Check whether given three numbers are adjacent primes
Given three numbers and check whether they are adjacent primes are not. Three prime numbers are said to be adjacent primes if there is no prime between them.
Examples :
Input : 2, 3, 5 Output : Yes Explanation: 2, 3, 5 are adjacent primes. Input : 11, 13, 19 Output : No Explanation: 11, 13, 19 are not adjacent primes. Because there exits 17 between 13 and 19 which is prime.
Approach:
We already know what is a prime number. Here we need to check weather given three numbers are adjacent primes or not. First we check given three numbers are prime or not. After that we will find next prime of first number and second number. If satisfies the condition of adjacent primes then it is clear that given three numbers are adjacent primes otherwise not.
C++
// CPP program to check given three numbers are// primes are not.#include <bits/stdc++.h>using namespace std;// checks weather given number is prime or not.bool isPrime(int n){ // check if n is a multiple of 2 if (n % 2 == 0) return false; // if not, then just check the odds for (int i = 3; i * i <= n; i += 2) if (n % i == 0) return false; return true;}// return next prime numberint nextPrime(int start){ // start with next number. int next = start + 1; // breaks after finding next prime number while (!isPrime(next)) next++; return next;}// check given three numbers are adjacent primes are not.bool areAdjacentPrimes(int a, int b, int c){ // check given three numbers are primes are not. if (!isPrime(a) || !isPrime(b) || !isPrime(c)) return false; // find next prime of a int next = nextPrime(a); // If next is not same as 'a' if (next != b) return false; // If next next is not same as 'c' if (nextPrime(b) != c) return false; return true;}// Driver code for above functionsint main(){ if (areAdjacentPrimes(11, 13, 19)) cout << "Yes"; else cout << "No"; return 0;} |
Java
// Java program to check given three numbers are// primes are not.import java.io.*;import java.util.*;class GFG{ public static boolean isPrime(int n) { // check if n is a multiple of 2 if (n % 2 == 0) return false; // if not, then just check the odds for (int i = 3; i * i <= n; i += 2) if (n % i == 0) return false; return true; } // return next prime number public static int nextPrime(int start) { // start with next number. int next = start + 1; // breaks after finding next prime number while (!isPrime(next)) next++; return next; } // check given three numbers are adjacent primes are not. public static boolean areAdjacentPrimes(int a, int b, int c) { // check given three numbers are primes are not. if (!isPrime(a) || !isPrime(b) || !isPrime(c)) return false; // find next prime of a int next = nextPrime(a); // If next is not same as 'a' if (next != b) return false; // If next next is not same as 'c' if (nextPrime(b) != c) return false; return true; } // Driver code for above functions public static void main (String[] args) { if (areAdjacentPrimes(11, 13, 19)) System.out.print("Yes"); else System.out.print("No"); }}// Mohit Gupta_OMG <(o_0)> |
Python
# Python3 program to check given # three numbers are primes are not.# Function checks whether given number is prime or not.def isPrime(n) : # Check if n is a multiple of 2 if (n % 2 == 0) : return False # If not, then just check the odds i = 3 while( i*i <= n) : if (n % i == 0) : return False i = i + 2 return True # Return next prime numberdef nextPrime(start) : # Start with next number nxt = start + 1 # Breaks after finding next prime number while (isPrime(nxt) == False) : nxt = nxt + 1 return nxt# Check given three numbers# are adjacent primes are notdef areAdjacentPrimes(a, b, c) : # Check given three numbers are primes are not if (isPrime(a) == False or isPrime(b) == False or isPrime(c) == False) : return False # Find next prime of a nxt = nextPrime(a) # If next is not same as 'a' if (nxt != b) : return False # If next next is not same as 'c' if (nextPrime(b) != c) : return False return True # Driver code for above functionsif (areAdjacentPrimes(11, 13, 19)) : print( "Yes"),else : print( "No") #This code is contributed by NIKITA TIWARI. |
C#
// Java program to check given three numbers are// primes are not.using System;class GFG{ public static bool isPrime(int n) { // check if n is a multiple of 2 if (n % 2 == 0) return false; // if not, then just check the odds for (int i = 3; i * i <= n; i += 2) if (n % i == 0) return false; return true; } // return next prime number public static int nextPrime(int start) { // start with next number. int next = start + 1; // breaks after finding next prime number while (!isPrime(next)) next++; return next; } // check given three numbers are adjacent primes are not. public static bool areAdjacentPrimes(int a, int b, int c) { // check given three numbers are primes are not. if (!isPrime(a) || !isPrime(b) || !isPrime(c)) return false; // find next prime of a int next = nextPrime(a); // If next is not same as 'a' if (next != b) return false; // If next next is not same as 'c' if (nextPrime(b) != c) return false; return true; } // Driver code public static void Main () { if (areAdjacentPrimes(11, 13, 19)) Console.WriteLine("Yes"); else Console.WriteLine("No"); }}// This article is contributed by vt_m. |
PHP
<?php// PHP program to check given// three numbers are primes or not.// checks weather given// number is prime or not.function isPrime($n){ // check if n is // a multiple of 2 if ($n % 2 == 0) return false; // if not, then just // check the odds for ($i = 3; $i * $i <= $n; $i += 2) if ($n % $i == 0) return false; return true;}// return next prime numberfunction nextPrime($start){ // start with next number. $next = $start + 1; // breaks after finding // next prime number while (!isPrime($next)) $next++; return $next;}// check given three numbers// are adjacent primes are not.function areAdjacentPrimes($a, $b, $c){ // check given three numbers // are primes are not. if (!isPrime($a) || !isPrime($b) || !isPrime($c)) return false; // find next prime of a $next = nextPrime($a); // If next is not same as 'a' if ($next != $b) return false; // If next next is // not same as 'c' if (nextPrime($b) != $c) return false; return true;}// Driver codeif (areAdjacentPrimes(11, 13, 19)) echo "Yes";else echo "No";// This article is contributed by mits?> |
Javascript
<script>// JavaScript program to check given// three numbers are// primes are not. function isPrime(n) { // check if n is a multiple of 2 if (n % 2 == 0) return false; // if not, then just check the odds for (let i = 3; i * i <= n; i += 2) if (n % i == 0) return false; return true; } // return next prime number function nextPrime(start) { // start with next number. let next = start + 1; // breaks after finding next prime number while (!isPrime(next)) next++; return next; } // check given three numbers are // adjacent primes are not. function areAdjacentPrimes(a, b, c) { // check given three numbers are primes are not. if (!isPrime(a) || !isPrime(b) || !isPrime(c)) return false; // find next prime of a let next = nextPrime(a); // If next is not same as 'a' if (next != b) return false; // If next next is not same as 'c' if (nextPrime(b) != c) return false; return true; }// Driver code if (areAdjacentPrimes(11, 13, 19)) document.write("Yes"); else document.write("No"); </script> |
Output :
No
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