# Largest palindromic prime in an array

Given an array arr[] of integers, the task is to print the largest palindromic prime from the array. If no element from the array is a palindromic prime then print -1.

Examples:

Input: arr[] = {11, 5, 121, 7, 89}
Output: 11
11, 5 and 7 are the only primes from the array which are palindromes.
11 is the maximum among them.

Input: arr[] = {2, 4, 6, 8, 10}
Output: 2

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

A simple approach is to go through every array element, check if it is prime and check if it is palindrome. If yes, the update the result if it is greater than current result also.

Efficient approach for large number of elements:

• Use Sieve of Eratosthenes to calculate whether a number is prime or not upto the maximum element from the array.
• Now, initialize a variable currentMax = -1 and start traversing the array arr[].
• For every i, if arr[i] is prime as well as palindrome and arr[i] > currentMax then update currentMax = arr[i].
• Print currentMax in the end.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function that returns true if n is a palindrome ` `bool` `isPal(``int` `n) ` `{ ` `    ``// Find the appropriate divisor ` `    ``// to extract the leading digit ` `    ``int` `divisor = 1; ` `    ``while` `(n / divisor >= 10) ` `        ``divisor *= 10; ` ` `  `    ``while` `(n != 0) { ` `        ``int` `leading = n / divisor; ` `        ``int` `trailing = n % 10; ` ` `  `        ``// If first and last digit ` `        ``// not same return false ` `        ``if` `(leading != trailing) ` `            ``return` `false``; ` ` `  `        ``// Removing the leading and trailing ` `        ``// digit from number ` `        ``n = (n % divisor) / 10; ` ` `  `        ``// Reducing divisor by a factor ` `        ``// of 2 as 2 digits are dropped ` `        ``divisor = divisor / 100; ` `    ``} ` `    ``return` `true``; ` `} ` ` `  `// Function to return the largest ` `// palindromic prime present in the array ` `int` `maxPalindromicPrime(``int` `arr[], ``int` `n) ` `{ ` `    ``int` `maxElement = *max_element(arr, arr + n); ` ` `  `    ``// Create a boolean array "prime[0..n]" and ` `    ``// initialize all entries it as true. A value ` `    ``// in prime[i] will finally be false if i is ` `    ``// Not a prime, else true. ` `    ``bool` `prime[maxElement + 1]; ` `    ``memset``(prime, ``true``, ``sizeof``(prime)); ` ` `  `    ``// 0 and 1 are not primes ` `    ``prime = prime = ``false``; ` `    ``for` `(``int` `p = 2; p * p <= maxElement; p++) { ` ` `  `        ``// If prime[p] is not changed, then it is ` `        ``// a prime ` `        ``if` `(prime[p] == ``true``) { ` ` `  `            ``// Update all multiples of p ` `            ``for` `(``int` `i = p * 2; i <= maxElement; i += p) ` `                ``prime[i] = ``false``; ` `        ``} ` `    ``} ` ` `  `    ``int` `currentMax = -1; ` `    ``for` `(``int` `i = 0; i < n; i++) ` ` `  `        ``// If arr[i] is prime as well as palindrome ` `        ``if` `(prime[arr[i]] && isPal(arr[i])) ` `            ``currentMax = max(currentMax, arr[i]); ` ` `  `    ``return` `currentMax; ` `} ` ` `  `// Driver Program ` `int` `main() ` `{ ` `    ``int` `arr[] = { 11, 5, 121, 7, 89 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `    ``cout << maxPalindromicPrime(arr, n); ` `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach  ` ` `  `import` `java.util.Arrays; ` `public` `class` `GFG{ ` `  `  `    ``// Function that returns true if n is a palindrome  ` `    ``static` `boolean` `isPal(``int` `n)  ` `    ``{  ` `        ``// Find the appropriate divisor  ` `        ``// to extract the leading digit  ` `        ``int` `divisor = ``1``;  ` `        ``while` `(n / divisor >= ``10``)  ` `            ``divisor *= ``10``;  ` `      `  `        ``while` `(n != ``0``) {  ` `            ``int` `leading = n / divisor;  ` `            ``int` `trailing = n % ``10``;  ` `      `  `            ``// If first and last digit  ` `            ``// not same return false  ` `            ``if` `(leading != trailing)  ` `                ``return` `false``;  ` `      `  `            ``// Removing the leading and trailing  ` `            ``// digit from number  ` `            ``n = (n % divisor) / ``10``;  ` `      `  `            ``// Reducing divisor by a factor  ` `            ``// of 2 as 2 digits are dropped  ` `            ``divisor = divisor / ``100``;  ` `        ``}  ` `        ``return` `true``;  ` `    ``}  ` `      `  `    ``// Function to return the largest  ` `    ``// palindromic prime present in the array  ` `    ``static` `int` `maxPalindromicPrime(``int` `[]arr, ``int` `n)  ` `    ``{  ` `        ``int` `maxElement = Arrays.stream(arr).max().getAsInt(); ` `      `  `        ``// Create a boolean array "prime[0..n]" and  ` `        ``// initialize all entries it as true. A value  ` `        ``// in prime[i] will finally be false if i is  ` `        ``// Not a prime, else true.  ` `        ``boolean` `[]prime = ``new` `boolean``[maxElement + ``1``];  ` `        ``for` `(``int` `i = ``0``; i < maxElement + ``1` `; i++) ` `            ``prime[i] = ``true` `; ` `  `  `        ``// 0 and 1 are not primes  ` `        ``prime[``0``] = prime[``1``] = ``false``;  ` `        ``for` `(``int` `p = ``2``; p * p <= maxElement; p++) {  ` `      `  `            ``// If prime[p] is not changed, then it is  ` `            ``// a prime  ` `            ``if` `(prime[p] == ``true``) {  ` `      `  `                ``// Update all multiples of p  ` `                ``for` `(``int` `i = p * ``2``; i <= maxElement; i += p)  ` `                    ``prime[i] = ``false``;  ` `            ``}  ` `        ``}  ` `      `  `        ``int` `currentMax = -``1``;  ` `        ``for` `(``int` `i = ``0``; i < n; i++)  ` `      `  `            ``// If arr[i] is prime as well as palindrome  ` `            ``if` `(prime[arr[i]] == ``true` `&& isPal(arr[i]) == ``true``)  ` `                ``currentMax = Math.max(currentMax, arr[i]);  ` `      `  `        ``return` `currentMax;  ` `    ``}  ` `      `  `    ``// Driver Program  ` `     ``public` `static` `void` `main(String []args) ` `    ``{  ` `        ``int` `[]arr = { ``11``, ``5``, ``121``, ``7``, ``89` `};  ` `        ``int` `n = arr.length ; ` `        ``System.out.println(maxPalindromicPrime(arr, n)) ;  ` `    ``}  ` `      `  `} ` `// This code is contributed by 29AjayKumar  `

## Python3

 `# Python 3 implementation of the approach ` `from` `math ``import` `sqrt ` ` `  `# Function that returns true  ` `# if n is a palindrome ` `def` `isPal(n): ` `     `  `    ``# Find the appropriate divisor ` `    ``# to extract the leading digit ` `    ``divisor ``=` `1` `    ``while` `(n ``/` `divisor >``=` `10``): ` `        ``divisor ``*``=` `10` ` `  `    ``while` `(n !``=` `0``): ` `        ``leading ``=` `int``(n ``/` `divisor) ` `        ``trailing ``=` `n ``%` `10` ` `  `        ``# If first and last digit ` `        ``# not same return false ` `        ``if` `(leading !``=` `trailing): ` `            ``return` `False` ` `  `        ``# Removing the leading and trailing ` `        ``# digit from number ` `        ``n ``=` `int``((n ``%` `divisor) ``/` `10``) ` ` `  `        ``# Reducing divisor by a factor ` `        ``# of 2 as 2 digits are dropped ` `        ``divisor ``=` `int``(divisor ``/` `100``) ` `     `  `    ``return` `True` ` `  `# Function to return the largest ` `# palindromic prime present in the array ` `def` `maxPalindromicPrime(arr, n): ` `    ``maxElement ``=` `arr[``0``] ` `    ``for` `i ``in` `range``(``len``(arr)): ` `        ``if` `(arr[i]>maxElement): ` `            ``maxElement ``=` `arr[i] ` ` `  `    ``# Create a boolean array "prime[0..n]" and ` `    ``# initialize all entries it as true. A value ` `    ``# in prime[i] will finally be false if i is ` `    ``# Not a prime, else true. ` `    ``prime ``=` `[``True` `for` `i ``in` `range``(maxElement ``+` `1``)] ` ` `  `    ``# 0 and 1 are not primes ` `    ``prime[``0``] ``=` `False` `    ``prime[``1``] ``=` `False` `    ``for` `p ``in` `range``(``2``, ``int``(sqrt(maxElement)) ``+` `1``, ``1``): ` `         `  `        ``# If prime[p] is not changed, ` `        ``# then it is a prime ` `        ``if` `(prime[p] ``=``=` `True``): ` `             `  `            ``# Update all multiples of p ` `            ``for` `i ``in` `range``(p ``*` `2``,maxElement ``+` `1``, p): ` `                ``prime[i] ``=` `False` `     `  `    ``currentMax ``=` `-``1` `    ``for` `i ``in` `range``(n): ` `         `  `        ``# If arr[i] is prime as well as palindrome ` `        ``if` `(prime[arr[i]] ``and` `isPal(arr[i])): ` `            ``currentMax ``=` `max``(currentMax, arr[i]) ` ` `  `    ``return` `currentMax ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``arr ``=` `[``11``, ``5``, ``121``, ``7``, ``89``] ` `    ``n ``=` `len``(arr) ` `    ``print``(maxPalindromicPrime(arr, n)) ` ` `  `# This code is contributed by ` `# Shashank_Shamra `

## C#

 `// C# implementation of the above approach  ` ` `  `using` `System ; ` `using` `System.Linq ; ` ` `  `public` `class` `GFG{ ` ` `  `    ``// Function that returns true if n is a palindrome  ` `    ``static` `bool` `isPal(``int` `n)  ` `    ``{  ` `        ``// Find the appropriate divisor  ` `        ``// to extract the leading digit  ` `        ``int` `divisor = 1;  ` `        ``while` `(n / divisor >= 10)  ` `            ``divisor *= 10;  ` `     `  `        ``while` `(n != 0) {  ` `            ``int` `leading = n / divisor;  ` `            ``int` `trailing = n % 10;  ` `     `  `            ``// If first and last digit  ` `            ``// not same return false  ` `            ``if` `(leading != trailing)  ` `                ``return` `false``;  ` `     `  `            ``// Removing the leading and trailing  ` `            ``// digit from number  ` `            ``n = (n % divisor) / 10;  ` `     `  `            ``// Reducing divisor by a factor  ` `            ``// of 2 as 2 digits are dropped  ` `            ``divisor = divisor / 100;  ` `        ``}  ` `        ``return` `true``;  ` `    ``}  ` `     `  `    ``// Function to return the largest  ` `    ``// palindromic prime present in the array  ` `    ``static` `int` `maxPalindromicPrime(``int` `[]arr, ``int` `n)  ` `    ``{  ` `        ``int` `maxElement = arr.Max() ; ` `     `  `        ``// Create a boolean array "prime[0..n]" and  ` `        ``// initialize all entries it as true. A value  ` `        ``// in prime[i] will finally be false if i is  ` `        ``// Not a prime, else true.  ` `        ``bool` `[]prime = ``new` `bool` `[maxElement + 1];  ` `        ``for` `(``int` `i = 0; i < maxElement + 1 ; i++) ` `            ``prime[i] = ``true` `; ` ` `  `        ``// 0 and 1 are not primes  ` `        ``prime = prime = ``false``;  ` `        ``for` `(``int` `p = 2; p * p <= maxElement; p++) {  ` `     `  `            ``// If prime[p] is not changed, then it is  ` `            ``// a prime  ` `            ``if` `(prime[p] == ``true``) {  ` `     `  `                ``// Update all multiples of p  ` `                ``for` `(``int` `i = p * 2; i <= maxElement; i += p)  ` `                    ``prime[i] = ``false``;  ` `            ``}  ` `        ``}  ` `     `  `        ``int` `currentMax = -1;  ` `        ``for` `(``int` `i = 0; i < n; i++)  ` `     `  `            ``// If arr[i] is prime as well as palindrome  ` `            ``if` `(prime[arr[i]] == ``true` `&& isPal(arr[i]) == ``true``)  ` `                ``currentMax = Math.Max(currentMax, arr[i]);  ` `     `  `        ``return` `currentMax;  ` `    ``}  ` `     `  `    ``// Driver Program  ` `     ``public` `static` `void` `Main() ` `    ``{  ` `        ``int` `[]arr = { 11, 5, 121, 7, 89 };  ` `        ``int` `n = arr.Length ; ` `        ``Console.WriteLine(maxPalindromicPrime(arr, n)) ;  ` `    ``}  ` `     `  `    ``// This code is contributed by Ryuga ` `} `

## PHP

 `= 10) ` `        ``\$divisor` `*= 10; ` ` `  `    ``while` `(``\$n` `!= 0) ` `    ``{ ` `        ``\$leading` `= (int)(``\$n` `/ ``\$divisor``); ` `        ``\$trailing` `= ``\$n` `% 10; ` ` `  `        ``// If first and last digit ` `        ``// not same return false ` `        ``if` `(``\$leading` `!= ``\$trailing``) ` `            ``return` `false; ` ` `  `        ``// Removing the leading and trailing ` `        ``// digit from number ` `        ``\$n` `= (int)((``\$n` `% ``\$divisor``) / 10); ` ` `  `        ``// Reducing divisor by a factor ` `        ``// of 2 as 2 digits are dropped ` `        ``\$divisor` `= (int)(``\$divisor` `/ 100); ` `    ``} ` `    ``return` `true; ` `} ` ` `  `// Function to return the largest ` `// palindromic prime present in the array ` `function` `maxPalindromicPrime(``\$arr``, ``\$n``) ` `{ ` `    ``\$maxElement` `= max(``\$arr``); ` ` `  `    ``// Create a boolean array "prime[0..n]" and ` `    ``// initialize all entries it as true. A value ` `    ``// in prime[i] will finally be false if i is ` `    ``// Not a prime, else true. ` `    ``\$prime` `= ``array_fill``(0, (``\$maxElement` `+ 1), true); ` ` `  `    ``// 0 and 1 are not primes ` `    ``\$prime`` = ``\$prime`` = false; ` `    ``for` `(``\$p` `= 2; ``\$p` `* ``\$p` `<= ``\$maxElement``; ``\$p``++)  ` `    ``{ ` ` `  `        ``// If prime[p] is not changed,  ` `        ``// then it is a prime ` `        ``if` `(``\$prime``[``\$p``] == true)  ` `        ``{ ` ` `  `            ``// Update all multiples of p ` `            ``for` `(``\$i` `= ``\$p` `* 2;  ` `                 ``\$i` `<= ``\$maxElement``; ``\$i` `+= ``\$p``) ` `                ``\$prime``[``\$i``] = false; ` `        ``} ` `    ``} ` ` `  `    ``\$currentMax` `= -1; ` `    ``for` `(``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++) ` ` `  `        ``// If arr[i] is prime as well as palindrome ` `        ``if` `(``\$prime``[``\$arr``[``\$i``]] && isPal(``\$arr``[``\$i``])) ` `            ``\$currentMax` `= max(``\$currentMax``, ``\$arr``[``\$i``]); ` ` `  `    ``return` `\$currentMax``; ` `} ` ` `  `// Driver Code ` `\$arr` `= ``array``( 11, 5, 121, 7, 89 ); ` `\$n` `= ``count``(``\$arr``); ` `echo` `maxPalindromicPrime(``\$arr``, ``\$n``); ` ` `  `// This code is contributed by mits ` `?> `

Output:

```11
```

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