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# Super Prime

• Difficulty Level : Easy
• Last Updated : 25 Mar, 2023

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 = isPrime = ``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 ` `#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 = isPrime = ``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 = isPrime = ``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

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## Javascript

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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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