Eratosthenes C ++算法筛

Question

I am trying to implement this algorithm and I have having a hard time working out the algorithm to work for finding the prime numbers up to 1000. I don't really understand but my code is not giving me the correct output, if you can suggest a way I should change my code I would greatly appreciate it.

#include <iostream>

using namespace std;

bool isPrime(int n);

int main() {
  int i;
  for(i = 1; i <= 1000; i++){
    if( isPrime(i)) cout << "This number " << i <<  " is a prime. " << endl;
  }
}

bool isPrime(int n){
  if(n <= 1){
    return false;
  }
  if(n == 2){
    return true;
  }
  for(int i = 2; i < n; i++){
    if(n % i == 0){
        return false;   
    }else{
        return true;
    }
  }
}

Answer 1

Your decision inside the for loop inside isPrime() is wrong. This is a criterion to terminate the loop:

if(n % i == 0){

but the else part is no reason to terminate. You have to wait until the for loop finished. Like this:

for(int i = 2; i < n; i++){
    if(n % i == 0){
        // Here, we are sure that n can be divided by any other numbers than 1 and n.
        return false;   
    }
}

// Here, we are sure that n cannot be divided by any number 2 .. (n-1).
return true;
}  

By the way, you only have to check until the square root of n. You can spare the rest.

Answer 2

The problem is in the isPrime function.

Your isPrime function says if the the first value of i (ie 2) is not divided by n then return true. So for eg. 21, 27 etc are also counted as a prime number.

You can use a flag variable in the isPrime function and used it to determine whether the n is prime or not. Like this

boolean prime = true;
for(int counter = 2; counter <= number / 2; counter++) {
    if(number % counter == 0) {
        prime = false;
        break;
    }
}
return prime;

I don't think this is Sieve of Eratosthenes algorithm. If you want to implement this algorithm then you can read from here .

Answer 3

There is problem in your isPrime function

bool isPrime(int n){
  if(n <= 1){
    return false;
  }
  if(n == 2){
    return true;
  }
  for(int i = 2; i < n; i++){
    if(n % i == 0){
        return false;   
    }
    else{
        return true; /* this line is very dangerous. When there is odd number it is not divisible by two so the control goes to else block and you get every odd number as your prime number */
    }
  }
}

Instead use this

bool isPrime(int n){
  if(n <= 1){
    return false;
  }
  if(n == 2){
    return true;
  }
  for(int i = 2; i < n; i++){
    if(n % i == 0){
        return false;   
    }
  }
  return true;
}

For Sieve Of Erastosthenes try this code it may help

int b;
    cout << "Enter upper limit" << endl;
    cin >> b;
    bool *x;
    x = new bool[b];
    x[2] = true;
    for (int i = 2; i < b; i++)
    {
        int count = 2;
        if (x[i])
        {
            cout << i << endl;

            while (i*count < b)
            {
                x[i*count] = false;
                count++;
            }
        }
    }