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Alternate Primes till N

  • Difficulty Level : Easy
  • Last Updated : 14 May, 2021

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++




/* 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
?>
Javascript



<script>
// javascript program to prvar all
// primes smaller than or
// equal to n using Naive approach.   
/*
     * Function for checking number is prime or not
     */
    function prime(num) {
        var 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
    function print_alternate_prime(n)
    {
     
        // counter is initialize with 0
        var 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 prvar prime number
                if (counter % 2 == 0)
                    document.write(num + " ");
 
                counter++;
            }
        }
    }
 
    // Driver code
    var n = 15;
    document.write("Following are the alternate " + "prime number smaller than " + "or equal to " + n+"<br/>");
 
    // Function calling
    print_alternate_prime(n);
 
// This code is contributed by Rajput-Ji
</script>
Output: 
Following are the alternate prime numbers smaller  than or equal to 15
2 5 11
 
Time Complexity: O(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
?>
Javascript



<script>
// Javascript 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.
let prime = new Array(n + 1);
for(let i = 0; i < prime.length; i++)
    prime[i] = true;
  
for (let 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 (let i = p * 2;
                 i <= n; i += p)
            prime[i] = false;
    }
}
  
// Print all prime numbers
let flag = true;
for (let p = 2; p <= n; p++)
{
    if (prime[p])
    {
        if (flag)
        {
            document.write(p + " ");
            flag = false;
        }
        else
        {
  
            // for next prime
            // to get printed
            flag = true;
        }
    }
}
}
 
// Driver Code
let  n = 15;
document.write("Following are the alternate" +
                           " prime numbers smaller " +
                            "than or equal to " + n +"<br>");
     
SieveOfEratosthenes(n);
// This code is contributed by avanitrachhadiya2155
</script>
Output: 
Following are the alternate prime numbers smaller  than or equal to 15
2 5 11
 
Time complexity: O(    *log(log(N))) for applying sieving and O(N) for traversing the sieve.
 
Attention reader! Don’t stop learning now. Get hold of all the important mathematical concepts for competitive programming with the Essential Maths for CP Course at a student-friendly price. To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.



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Article Contributed By :
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Shashank_Pathak
@Shashank_Pathak
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