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Find the sum of all prime numbers in Python

mahmoud2506
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2022-05-19
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Sieve of Eratosthenes and its algorithm

It is a simple and ancient method for finding all Prime numbers less than or equal to N and here the value of N is one thousand.

Algorithm to find the sum of Prime numbers less than or equal to one thousand by Sieve of Eratosthenes,

  • We create a boolean array of size equal to the given number (N) and mark each position in the array True.
  • We initialize a variable p equal to 2 and s equal to 0.
  • If the variable p is prime then mark each multiple of number False in the array.
  • Update the variable p by an increment of 1 i.e p = p+1.
  • Repeat step 2 until the square of the variable is less than the given number (N).
  • The elements in the array with True contain all Prime numbers less than or equal to the given number and the elements of the array which is our Prime number.
  • After the above process, we will simply find the sum of the prime numbers.
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mahmoud2506
2022-05-19
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Code:

N=1000
s=0  # variable s will be used to find the sum of all prime.
Primes=[True for k in range(N+1)] 
p=2 
Primes[0]=False # zero is not a prime number.
Primes[1]=False #one is also not a prime number.
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]: 
        s+=i 
print('The sum of prime numbers:',s)

Output

The sum of prime numbers: 76127

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