the variable p by increment.
  3. Repeat step 2 until the square of the variable p is less than or equal to N.
  4. Return, the elements in the array with True contains all Prime numbers.
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mahmoud2506
2022-05-19
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Implementation of the above algorithm using python program

# input the value of N
N=int(input("Input the value of N: "))

Primes=[True for k in range(N+1)]
p=2
Primes[1]=False
Primes[0]=False

while(p*p<=N):
    if Primes[p]==True:
        for j in range(p*p,N+1,p):
            Primes[j]=False
    p+=1

for i in range(2,N):
    if Primes[i]:
        print(i,end=' ')

Output

Input the value of N: 50
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47

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