Los números superprimos (también conocidos como números primos de orden superior ) son la subsecuencia de números primos que ocupan posiciones de números primos dentro de la secuencia de todos los números primos. Los primeros Súper-Primos son 3, 5, 11 y 17.
La tarea es imprimir todos los Súper-Primos menores o iguales al número entero positivo N.
Ejemplos:
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
La idea es generar todos los números primos menores o iguales al número N dado usando la Criba de Eratóstenes. Una vez que hemos generado todos esos números primos, iteramos a través de todos los números y los almacenamos en la array. Una vez que hemos almacenado todos los primos en la array, iteramos a través de la array e imprimimos todos los números primos que ocupan la posición de números primos en la 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>
Producción:
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
Referencias: https://en.wikipedia.org/wiki/Super-prime
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA