Super Prime

Super-prime numbers (also known as higher order primes) are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. First few Super-Primes are 3, 5, 11 and 17. 
The task is to print all the Super-Primes less than or equal to the given positive integer N.

Examples:

Input: 7
Output: 3 5 
3 is super prime because it appears at second
position in list of primes (2, 3, 5, 7, 11, 13, 
17, 19, 23, ...) and 2 is also prime. Similarly
5 appears at third position and 3 is a prime.

Input: 17
Output: 3 5 11 17

The idea is to generate all the primes less than or equal to the given number N using Sieve of Eratosthenes. Once we have generated all such primes, we iterate through all numbers and store it in the array. Once we have stored all the primes in the array, we iterate through the array and print all prime number which occupies prime number position in the array. 

C++

// C++ program to print super primes less than  or equal to n.
#include <bits/stdc++.h>
using namespace std;

// Generate all prime numbers less than n.
bool SieveOfEratosthenes(int n, bool isPrime[])
{
    // Initialize all entries of boolean array as true. A
    // value in isPrime[i] will finally be false if i is Not
    // a prime, else true bool isPrime[n+1];
    isPrime[0] = isPrime[1] = false;
    for (int i = 2; i <= n; i++)
        isPrime[i] = true;

    for (int p = 2; p * p <= n; p++) {
        // If isPrime[p] is not changed, then it is  a prime
        if (isPrime[p] == true) {
            // Update all multiples of p
            for (int i = p * 2; i <= n; i += p)
                isPrime[i] = false;
        }
    }
}

// Prints all super primes less than or equal to n.
void superPrimes(int n)
{
    // Generating primes using Sieve
    bool isPrime[n + 1];
    SieveOfEratosthenes(n, isPrime);

    // Storing all the primes generated in a an array
    // primes[]
    int primes[n + 1], j = 0;
    for (int p = 2; p <= n; p++)
        if (isPrime[p])
            primes[j++] = p;

    // Printing all those prime numbers that occupy prime
    // numbered position in sequence of prime numbers.
    for (int k = 0; k < j; k++)
        if (isPrime[k + 1])
            cout << primes[k] << " ";
}

// Driven program
int main()
{
    int n = 241;
    cout << "Super-Primes less than or equal to " << n
         << " are :" << endl;
    superPrimes(n);
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

C

// C program to print super primes less than  or equal to n.
#include <stdbool.h>
#include <stdio.h>

// Generate all prime numbers less than n.
bool SieveOfEratosthenes(int n, bool isPrime[])
{
    // Initialize all entries of boolean array as true. A
    // value in isPrime[i] will finally be false if i is Not
    // a prime, else true bool isPrime[n+1];
    isPrime[0] = isPrime[1] = false;
    for (int i = 2; i <= n; i++)
        isPrime[i] = true;

    for (int p = 2; p * p <= n; p++) {
        // If isPrime[p] is not changed, then it is  a prime
        if (isPrime[p] == true) {
            // Update all multiples of p
            for (int i = p * 2; i <= n; i += p)
                isPrime[i] = false;
        }
    }
}

// Prints all super primes less than or equal to n.
void superPrimes(int n)
{
    // Generating primes using Sieve
    bool isPrime[n + 1];
    SieveOfEratosthenes(n, isPrime);

    // Storing all the primes generated in a an array
    // primes[]
    int primes[n + 1], j = 0;
    for (int p = 2; p <= n; p++)
        if (isPrime[p])
            primes[j++] = p;

    // Printing all those prime numbers that occupy prime
    // numbered position in sequence of prime numbers.
    for (int k = 0; k < j; k++)
        if (isPrime[k + 1])
            printf("%d ", primes[k]);
}

// Driven program
int main()
{
    int n = 241;
    printf("Super-Primes less than or equal to %d are :\n", n);
    superPrimes(n);
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

Java

// Java program to print super primes less than or equal to n.
import java.io.*;

class GFG {

    // Generate all prime numbers less than n.
    static void SieveOfEratosthenes(int n, boolean isPrime[])
    {
        // Initialize all entries of boolean array as true.
        // A value in isPrime[i] will finally be false if i
        // is Not a prime, else true bool isPrime[n+1];
        isPrime[0] = isPrime[1] = false;
        for (int i = 2; i <= n; i++)
            isPrime[i] = true;

        for (int p = 2; p * p <= n; p++) {
            // If isPrime[p] is not changed, then it is a prime
            if (isPrime[p] == true) {
                // Update all multiples of p
                for (int i = p * 2; i <= n; i += p)
                    isPrime[i] = false;
            }
        }
    }

    // Prints all super primes less than or equal to n.
    static void superPrimes(int n)
    {

        // Generating primes using Sieve
        boolean isPrime[] = new boolean[n + 1];
        SieveOfEratosthenes(n, isPrime);

        // Storing all the primes generated in a an array primes[]
        int primes[] = new int[n + 1];
        int j = 0;

        for (int p = 2; p <= n; p++)
            if (isPrime[p])
                primes[j++] = p;

        // Printing all those prime numbers that occupy prime
        // numbered position in sequence of prime numbers.
        for (int k = 0; k < j; k++)
            if (isPrime[k + 1])
                System.out.print(primes[k] + " ");
    }

    // Driven program
    public static void main(String args[])
    {
        int n = 241;
        System.out.println(
            "Super-Primes less than or equal to " + n + " are :");
        superPrimes(n);
    }
}

// This code is contributed by Aditya Kumar (adityakumar129)

Python3

# Python program to print super primes less than
# or equal to n.

# Generate all prime numbers less than n.
def SieveOfEratosthenes(n, isPrime):
    # Initialize all entries of boolean array
    # as true. A value in isPrime[i] will finally
    # be false if i is Not a prime, else true
    # bool isPrime[n+1]
    isPrime[0] = isPrime[1] = False
    for i in range(2,n+1):
        isPrime[i] = True

    for p in range(2,n+1):
        # If isPrime[p] is not changed, then it is
        # a prime
        if (p*p<=n and isPrime[p] == True):
            # Update all multiples of p
            for i in range(p*2,n+1,p):
                isPrime[i] = False
                p += 1
def superPrimes(n):

    # Generating primes using Sieve
    isPrime = [1 for i in range(n+1)]
    SieveOfEratosthenes(n, isPrime)

    # Storing all the primes generated in a
    # an array primes[]
    primes = [0 for i in range(2,n+1)]
    j = 0
    for p in range(2,n+1):
       if (isPrime[p]):
           primes[j] = p
           j += 1

    # Printing all those prime numbers that
    # occupy prime numbered position in
    # sequence of prime numbers.
    for k in range(j):
        if (isPrime[k+1]):
            print (primes[k],end=" ")

n = 241
print ("\nSuper-Primes less than or equal to ", n, " are :",)
superPrimes(n)
# Contributed by: Afzal

C#

// Program to print super primes
// less than or equal to n.
using System;

class GFG {

    // Generate all prime
    // numbers less than n.
    static void SieveOfEratosthenes(int n, bool[] isPrime)
    {
        // Initialize all entries of boolean
        // array as true. A value in isPrime[i]
        // will finally be false if i is Not
        // a prime, else true bool isPrime[n+1];
        isPrime[0] = isPrime[1] = false;

        for (int i = 2; i <= n; i++)
            isPrime[i] = true;

        for (int p = 2; p * p <= n; p++) {
            // If isPrime[p] is not changed,
            // then it is a prime
            if (isPrime[p] == true) {
                // Update all multiples of p
                for (int i = p * 2; i <= n; i += p)
                    isPrime[i] = false;
            }
        }
    }

    // Prints all super primes less
    // than or equal to n.
    static void superPrimes(int n)
    {

        // Generating primes using Sieve
        bool[] isPrime = new bool[n + 1];
        SieveOfEratosthenes(n, isPrime);

        // Storing all the primes generated
        // in a an array primes[]
        int[] primes = new int[n + 1];
        int j = 0;

        for (int p = 2; p <= n; p++)
            if (isPrime[p])
                primes[j++] = p;

        // Printing all those prime numbers
        // that occupy prime number position
        // in sequence of prime numbers.
        for (int k = 0; k < j; k++)
            if (isPrime[k + 1])
                Console.Write(primes[k] + " ");
    }

    // Driven program
    public static void Main()
    {
        int n = 241;
        Console.WriteLine("Super-Primes less than or equal to "
                          + n + " are :");
        superPrimes(n);
    }
}

// This code is contributed by Anant Agarwal.

PHP

<?php
// PHP program to print super primes
// less than or equal to n.

// Generate all prime numbers less than n.
function SieveOfEratosthenes($n, &$isPrime)
{
    // Initialize all entries of boolean array
    // as true. A value in isPrime[i] will
    // finally be false if i is Not a prime,
    // else true bool isPrime[n+1];
    $isPrime[0] = $isPrime[1] = false;
    for ($i = 2; $i <= $n; $i++)
        $isPrime[$i] = true;

    for ($p = 2; $p * $p <= $n; $p++)
    {
        // If isPrime[p] is not changed,
        // then it is a prime
        if ($isPrime[$p] == true)
        {
            // Update all multiples of p
            for ($i = $p * 2; $i <= $n; $i += $p)
                $isPrime[$i] = false;
        }
    }
}

// Prints all super primes less
// than or equal to n.
function superPrimes($n)
{
    // Generating primes using Sieve
    $isPrime = array_fill(0, $n + 1, false);
    SieveOfEratosthenes($n, $isPrime);

    // Storing all the primes generated
    // in a an array primes[]
    $primes = array_fill(0, $n + 1, 0);
    $j = 0;
    for ($p = 2; $p <= $n; $p++)
    if ($isPrime[$p])
        $primes[$j++] = $p;

    // Printing all those prime numbers
    // that occupy prime numbered position
    // in sequence of prime numbers.
    for ($k = 0; $k < $j; $k++)
        if ($isPrime[$k + 1])
            echo $primes[$k] . " ";
}

// Driver Code
$n = 241;
echo "Super-Primes less than or equal to " .
                            $n . " are :\n";
superPrimes($n);

// This code is contributed by mits
?>

Javascript

<script>

// JavaScript program to print super
// primes less than or equal to n.

    // Generate all prime
    // numbers less than n.
    function SieveOfEratosthenes
                (n, isPrime)
    {
        // Initialize all entries of boolean
        // array as true. A value in isPrime[i]
        // will finally be false if i is Not
        // a prime, else true bool isPrime[n+1];
        isPrime[0] = isPrime[1] = false;
        for (let i = 2; i <= n; i++)
            isPrime[i] = true;

        for (let p = 2; p * p <= n; p++)
        {
            // If isPrime[p] is not changed,
            // then it is a prime
            if (isPrime[p] == true)
            {
                // Update all multiples of p
                for (let i = p * 2; i <= n; i += p)
                    isPrime[i] = false;
            }
        }
    }

    // Prints all super primes less
    // than or equal to n.
    function superPrimes(n)
    {

        // Generating primes using Sieve
        let isPrime = [];
        SieveOfEratosthenes(n, isPrime);

        // Storing all the primes generated
        // in a an array primes[]
        let primes = [];
        let j = 0;

        for (let p = 2; p <= n; p++)
            if (isPrime[p] != 0)
                primes[j++] = p;

        // Printing all those prime numbers that
        // occupy prime numbered position in
        // sequence of prime numbers.
        for (let k = 0; k < j; k++)
            if (isPrime[k + 1])
                document.write(primes[k]+ " ");
    }

// Driver Code
        let n = 241;
        document.write("Super-Primes less than or equal to "
                            +n+" are :" + "<br/>");
        superPrimes(n);

// This code is contributed by code_hunt.
</script>

Output:

Super-Primes less than or equal to 241 are :
3 5 11 17 31 41 59 67 83 109 127 157 179 191 211 241 

Time complexity : – O(n*log(log(n)))
Auxiliary Space:- O(N)

References: https://en.wikipedia.org/wiki/Super-prime
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