# Check whether N is a Dihedral Prime Number or not

Given an integer N, the task is to check if N is a Dihedral prime number or not. A Dihedral prime is a prime number that can be read as itself or as another prime number when read in a seven-segment display, regardless of different orientation and surface.

Examples:

Input: N = 108881
Output: Yes

Input: N = 789
Output: No

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

Approach: Pre-calculate Prime number sieve for primality testing. Sieve of Eratosthenes can be calculated in n*logn*logn time. Run a primality test for the number and its different orientations. If the number pass the primality tests, check if any digits belong to the exclusion set [3, 4, 6, 7, 9]. Return true if the number passes both tests.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the above approach ` `#include ` `using` `namespace` `std; ` ` `  `bool` `isPrime[``int``(1e5) + 5]; ` ` `  `// Function to return the reverse ` `// of a number ` `int` `reverse(``int` `n) ` `{ ` `    ``int` `temp = n; ` `    ``int` `sum = 0; ` `    ``while` `(temp > 0) { ` `        ``int` `rem = temp % 10; ` `        ``sum = sum * 10 + rem; ` `        ``temp /= 10; ` `    ``} ` `    ``return` `sum; ` `} ` ` `  `// Function to generate mirror reflection ` `// of a number ` `int` `mirror(``int` `n) ` `{ ` `    ``int` `temp = n; ` `    ``int` `sum = 0; ` `    ``while` `(temp > 0) { ` `        ``int` `rem = temp % 10; ` `        ``if` `(rem == 2) ` `            ``rem = 5; ` `        ``else` `if` `(rem == 5) ` `            ``rem = 2; ` `        ``sum = sum * 10 + rem; ` `        ``temp /= 10; ` `    ``} ` `    ``return` `sum; ` `} ` ` `  `// Function to initialize prime number sieve ` `bool` `sieve() ` `{ ` `    ``memset``(isPrime, ``true``, ``sizeof` `isPrime); ` ` `  `    ``isPrime[0] = isPrime[1] = ``false``; ` ` `  `    ``for` `(``int` `i = 2; i <= ``int``(1e5); i++) { ` `        ``for` `(``int` `j = 2; i * j <= ``int``(1e5); j++) { ` `            ``isPrime[i * j] = ``false``; ` `        ``} ` `    ``} ` `} ` ` `  `// Function that returns true if n is ` `// Dihedral Prime number ` `bool` `isDihedralPrime(``int` `n) ` `{ ` `    ``// Check if the orientations of n  ` `    ``// is also prime ` `    ``if` `(!isPrime[n] ` `        ``|| !isPrime[mirror(n)] ` `        ``|| !isPrime[reverse(n)] ` `        ``|| !isPrime[reverse(mirror(n))]) ` `        ``return` `false``; ` ` `  `    ``int` `temp = n; ` ` `  `    ``while` `(temp > 0) { ` `        ``int` `rem = temp % 10; ` `        ``if` `(rem == 3 || rem == 4 || rem == 6 ` `            ``|| rem == 7 || rem == 9) ` `            ``return` `false``; ` `        ``temp /= 10; ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``sieve(); ` ` `  `    ``int` `n = 18181; ` `    ``if` `(isDihedralPrime(n)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the above approach  ` `import` `java.util.*; ` ` `  `class` `GFG  ` `{ ` ` `  `    ``static` `boolean``[] isPrime = ``new` `boolean``[(``int``) (1e5) + ``5``]; ` ` `  `    ``// Function to return the reverse  ` `    ``// of a number  ` `    ``static` `int` `reverse(``int` `n) ` `    ``{ ` `        ``int` `temp = n; ` `        ``int` `sum = ``0``; ` `        ``while` `(temp > ``0``) ` `        ``{ ` `            ``int` `rem = temp % ``10``; ` `            ``sum = sum * ``10` `+ rem; ` `            ``temp /= ``10``; ` `        ``} ` `        ``return` `sum; ` `    ``} ` ` `  `    ``// Function to generate mirror reflection  ` `    ``// of a number  ` `    ``static` `int` `mirror(``int` `n)  ` `    ``{ ` `        ``int` `temp = n; ` `        ``int` `sum = ``0``; ` `        ``while` `(temp > ``0``) ` `        ``{ ` `            ``int` `rem = temp % ``10``; ` `            ``if` `(rem == ``2``)  ` `            ``{ ` `                ``rem = ``5``; ` `            ``}  ` `             `  `            ``else` `if` `(rem == ``5``)  ` `            ``{ ` `                ``rem = ``2``; ` `            ``} ` `            ``sum = sum * ``10` `+ rem; ` `            ``temp /= ``10``; ` `        ``} ` `        ``return` `sum; ` `    ``} ` ` `  `    ``// Function to initialize ` `    ``// prime number sieve  ` `    ``static` `void` `sieve()  ` `    ``{ ` `        ``Arrays.fill(isPrime, ``true``); ` ` `  `        ``isPrime[``0``] = isPrime[``1``] = ``false``; ` ` `  `        ``for` `(``int` `i = ``2``;  ` `                 ``i <= (``int``) 1e5; i++) ` `        ``{ ` `            ``for` `(``int` `j = ``2``;  ` `                     ``i * j <= (``int``) 1e5; j++) ` `            ``{ ` `                ``isPrime[i * j] = ``false``; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Function that returns true if n is  ` `    ``// Dihedral Prime number  ` `    ``static` `boolean` `isDihedralPrime(``int` `n)  ` `    ``{ ` `         `  `        ``// Check if the orientations of n  ` `        ``// is also prime  ` `        ``if` `(!isPrime[n] ||  ` `            ``!isPrime[mirror(n)] ||  ` `            ``!isPrime[reverse(n)] ||  ` `            ``!isPrime[reverse(mirror(n))]) ` `        ``{ ` `            ``return` `false``; ` `        ``} ` ` `  `        ``int` `temp = n; ` ` `  `        ``while` `(temp > ``0``) ` `        ``{ ` `            ``int` `rem = temp % ``10``; ` `            ``if` `(rem == ``3` `|| rem == ``4` `||  ` `                ``rem == ``6` `|| rem == ``7` `||  ` `                ``rem == ``9``)  ` `            ``{ ` `                ``return` `false``; ` `            ``} ` `            ``temp /= ``10``; ` `        ``} ` ` `  `        ``return` `true``; ` `    ``} ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``sieve(); ` ` `  `        ``int` `n = ``18181``; ` `        ``if` `(isDihedralPrime(n)) ` `        ``{ ` `            ``System.out.println(``"Yes"``); ` `        ``} ` `        ``else`  `        ``{ ` `            ``System.out.println(``"No"``); ` `        ``} ` `    ``} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## Python3

 `# Python implementation of the above approach ` `isPrime ``=` `(``int``(``1e5``)``+``5``)``*``[``True``] ` ` `  `# Function to return the reverse ` `# of a number ` `def` `reverse(n): ` `    ``temp ``=` `n ` `    ``sum` `=` `0` `    ``while` `temp>``0``: ` `        ``rem ``=` `temp ``%` `10` `        ``sum` `=` `sum` `*` `10` `+` `rem ` `        ``temp``/``/``=` `10` ` `  `    ``return` `sum` ` `  `# Function to generate mirror reflection ` `# of a number ` `def` `mirror(n): ` `    ``temp ``=` `n ` `    ``sum` `=` `0` `    ``while` `temp>``0``: ` `        ``rem ``=` `temp ``%` `10` `        ``if` `rem ``=``=` `2``: ` `            ``rem ``=` `5` `        ``elif` `rem ``=``=` `5``: ` `            ``rem ``=` `2` `        ``sum` `=` `sum` `*` `10` `+` `rem ` `        ``temp``/``/``=` `10` ` `  `    ``return` `sum` ` `  `# Function to initialize prime number sieve ` `def` `sieve(): ` ` `  `    ``isPrime[``0``] ``=` `isPrime[``1``] ``=` `False` ` `  `    ``for` `i ``in` `range``(``2``, ``int``(``1e5``)``+``1``): ` `        ``j ``=` `2` `        ``while` `i ``*` `j<``=` `int``(``1e5``): ` `            ``isPrime[i ``*` `j] ``=` `False` `            ``j``+``=` `1` ` `  ` `  `# Function that returns true if n is ` `# Dihedral Prime number ` `def` `isDihedralPrime(n): ` `     `  `    ``# Check if the orientations of n is also prime ` `    ``if` `(``not` `isPrime[n]) ``or` `(``not` `isPrime[mirror(n)]) \ ` `        ``or` `(``not` `isPrime[reverse(n)]) \ ` `        ``or` `(``not` `isPrime[reverse(mirror(n))]): ` `        ``return` `False` ` `  `    ``temp ``=` `n ` ` `  `    ``while` `temp>``0``: ` `        ``rem ``=` `temp ``%` `10``; ` `        ``if` `rem ``=``=` `3` `or` `rem ``=``=` `4` `or` `\ ` `            ``rem ``=``=` `6` `or` `rem ``=``=` `7` `or` `rem ``=``=` `9``: ` `            ``return` `False` `        ``temp``/``/``=` `10` ` `  `    ``return` `True` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` ` `  `    ``sieve() ` `     `  `    ``n ``=` `18181` `    ``if` `isDihedralPrime(n): ` `        ``print``(``"Yes"``) ` `    ``else` `: ` `        ``print``(``"No"``) `

## C#

 `// C# implementation of the above approach ` `using` `System; ` `     `  `class` `GFG  ` `{ ` `    ``static` `Boolean[] isPrime = ``new` `Boolean[(``int``) (1e5) + 5]; ` ` `  `    ``// Function to return the reverse  ` `    ``// of a number  ` `    ``static` `int` `reverse(``int` `n) ` `    ``{ ` `        ``int` `temp = n; ` `        ``int` `sum = 0; ` `        ``while` `(temp > 0) ` `        ``{ ` `            ``int` `rem = temp % 10; ` `            ``sum = sum * 10 + rem; ` `            ``temp /= 10; ` `        ``} ` `        ``return` `sum; ` `    ``} ` ` `  `    ``// Function to generate mirror reflection  ` `    ``// of a number  ` `    ``static` `int` `mirror(``int` `n)  ` `    ``{ ` `        ``int` `temp = n; ` `        ``int` `sum = 0; ` `        ``while` `(temp > 0) ` `        ``{ ` `            ``int` `rem = temp % 10; ` `            ``if` `(rem == 2)  ` `            ``{ ` `                ``rem = 5; ` `            ``}  ` `             `  `            ``else` `if` `(rem == 5)  ` `            ``{ ` `                ``rem = 2; ` `            ``} ` `            ``sum = sum * 10 + rem; ` `            ``temp /= 10; ` `        ``} ` `        ``return` `sum; ` `    ``} ` ` `  `    ``// Function to initialize ` `    ``// prime number sieve  ` `    ``static` `void` `sieve()  ` `    ``{ ` `        ``for``(``int` `k = 0; k < isPrime.Length; k++) ` `            ``isPrime[k] = ``true``; ` ` `  `        ``isPrime[0] = isPrime[1] = ``false``; ` ` `  `        ``for` `(``int` `i = 2;  ` `                 ``i <= (``int``) 1e5; i++) ` `        ``{ ` `            ``for` `(``int` `j = 2;  ` `                     ``i * j <= (``int``) 1e5; j++) ` `            ``{ ` `                ``isPrime[i * j] = ``false``; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``// Function that returns true if n is  ` `    ``// Dihedral Prime number  ` `    ``static` `Boolean isDihedralPrime(``int` `n)  ` `    ``{ ` `         `  `        ``// Check if the orientations of n  ` `        ``// is also prime  ` `        ``if` `(!isPrime[n] ||  ` `            ``!isPrime[mirror(n)] ||  ` `            ``!isPrime[reverse(n)] ||  ` `            ``!isPrime[reverse(mirror(n))]) ` `        ``{ ` `            ``return` `false``; ` `        ``} ` ` `  `        ``int` `temp = n; ` ` `  `        ``while` `(temp > 0) ` `        ``{ ` `            ``int` `rem = temp % 10; ` `            ``if` `(rem == 3 || rem == 4 ||  ` `                ``rem == 6 || rem == 7 ||  ` `                ``rem == 9)  ` `            ``{ ` `                ``return` `false``; ` `            ``} ` `            ``temp /= 10; ` `        ``} ` ` `  `        ``return` `true``; ` `    ``} ` ` `  `    ``// Driver code  ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``sieve(); ` ` `  `        ``int` `n = 18181; ` `        ``if` `(isDihedralPrime(n)) ` `        ``{ ` `            ``Console.WriteLine(``"Yes"``); ` `        ``} ` `        ``else` `        ``{ ` `            ``Console.WriteLine(``"No"``); ` `        ``} ` `    ``} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

## PHP

 ` 0) ` `    ``{  ` `        ``\$rem` `= ``\$temp` `% 10;  ` `        ``\$sum` `= ``\$sum` `* 10 + ``\$rem``;  ` `        ``\$temp` `= ``floor``(``\$temp` `/ 10);  ` `    ``}  ` `    ``return` `\$sum``;  ` `}  ` ` `  `// Function to generate mirror reflection  ` `// of a number  ` `function` `mirror(``\$n``)  ` `{  ` `    ``\$temp` `= ``\$n``;  ` `    ``\$sum` `= 0;  ` `    ``while` `(``\$temp` `> 0)  ` `    ``{  ` `        ``\$rem` `= ``\$temp` `% 10;  ` `        ``if` `(``\$rem` `== 2)  ` `            ``\$rem` `= 5;  ` `        ``else` `if` `(``\$rem` `== 5)  ` `            ``\$rem` `= 2;  ` `        ``\$sum` `= ``\$sum` `* 10 + ``\$rem``;  ` `        ``\$temp` `= ``floor``(``\$temp` `/ 10);  ` `    ``}  ` `    ``return` `\$sum``;  ` `}  ` ` `  `// Function to initialize prime number sieve  ` `function` `sieve()  ` `{  ` `    ``\$GLOBALS``[``'isPrime'``][0] = ``\$GLOBALS``[``'isPrime'``][1] = false;  ` ` `  `    ``for` `(``\$i` `= 2; ``\$i` `<= ``floor``(1e4); ``\$i``++)  ` `    ``{  ` `        ``for` `(``\$j` `= 2; ``\$i` `* ``\$j` `<= ``floor``(1e4); ``\$j``++)  ` `        ``{  ` `            ``\$GLOBALS``[``'isPrime'``][``\$i` `* ``\$j``] = false;  ` `        ``}  ` `    ``}  ` `}  ` ` `  `// Function that returns true if n is  ` `// Dihedral Prime number  ` `function` `isDihedralPrime(``\$n``)  ` `{  ` `    ``// Check if the orientations of n  ` `    ``// is also prime  ` `    ``if` `(!``\$GLOBALS``[``'isPrime'``][``\$n``] ||  ` `        ``!``\$GLOBALS``[``'isPrime'``][mirror(``\$n``)] || ` `        ``!``\$GLOBALS``[``'isPrime'``][reverse(``\$n``)] ||  ` `        ``!``\$GLOBALS``[``'isPrime'``][reverse(mirror(``\$n``))])  ` `        ``return` `false;  ` ` `  `    ``\$temp` `= ``\$n``;  ` ` `  `    ``while` `(``\$temp` `> 0)  ` `    ``{  ` `        ``\$rem` `= ``\$temp` `% 10;  ` `        ``if` `(``\$rem` `== 3 || ``\$rem` `== 4 ||  ` `            ``\$rem` `== 6 || ``\$rem` `== 7 || ``\$rem` `== 9)  ` `            ``return` `false;  ` `             `  `        ``\$temp` `= ``floor``(``\$temp` `/ 10);  ` `    ``}  ` ` `  `    ``return` `true;  ` `}  ` ` `  `// Driver code  ` `sieve();  ` ` `  `\$n` `= 18181;  ` `if` `(isDihedralPrime(``\$n``))  ` `    ``echo` `"Yes"``;  ` `else` `    ``echo` `"No"``;  ` ` `  `// This code is contributed by Ryuga  ` `?> `

Output:

```Yes
```

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Improved By : AnkitRai01, Rajput-Ji