Dado un entero positivo n, imprima cada Cuatrillizo primo a continuación 
.
Prime quadruplet: en matemáticas, Prime Quadruplet es un conjunto de cuatro números primos de la forma { p, p+2, p+6, p+8 } .
Ejemplo :
Input : N = 15
Output : 5 7 11 13
Input : N = 20
Output : 5 7 11 13
11 13 17 19
Una solución simple para generar todos los cuatrillizos primos hasta n es atravesar todos los enteros positivos ‘i’ desde i=1 an y comprobar si i, i+2, i+6 e i+8 son primos o no.
Una solución eficiente es utilizar la criba de Eratóstenes para calcular previamente todos los números primos de una array en un rango determinado.
Enfoque :
- Precalcule los números primos usando Sieve Of Eratosthenes ( consulte esto )
- Recorra de i=0 a n-7 y verifique si i, i+2, i+6 e i+8 también son primos o no.
- En caso afirmativo, imprima i, i+2, i+6, i+8; de
lo contrario, incremente i y vuelva a comprobar
A continuación se muestra la implementación de la idea anterior:
C++
// CPP Program to print prime quadruplet
#include <bits/stdc++.h>
using namespace std;
#define MAX 100000
bool prime[MAX];
// Utility function to generate prime numbers
void sieve()
{
// Sieve Of Eratosthenes for generating
// prime number.
memset(prime, true, sizeof(prime));
for (int p = 2; p * p < MAX; p++) {
// If prime[p] is not changed,
// then it is a prime
if (prime[p] == true) {
// Update all multiples of p
for (int i = p * 2; i < MAX; i += p)
prime[i] = false;
}
}
}
// Function to print Prime quadruplet
void printPrimeQuad(int n)
{
for (int i = 0; i < n - 7; i++) {
if (prime[i] && prime[i + 2] && prime[i + 6]
&& prime[i + 8]) {
cout << i << " " << i + 2 << " " << i + 6
<< " " << i + 8 << "\n";
}
}
}
// Driver Code
int main()
{
sieve();
int n = 20;
printPrimeQuad(20);
return 0;
}
Java
// Java code to print prime Quarduplet in a range
import java.util.Arrays;
import java.util.Collections;
class GFG {
static final int MAX = 1000000;
static boolean[] prime = new boolean[MAX];
// utility function to generate prime number
public static void sieve()
{
// Sieve Of Eratosthenes for generating
// prime number.
// memset(prime, true, sizeof(prime));
Arrays.fill(prime, true);
for (int p = 2; p * p < MAX; p++) {
// If prime[p] is not changed,
// then it is a prime
if (prime[p] == true) {
// Update all multiples of p
for (int i = p * 2; i < MAX; i += p)
prime[i] = false;
}
}
}
// function to print prime Quadruplet
static void printPrimeQuad(int n)
{
for (int i = 0; i < n - 7; i++) {
if (prime[i] && prime[i + 2] && prime[i + 6]
&& prime[i + 8]) {
System.out.println(i + " " + (i + 2) + " "
+ (i + 6) + " " + (i + 8));
}
}
}
// Driver Code
public static void main(String[] args)
{
int n = 20;
sieve();
printPrimeQuad(n);
}
}
Python3
# Python3 Program to print # prime quadruplet # from math lib import sqrt method from math import sqrt MAX = 100000 # Sieve Of Eratosthenes for generating # prime number. prime = [True] * MAX # Utility function to generate # prime numbers def sieve() : for p in range(2, int(sqrt(MAX)) + 1) : # If prime[p] is not changed, # then it is a prime if prime[p] == True : # Update all multiples of p for i in range(p * 2 , MAX, p) : prime[i] = False # Function to print Prime quadruplet def printPrimeQuad(n) : for i in range(n - 7) : if ( prime[i] and prime[i + 2] and prime[i + 6] and prime[i + 8]) : print(i,i + 2,i + 6,i + 8) # Driver code if __name__ == "__main__" : sieve() n = 20 printPrimeQuad(20) # This code is contributed by # ANKITRAI1
C#
// C# code to print prime Quarduplet in a range
using System;
class GFG {
const int MAX = 1000000;
static bool[] prime = new bool[MAX];
// utility function to generate prime number
public static void sieve()
{
// Sieve Of Eratosthenes for generating
// prime number.
// memset(prime, true, sizeof(prime));
for(int i=0;i<MAX;i++) prime[i]=true;
for (int p = 2; p * p < MAX; p++) {
// If prime[p] is not changed,
// then it is a prime
if (prime[p] == true) {
// Update all multiples of p
for (int i = p * 2; i < MAX; i += p)
prime[i] = false;
}
}
}
// function to print prime Quadruplet
static void printPrimeQuad(int n)
{
for (int i = 0; i < n - 7; i++) {
if (prime[i] && prime[i + 2] && prime[i + 6]
&& prime[i + 8]) {
Console.WriteLine(i + " " + (i + 2) + " "
+ (i + 6) + " " + (i + 8));
}
}
}
// Driver Code
public static void Main()
{
int n = 20;
sieve();
printPrimeQuad(n);
}
}
PHP
<?php
// PHP Program to print prime quadruplet
$MAX = 100000;
// Sieve Of Eratosthenes for generating
// prime number.
$prime = array_fill(0, $MAX, true);
// Utility function to generate
// prime numbers
function sieve()
{
global $MAX, $prime;
for ($p = 2; $p * $p < $MAX; $p++)
{
// If prime[p] is not changed,
// then it is a prime
if ($prime[$p] == true)
{
// Update all multiples of p
for ($i = $p * 2; $i < $MAX; $i += $p)
$prime[$i] = false;
}
}
}
// Function to print Prime quadruplet
function printPrimeQuad($n)
{
global $MAX, $prime;
for ($i = 0; $i < $n - 7; $i++)
{
if ($prime[$i] && $prime[$i + 2] &&
$prime[$i + 6] && $prime[$i + 8])
{
echo $i . " " . ($i + 2) . " " .
($i + 6) . " " . ($i + 8) . "\n";
}
}
}
// Driver Code
sieve();
$n = 20;
printPrimeQuad(20);
// This code is contributed by mits
?>
Javascript
<script>
// Javascript Program to print prime quadruplet
var MAX = 100000;
var prime = Array(MAX).fill(true);
// Utility function to generate prime numbers
function sieve()
{
// Sieve Of Eratosthenes for generating
// prime number.
for (var p = 2; p * p < MAX; p++) {
// If prime[p] is not changed,
// then it is a prime
if (prime[p] == true) {
// Update all multiples of p
for (var i = p * 2; i < MAX; i += p)
prime[i] = false;
}
}
}
// Function to print Prime quadruplet
function printPrimeQuad(n)
{
for (var i = 0; i < n - 7; i++) {
if (prime[i] && prime[i + 2] && prime[i + 6]
&& prime[i + 8]) {
document.write( i + " " + (i + 2) + " "
+ (i + 6) + " " + (i + 8) + "<br>");
}
}
}
// Driver Code
sieve();
var n = 20;
printPrimeQuad(20);
</script>
Producción:
5 7 11 13 11 13 17 19
Ver también: