Check whether given three numbers are adjacent primes - GeeksforGeeks

12 May, 2022
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 whether the 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++
Java
Python
C#
PHP
Javascript
// CPP program to check given three numbers are// primes are not. #include <bits/stdc++.h>using namespace std; // checks whether 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 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 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 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)>
# 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 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.
// 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 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 program to check given// three numbers are primes or not. // checks whether 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 != $b)        return false;     // If next is    // not same as 'c'    if (nextPrime($b) != $c)        return false;     return true;} // Driver codeif (areAdjacentPrimes(11, 13, 19))    echo "Yes";else    echo "No"; // This article is contributed by mits?>
<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 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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