Dado un número entero N , la tarea es imprimir todos los primos seguros por debajo de N primos seguros . Un primo seguro es un número primo de la forma (2 * p) + 1 donde p también es un primo .
Los primeros primos seguros son 5, 7, 11, 23, 47,…
Ejemplos:
Entrada: N = 13
Salida: 5 7 11
5 = 2 * 2 + 1
7 = 2 * 3 + 1
11 = 2 * 5 + 1Entrada: N = 6
Salida: 5 7
Enfoque: Primero calcule previamente todos los números primos hasta N usando la criba de Eratóstenes y luego, a partir de 2 , verifique si el número primo actual también es un número primo seguro. En caso afirmativo , imprímalo; de lo contrario, salte al siguiente número principal.
A continuación se muestra la implementación del enfoque anterior:
C++
// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
// Function to print first n safe primes
void printSafePrimes(int n)
{
int prime[n + 1];
// Initialize all entries of integer array
// as 1. A value in prime[i] will finally
// be 0 if i is Not a prime, else 1
for (int i = 2; i <= n; i++)
prime[i] = 1;
// 0 and 1 are not primes
prime[0] = prime[1] = 0;
for (int p = 2; p * p <= n; p++) {
// If prime[p] is not changed, then
// it is a prime
if (prime[p] == 1) {
// Update all multiples of p
for (int i = p * 2; i <= n; i += p)
prime[i] = 0;
}
}
for (int i = 2; i <= n; i++) {
// If i is prime
if (prime[i] != 0) {
// 2p + 1
int temp = (2 * i) + 1;
// If 2p + 1 is also a prime
// then set prime[2p + 1] = 2
if (temp <= n && prime[temp] != 0)
prime[temp] = 2;
}
}
for (int i = 5; i <= n; i++)
// i is a safe prime
if (prime[i] == 2)
cout << i << " ";
}
// Driver code
int main()
{
int n = 20;
printSafePrimes(n);
return 0;
}
Java
// Java implementation of the approach
class GFG{
// Function to print first n safe primes
static void printSafePrimes(int n)
{
int prime[] = new int [n + 1];
// Initialize all entries of integer array
// as 1. A value in prime[i] will finally
// be 0 if i is Not a prime, else 1
for (int i = 2; i <= n; i++)
prime[i] = 1;
// 0 and 1 are not primes
prime[0] = prime[1] = 0;
for (int p = 2; p * p <= n; p++)
{
// If prime[p] is not changed, then
// it is a prime
if (prime[p] == 1)
{
// Update all multiples of p
for (int i = p * 2; i <= n; i += p)
prime[i] = 0;
}
}
for (int i = 2; i <= n; i++)
{
// If i is prime
if (prime[i] != 0)
{
// 2p + 1
int temp = (2 * i) + 1;
// If 2p + 1 is also a prime
// then set prime[2p + 1] = 2
if (temp <= n && prime[temp] != 0)
prime[temp] = 2;
}
}
for (int i = 5; i <= n; i++)
// i is a safe prime
if (prime[i] == 2)
System.out.print(i + " ");
}
// Driver code
public static void main(String []args)
{
int n = 20;
printSafePrimes(n);
}
}
// This code is contributed by Ryuga
Python3
# Python 3 implementation of the approach from math import sqrt # Function to print first n safe primes def printSafePrimes(n): prime = [0 for i in range(n + 1)] # Initialize all entries of integer # array as 1. A value in prime[i] # will finally be 0 if i is Not a # prime, else 1 for i in range(2, n + 1): prime[i] = 1 # 0 and 1 are not primes prime[0] = prime[1] = 0 for p in range(2, int(sqrt(n)) + 1, 1): # If prime[p] is not changed, # then it is a prime if (prime[p] == 1): # Update all multiples of p for i in range(p * 2, n + 1, p): prime[i] = 0 for i in range(2, n + 1, 1): # If i is prime if (prime[i] != 0): # 2p + 1 temp = (2 * i) + 1 # If 2p + 1 is also a prime # then set prime[2p + 1] = 2 if (temp <= n and prime[temp] != 0): prime[temp] = 2 for i in range(5, n + 1): # i is a safe prime if (prime[i] == 2): print(i, end = " ") # Driver code if __name__ == '__main__': n = 20 printSafePrimes(n) # This code is contributed by # Sanjit_Prasad
C#
// C# implementation of the approach
using System;
class GFG{
// Function to print first n safe primes
static void printSafePrimes(int n)
{
int[] prime = new int [n + 1];
// Initialize all entries of integer array
// as 1. A value in prime[i] will finally
// be 0 if i is Not a prime, else 1
for (int i = 2; i <= n; i++)
prime[i] = 1;
// 0 and 1 are not primes
prime[0] = prime[1] = 0;
for (int p = 2; p * p <= n; p++)
{
// If prime[p] is not changed, then
// it is a prime
if (prime[p] == 1)
{
// Update all multiples of p
for (int i = p * 2; i <= n; i += p)
prime[i] = 0;
}
}
for (int i = 2; i <= n; i++)
{
// If i is prime
if (prime[i] != 0)
{
// 2p + 1
int temp = (2 * i) + 1;
// If 2p + 1 is also a prime
// then set prime[2p + 1] = 2
if (temp <= n && prime[temp] != 0)
prime[temp] = 2;
}
}
for (int i = 5; i <= n; i++)
// i is a safe prime
if (prime[i] == 2)
Console.Write(i + " ");
}
// Driver code
public static void Main()
{
int n = 20;
printSafePrimes(n);
}
}
// This code is contributed by Ita_c.
PHP
<?php
// PHP implementation of the approach
// Function to print first n safe primes
function printSafePrimes($n)
{
$prime = array();
// Initialize all entries of integer array
// as 1. A value in prime[i] will finally
// be 0 if i is Not a prime, else 1
for ($i = 2; $i <= $n; $i++)
$prime[$i] = 1;
// 0 and 1 are not primes
$prime[0] = $prime[1] = 0;
for ($p = 2; $p * $p <= $n; $p++)
{
// If prime[p] is not changed,
// then it is a prime
if ($prime[$p] == 1)
{
// Update all multiples of p
for ($i = $p * 2;
$i <= $n; $i += $p)
$prime[$i] = 0;
}
}
for ($i = 2; $i <= $n; $i++)
{
// If i is prime
if ($prime[$i] != 0)
{
// 2p + 1
$temp = (2 * $i) + 1;
// If 2p + 1 is also a prime
// then set prime[2p + 1] = 2
if ($temp <= $n &&
$prime[$temp] != 0)
$prime[$temp] = 2;
}
}
for ($i = 5; $i <= $n; $i++)
// i is a safe prime
if ($prime[$i] == 2)
echo $i, " ";
}
// Driver code
$n = 20;
printSafePrimes($n);
// This code is contributed
// by aishwarya.27
?>
Javascript
<script>
// Javascript implementation of the approach
// Function to print first n safe primes
function printSafePrimes(n)
{
let prime = new Array(n + 1);
// Initialize all entries of integer array
// as 1. A value in prime[i] will finally
// be 0 if i is Not a prime, else 1
for(let i = 2; i <= n; i++)
prime[i] = 1;
// 0 and 1 are not primes
prime[0] = prime[1] = 0;
for(let p = 2; p * p <= n; p++)
{
// If prime[p] is not changed, then
// it is a prime
if (prime[p] == 1)
{
// Update all multiples of p
for(let i = p * 2; i <= n; i += p)
prime[i] = 0;
}
}
for(let i = 2; i <= n; i++)
{
// If i is prime
if (prime[i] != 0)
{
// 2p + 1
let temp = (2 * i) + 1;
// If 2p + 1 is also a prime
// then set prime[2p + 1] = 2
if (temp <= n && prime[temp] != 0)
prime[temp] = 2;
}
}
for(let i = 5; i <= n; i++)
// i is a safe prime
if (prime[i] == 2)
document.write(i + " ");
}
// Driver code
let n = 20;
printSafePrimes(n);
// This code is contributed by unknown2108
</script>
Producción:
5 7 11
Complejidad temporal: O(nlog(logn)) igual que Tamiz de Eratóstenes
Espacio Auxiliar: O(n), ya que se han tomado n espacios extra.
Publicación traducida automáticamente
Artículo escrito por mohit kumar 29 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA