# 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.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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 number ` `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. ` `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 functions ` `int` `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 number ` `def` `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 not ` `def` `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 functions ` `if` `(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

 ` `

Output :

```No
```

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