Super Prime

2.2

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++

// 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;
        }
    }
}

// Primts 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;
}

Python

# 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],

n = 241
print "Super-Primes less than or equal to ", n, " are :n",
superPrimes(n)

# Contributed by: Afzal


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 

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 contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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