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# 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
Recommended Practice

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 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 programint 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 #include  // 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 programint 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 += 1def 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 = 241print ("\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.



## Javascript



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
This article is contributed by Rahul Agrawal. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.