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++

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// 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 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;
}

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Java

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// 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)>

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Python

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# 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.

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C#

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// 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.

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PHP

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<?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 number
function 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 code 
if (areAdjacentPrimes(11, 13, 19))
    echo "Yes";
else
    echo "No";
  
// This article is contributed by mits
?>

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Output :

No


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