Alternate Primes till N

We have to print alternate prime numbers till N.

Examples:

Input : N = 10
Output : 2 5 

Input : N = 15
Output : 2 5 11 

Naive Approach:We can just simply iterate over N and check whether the number is prime or not and print the alternate number just by keeping a simple altering flag variable.

C++

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/* C++ program to print all
primes smaller than or 
equal to n using Naive approach.*/
#include<bits/stdc++.h>
using namespace std;
  
/* Function for checking 
number is prime or not */
int prime(int num)
{
    int i, flag = 0;
    for(i = 2; i<= num / 2; i++)
    {
        if(num % i == 0)
        {
            flag = 1;
            break;
        }
    }
      
    // if flag = 0 then number 
    // is prime and return 1
    // otherwise return 0
    if(flag == 0)
        return 1;
    else
        return 0;
}
  
// Function for printing 
// alternate prime number
void print_alternate_prime(int n)
{
    // counter is initialize with 0
    int counter = 0;
  
    // looping through 2 to n-1
    for(int num = 2; num < n; num++)
    {
        // function calling along 
        // with if condition
        if (prime(num) == 1)
        
            // if counter is multiple of 2 
            // then only print prime number
            if (counter % 2 == 0)
                cout << num << " ";
                  
            counter ++;
        }
    }
}
  
// Driver code
int main()
{
    int n = 15;
    cout << "Following are the alternate prime"
         << " number smaller than or equal to " 
         << n << endl;
           
    // Function calling 
    print_alternate_prime(n);
}
          
// This code is contributed 
// by ChitraNayal

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Java

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// Java program to print all
// primes smaller than or 
// equal to n using Naive approach.
class GFG 
{
      
/* Function for checking 
number is prime or not */
static int prime(int num)
{
int i, flag = 0;
for(i = 2; i<= num / 2; i++)
{
    if(num % i == 0)
    {
        flag = 1;
        break;
    }
}
  
// if flag = 0 then number is prime
// and return 1 otherwise return 0
if(flag == 0)
    return 1;
else
    return 0;
}
  
// Function for printing 
// alternate prime number
static void print_alternate_prime(int n)
{
// counter is initialize with 0
int counter = 0;
  
// looping through 2 to n-1
for(int num = 2; num < n; num++)
{
    // function calling along 
    // with if condition
    if (prime(num) == 1)
    
        // if counter is multiple of 2 
        // then only print prime number
        if (counter % 2 == 0)
            System.out.print(num + " ");
                  
        counter ++;
    }
}
}
  
// Driver code
public static void main(String[] args) 
{
    int n = 15;
    System.out.println("Following are the alternate "
                         "prime number smaller than " +
                                   "or equal to " + n);
  
    // Function calling 
    print_alternate_prime(n);
}
  
// This code is contributed
// by ChitraNayal

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Python3

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# Python3 program to print all
# primes smaller than or 
# equal to n using Naive approach.
  
# Function for checking number 
# is prime or not
def prime(num) :
    flag = 0
    for i in range(2,num // 2 + 1) :
        if num % i == 0 :
            flag = 1
            break
    # if flag = 0 then number is prime
    # and return 1 otherwise return 0
    if flag == 0 :
        return 1
    else :
        return 0
  
# Function for printing alternate prime number
def print_alternate_prime(n):
      
    # counter is initialize with 0
    counter = 0
  
    # looping through 2 to n-1
    for num in range(2,n) :
          
        # function calling along with if condition
        if prime(num) == 1 :
              
            # if counter is multiple of 2 then
            # only print prime number
            if counter % 2 == 0 :
                print(num,end =" ")
                  
            counter += 1
  
# Driver code
if __name__ == "__main__":
    n = 15
    print("Following are the alternate prime"
          +"number smaller than or equal to",n)
  
           
  
    # Function calling 
    print_alternate_prime(n)
         

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C#

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// C# program to print all
// primes smaller than or 
// equal to n using Naive approach.
using System;
class GFG 
{
/* Function for checking 
number is prime or not */
static int prime(int num)
{
int i, flag = 0;
for(i = 2; i <= num / 2; i++)
{
    if(num % i == 0)
    {
        flag = 1;
        break;
    }
}
  
// if flag = 0 then number is prime
// and return 1 otherwise return 0
if(flag == 0)
    return 1;
else
    return 0;
}
  
// Function for printing
// alternate prime number
static void print_alternate_prime(int n)
{
// counter is initialize with 0
int counter = 0;
  
// looping through 2 to n-1
for(int num = 2; num < n; num++)
{
    // function calling along
    // with if condition
    if (prime(num) == 1)
    
        // if counter is multiple of 2 
        // then only print prime number
        if (counter % 2 == 0)
            Console.Write(num + " ");
                  
        counter ++;
    }
}
}
  
// Driver code
public static void Main()
{
    int n = 15;
    Console.Write("Following are the alternate "
                    "prime number smaller than " +
                       "or equal to " + n + "\n");
  
    // Function calling 
    print_alternate_prime(n);
}
  
// This code is contributed
// by ChitraNayal

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PHP

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<?php
// PHP program to print all
// primes smaller than or 
// equal to n using Naive approach.
  
// Function for checking number 
// is prime or not
function prime($num)
{
    $flag = 0;
    for($i = 2; $i <= $num / 2; $i++)
    {
        if ($num % $i == 0)
        {
            $flag = 1;
            break;
        }
    }
      
    // if flag = 0 then number is prime
    // and return 1 otherwise return 0
    if ($flag == 0)
        return 1;
    else
        return 0;
}
  
// Function for printing 
// alternate prime number
function print_alternate_prime($n)
{
      
    // counter is initialize with 0
    $counter = 0;
  
    // looping through 2 to n-1
    for($num = 2; $num < $n; $num++)
    {
        // function calling along
        // with if condition
        if(prime($num) == 1)
        
            // if counter is multiple of 2 
            // then only print prime number
            if ($counter % 2 == 0 )
                echo $num . " ";
                  
            $counter += 1;
        }
    }
}
  
// Driver code
$n = 15;
echo "Following are the alternate prime ".
      "number smaller than or equal to "
                                $n . "\n";
// Function calling 
print_alternate_prime($n);
  
// This code is contributed
// by ChitraNayal
?>

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Output:

Following are the alternate prime numbers smaller  than or equal to 15
2 5 11

Time Complexity: O(N * \sqrt{N})

Efficient approach: Using Sieve of Eratosthenes we can just print all the alternate true values in the sieve.

C++

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// C++ program to print all primes smaller than or
// equal to n using Sieve of Eratosthenes
#include <bits/stdc++.h>
using namespace std;
  
void SieveOfEratosthenes(int n)
{
    // Create a boolean array "prime[0..n]" and initialize
    // all entries it as true. A value in prime[i] will
    // finally be false if i is Not a prime, else true.
    bool prime[n + 1];
    memset(prime, true, sizeof(prime));
  
    for (int p = 2; p * p <= n; p++) {
  
        // If prime[p] is not changed, then
        // it is a prime
        if (prime[p] == true) {
  
            // Update all multiples of p
            for (int i = p * 2; i <= n; i += p)
                prime[i] = false;
        }
    }
  
    // Print all prime numbers
    bool flag = true;
    for (int p = 2; p <= n; p++) {
        if (prime[p]) {
            if (flag) {
                cout << p << " ";
                flag = false;
            }
            else {
  
                // for next prime to get printed
                flag = true;
            }
        }
    }
}
  
// Driver Program to test above function
int main()
{
    int n = 15;
    cout << "Following are the alternate"
         << " prime numbers smaller "
         << " than or equal to " << n << endl;
    SieveOfEratosthenes(n);
    return 0;
}

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Java

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// Java program to print all primes 
// smaller than or equal to n using
// Sieve of Eratosthenes
class GFG 
{
static void SieveOfEratosthenes(int n)
{
// Create a boolean array "prime[0..n]" 
// and initialize all entries it as 
// true. A value in prime[i] will
// finally be false if i is Not a 
// prime, else true.
boolean []prime = new boolean[n + 1];
for(int i = 0; i < prime.length; i++)
    prime[i] = true;
  
for (int p = 2; p * p <= n; p++) 
{
  
    // If prime[p] is not changed,
    // then it is a prime
    if (prime[p] == true)
    {
  
        // Update all multiples of p
        for (int i = p * 2;
                 i <= n; i += p)
            prime[i] = false;
    }
}
  
// Print all prime numbers
boolean flag = true;
for (int p = 2; p <= n; p++)
{
    if (prime[p])
    {
        if (flag)
        {
            System.out.print(p + " ");
            flag = false;
        }
        else 
        {
  
            // for next prime 
            // to get printed
            flag = true;
        }
    }
}
}
  
// Driver Code
public static void main(String[] args)
{
    int n = 15;
    System.out.println("Following are the alternate"
                           " prime numbers smaller "
                            "than or equal to " + n );
    SieveOfEratosthenes(n);
}
}
  
// This code is contributed
// by ChitraNayal

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Python 3

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# Python 3 program to print all 
# equal to n using Sieve of Eratosthenes
  
def SieveOfEratosthenes(n):
  
    # Create a boolean array 
    # "prime[0..n]" and initialize
    # all entries it as true. A value 
    # in prime[i] will finally be false
    # if i is Not a prime, else true.
    prime = [None] * (n + 1)
    for i in range(len(prime)):
        prime[i] = True
  
    p = 2
    while p * p <= n:
  
        # If prime[p] is not changed, 
        # then it is a prime
        if (prime[p] == True):
  
            # Update all multiples of p
            for i in range(p * 2, n + 1, p):
                prime[i] = False
                  
        p += 1
  
    # Print all prime numbers
    flag = True
    for p in range(2, n + 1):
        if (prime[p]):
            if (flag):
                print(str(p), end = " ")
                flag = False
              
            else:
  
                # for next prime to get printed
                flag = True
  
# Driver Code
if __name__ == "__main__":
    n = 15
    print("Following are the alternate" + 
              " prime numbers smaller " + 
            "than or equal to " + str(n))
    SieveOfEratosthenes(n)
  
# This code is contributed 
# by ChitraNayal

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C#

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// C# program to print all primes 
// smaller than or equal to n using
// Sieve of Eratosthenes
using System;
  
class GFG 
{
static void SieveOfEratosthenes(int n)
{
      
// Create a bool array "prime[0..n]" 
// and initialize all entries it as 
// true. A value in prime[i] will 
// finally be false if i is Not a 
// prime, else true.
bool[] prime = new bool[n + 1];
for(int i = 0; i < prime.Length; i++)
    prime[i] = true;
  
for (int p = 2; p * p <= n; p++)
{
  
    // If prime[p] is not changed, 
    // then it is a prime
    if (prime[p] == true)
    {
  
        // Update all multiples of p
        for (int i = p * 2;
                 i <= n; i += p)
            prime[i] = false;
    }
}
  
// Print all prime numbers
bool flag = true;
for (int p = 2; p <= n; p++)
{
    if (prime[p]) 
    {
        if (flag)
        {
            Console.Write(p + " ");
            flag = false;
        }
        else
        {
  
            // for next prime to 
            // get printed
            flag = true;
        }
    }
}
}
  
// Driver Code
public static void Main()
{
    int n = 15;
    Console.Write("Following are the alternate"
                      " prime numbers smaller "
                 "than or equal to " + n + "\n");
    SieveOfEratosthenes(n);
}
}
  
// This code is contributed 
// by ChitraNayal

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PHP

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<?php 
// PHP program to print all 
// primes smaller than or
// equal to n using Sieve 
// of Eratosthenes
function SieveOfEratosthenes($n)
{
    // Create a boolean array 
    // "prime[0..n]" and initialize
    // all entries it as true. A value 
    // in prime[i] will finally be
    // false if i is Not a prime, else true.
    $prime = array();
    for( $i = 0; $i <= $n; $i++)
        $prime[$i] = true;
  
    for ($p = 2; $p * $p <= $n; $p++) 
    {
  
        // If prime[p] is not changed, 
        // then it is a prime
        if ($prime[$p] == true)
        {
  
            // Update all multiples of p
            for ($i = $p * 2; 
                 $i <= $n; $i += $p)
                $prime[$i] = false;
        }
    }
  
    // Print all prime numbers
    $flag = true;
    for ($p = 2; $p <= $n; $p++)
    {
        if ($prime[$p]) 
        {
            if ($flag)
            {
                echo $p . " ";
                $flag = false;
            }
            else 
            {
  
                // for next prime to
                // get printed
                $flag = true;
            }
        }
    }
}
  
// Driver Code
$n = 15;
echo "Following are the alternate".
         " prime numbers smaller ".
   "than or equal to " . $n . "\n";
SieveOfEratosthenes($n);
  
// This code is contributed 
// by ChitraNayal
?>

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Output:

Following are the alternate prime numbers smaller  than or equal to 15
2 5 11

Time complexity: O(\sqrt{N} *log(log(N))) for applying sieving and O(N) for traversing the sieve.



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Maths is the language of nature

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