Alternate Primes till N - GeeksforGeeks

We have to print alternate prime numbers till N.

Examples:

Input : N = 10
Output : 2 5 

Input : N = 15
Output : 2 5 11

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

/* 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 

Java

// 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 

Python3

# 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) 
         

C#

// 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 

PHP

<?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 
?> 

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++

// 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; 
} 

Java

// 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 

Python 3

# 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 

C#

// 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 

PHP

<?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 
?> 

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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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

PHP

C++

Java

Python 3

C#

PHP

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