Dado un número n positivo, la tarea es verificar si el número dado es Interprime o no. Si el número dado es Interprime, escriba ‘SÍ’. De lo contrario, escriba ‘NO’.
Interprime : en matemáticas, un interprime es un número entero positivo que representa el promedio de dos números primos impares consecutivos.
Los primeros interprimos son:
4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99
Ejemplos:
Entrada: 12
Salida: SÍ
Explicación: 12 es el promedio de los números primos consecutivos 11 y 13.
Entrada: 20
Salida: NO
Una solución simple de este problema es generar números primos y verificar si podemos obtener el promedio dado de números primos impares consecutivos o no.
Acercarse :
- Comience a generar el número primo ‘p’ de i=3 al número primo p > n
- si encontramos el promedio de p y p+1 como el número dado n, entonces deténgase e imprima ‘SÍ’
- Si no encontramos tal p y p+1 con el promedio dado, imprima ‘NO’.
Una solución eficiente es verificar el promedio de los números primos p1 y p2 únicamente, de modo que p1 y p2 sean consecutivos y p1 < n < p2.
Acercarse :
- calcular los números primos consecutivos p1 y p2. tal que p1 < n < p2.
- calcular el promedio de p1 y p2.
- Imprimir ‘SÍ’ si obtenemos el promedio dado De lo contrario, imprimir ‘NO’.
C++
// CPP program to check if a number is
// interprime or not
#include <bits/stdc++.h>
using namespace std;
// Function to check if a number is prime or not
bool isPrime(int n)
{
// Corner cases
if (n <= 1)
return false;
if (n <= 3)
return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0)
return false;
for (int i = 5; i * i <= n; i = i + 6) {
if (n % i == 0 || n % (i + 2) == 0) {
return false;
}
}
return true;
}
// Function to check
// if the given number is interprime or not
bool isInterprime(int n)
{
// Smallest Interprime is 4
// So the number less than 4
// can not be a Interprime
if (n < 4)
return false;
int prev_prime = n;
int next_prime = n;
// Calculate first prime number < n
while (!isPrime(prev_prime)) {
prev_prime--;
}
// Calculate first prime number > n
while (!isPrime(next_prime)) {
next_prime++;
}
// Check if prev_prime and next_prime
// have the same average
if ((prev_prime + next_prime) == 2 * n)
return true;
else
return false;
}
int main()
{
int n = 9;
if (isInterprime(n))
cout << "YES";
else
cout << "NO";
return 0;
}
Java
// JAVA program to check if a number is
// interprime or not
class GFG {
// Function to check if a number is prime or not
static boolean isPrime(int n)
{
// Corner cases
if (n <= 1)
return false;
if (n <= 3)
return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0)
return false;
for (int i = 5; i * i <= n; i = i + 6) {
if (n % i == 0 || n % (i + 2) == 0) {
return false;
}
}
return true;
}
// Function to check
// if the given number is interprime or not
static boolean isInterprime(int n)
{
// Smallest Interprime is 4
// So the number less than 4
// can not be a Interprime
if (n < 4)
return false;
int prev_prime = n;
int next_prime = n;
// Calculate first prime number < n
while (!isPrime(prev_prime)) {
prev_prime--;
}
// Calculate first prime number > n
while (!isPrime(next_prime)) {
next_prime++;
}
// check if next_prime and prev_prime
// have the same average
if ((prev_prime + next_prime) == 2 * n)
return true;
else
return false;
}
public static void main(String[] args)
{
int n = 9;
if (isInterprime(n))
System.out.println("YES");
else
System.out.println("NO");
}
}
Python3
# Python 3 program to check if a number is
# interprime or not
# Utility function to check
# if a number is prime or not
def isPrime(n) :
# Corner cases
if (n <= 1) :
return False
if (n <= 3) :
return True
# This is checked so that we can skip
# middle five numbers in below loop
if (n % 2 == 0 or n % 3 == 0) :
return False
i = 5
while (i * i <= n) :
if (n % i == 0 or n % (i + 2) == 0) :
return False
i = i + 6
return True
# Function to check
# if the given number is interprime or not
def isInterprime( n):
# Smallest Interprime is 4
# So the number less than 4
# can not be a Interprime
if (n < 4):
return False
prev_prime = n
next_prime = n
# Calculate first prime number < n
while (isPrime(prev_prime)== 0):
prev_prime = prev_prime-1
# Calculate first prime number > n
while (isPrime(next_prime)== 0):
next_prime = next_prime + 1
# check if next_prime and prev_prime
# have the same average
if ((prev_prime + next_prime)== 2 * n):
return True
else:
return False
n = 9
if(isInterprime(n)):
print("YES")
else:
print("NO")
C#
// C# program to check if a number is
// interprime or not
using System;
class GFG {
// Function to check if a number is prime or not
static bool isPrime(int n)
{
// Corner cases
if (n <= 1)
return false;
if (n <= 3)
return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0)
return false;
for (int i = 5; i * i <= n; i = i + 6) {
if (n % i == 0 || n % (i + 2) == 0) {
return false;
}
}
return true;
}
// Function to check
// if the given number is interprime or not
static bool isInterprime(int n)
{
// Smallest Interprime is 4
// So the number less than 4
// can not be a Interprime
if (n < 4)
return false;
int prev_prime = n;
int next_prime = n;
// Calculate first prime number < n
while (!isPrime(prev_prime)) {
prev_prime--;
}
// Calculate first prime number > n
while (!isPrime(next_prime)) {
next_prime++;
}
// check if next_prime and prev_prime
// have the same average
if ((prev_prime + next_prime) == 2 * n)
return true;
else
return false;
}
public static void Main()
{
int n = 9;
if (isInterprime(n))
Console.WriteLine("YES");
else
Console.WriteLine("NO");
}
}
PHP
<?php
// PHP program to check if a
// number is interprime or not
// Function to check if a
// number is prime or not
function isPrime($n)
{
// Corner cases
if ($n <= 1)
return false;
if ($n <= 3)
return true;
// This is checked so that we
// can skip middle five numbers
// in below loop
if ($n % 2 == 0 or $n % 3 == 0)
return false;
for ($i = 5;
$i * $i <= $n; $i = $i + 6)
{
if ($n % $i == 0 or
$n % ($i + 2) == 0)
{
return false;
}
}
return true;
}
// Function to check if the
// given number is interprime or not
function isInterprime($n)
{
// Smallest Interprime is 4
// So the number less than 4
// can not be a Interprime
if ($n < 4)
return false;
$prev_prime = $n;
$next_prime = $n;
// Calculate first prime
// number < n
while (!isPrime($prev_prime))
{
$prev_prime--;
}
// Calculate first prime
// number > n
while (!isPrime($next_prime))
{
$next_prime++;
}
// Check if prev_prime and
// next_prime have the same average
if (($prev_prime +
$next_prime) == 2 * $n)
return true;
else
return false;
}
// Driver Code
$n = 9;
if (isInterprime($n))
echo "YES";
else
echo "NO";
// This code is contributed
// by Shashank
?>
Javascript
<script>
// Javascript program to check if a number is
// interprime or not
// Function to check if a number is prime or not
function isPrime(n)
{
// Corner cases
if (n <= 1)
return false;
if (n <= 3)
return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0)
return false;
for (var i = 5; i * i <= n; i = i + 6) {
if (n % i == 0 || n % (i + 2) == 0) {
return false;
}
}
return true;
}
// Function to check
// if the given number is interprime or not
function isInterprime(n)
{
// Smallest Interprime is 4
// So the number less than 4
// can not be a Interprime
if (n < 4)
return false;
var prev_prime = n;
var next_prime = n;
// Calculate first prime number < n
while (!isPrime(prev_prime)) {
prev_prime--;
}
// Calculate first prime number > n
while (!isPrime(next_prime)) {
next_prime++;
}
// Check if prev_prime and next_prime
// have the same average
if ((prev_prime + next_prime) == 2 * n)
return true;
else
return false;
}
var n = 9;
if (isInterprime(n))
document.write( "YES");
else
document.write( "NO");
// This code is contributed by noob2000.
</script>
Producción:
YES