# Largest number with prime digits

• Difficulty Level : Medium
• Last Updated : 15 Dec, 2022

Given a huge integer value n, find the largest integer value x such that x <= n and all the digits of x are prime.
Examples:

```Input : n = 45
Output : 37
37 is the largest number smaller than
or equal to with all prime digits.

Input : n = 1000
Output : 777

Input : n = 7721
Output : 7577

Input : n = 7221
Output : 5777```

We know that the prime digits are 2, 3, 5 and 7. Also since we have to manipulate each digit of a very large number it will be easier if we do it as a string. The main idea is to find the first non-prime digit and then
find the first digit greater than 2 in its left. Now we can replace the found digit with the prime digit that is just less than it. If the digit is 2, we have to erase it and replace the next digit with 7. After this we can replace the remaining digits to its right by 7.
Following is the implementation of the above algorithm:

## C++

 `// CPP program to find largest number smaller than``// equal to n with all prime digits.``#include ``using` `namespace` `std;` `// check if character is prime``bool` `isPrime(``char` `c)``{``    ``return` `(c == ``'2'` `|| c == ``'3'` `|| c == ``'5'` `|| c == ``'7'``);``}` `// replace with previous prime character``void` `decrease(string& s, ``int` `i)``{``    ``// if 2 erase s[i] and replace next with 7``    ``if` `(s[i] <= ``'2'``) {``        ``s.erase(i, 1);``        ``s[i] = ``'7'``;``    ``}` `    ``else` `if` `(s[i] == ``'3'``)``        ``s[i] = ``'2'``;``    ``else` `if` `(s[i] <= ``'5'``)``        ``s[i] = ``'3'``;``    ``else` `if` `(s[i] <= ``'7'``)``        ``s[i] = ``'5'``;``    ``else``        ``s[i] = ``'7'``;` `    ``return``;``}` `string primeDigits(string s)``{``    ``for` `(``int` `i = 0; i < s.length(); i++) {` `        ``// find first non prime char``        ``if` `(!isPrime(s[i])) {` `            ``// find first char greater than 2``            ``while` `(s[i] <= ``'2'` `&& i >= 0)``                ``i--;` `            ``// like 20``            ``if` `(i < 0) {``                ``i = 0;``                ``decrease(s, i);``            ``}` `            ``// like 7721``            ``else``                ``decrease(s, i);` `            ``// replace remaining with 7``            ``for` `(``int` `j = i + 1; j < s.length(); j++)``                ``s[j] = ``'7'``;           ` `            ``break``;``        ``}``    ``}` `    ``return` `s;``}` `// Driver code``int` `main()``{``    ``string s = ``"45"``;``    ``cout << primeDigits(s) << endl;` `    ``s = ``"1000"``;``    ``cout << primeDigits(s) << endl;` `    ``s = ``"7721"``;``    ``cout << primeDigits(s) << endl;` `    ``s = ``"7221"``;``    ``cout << primeDigits(s) << endl;` `    ``s = ``"74545678912345689748593275897894708927680"``;``    ``cout << primeDigits(s) << endl;` `    ``return` `0;``}`

## Java

 `// Java program to find largest number smaller than``// equal to n with all prime digits.``import` `java.io.*;``public` `class` `GFG``{` `    ``// check if character is prime``    ``public` `static` `boolean` `isPrime(``char` `c)``    ``{``        ``return` `(c == ``'2'` `|| c == ``'3'` `|| c == ``'5'` `|| c == ``'7'``);``    ``}` `    ``// replace with previous prime character``    ``public` `static` `void` `decrease(StringBuilder s, ``int` `i)``    ``{``        ``if` `(s.charAt(i) <= ``'2'``)``        ``{` `            ``// if 2 erase s[i] and replace next with 7``            ``s.deleteCharAt(i);``            ``s.setCharAt(i, ``'7'``);``        ``}``        ``else` `if` `(s.charAt(i) == ``'3'``)``            ``s.setCharAt(i, ``'2'``);``        ``else` `if` `(s.charAt(i) <= ``'5'``)``            ``s.setCharAt(i, ``'3'``);``        ``else` `if` `(s.charAt(i) <= ``'7'``)``            ``s.setCharAt(i, ``'5'``);``        ``else``            ``s.setCharAt(i, ``'7'``);` `        ``return``;``    ``}` `    ``public` `static` `String primeDigits(StringBuilder s)``    ``{``        ``for` `(``int` `i = ``0``; i < s.length(); i++)``        ``{` `            ``// find first non prime char``            ``if` `(!isPrime(s.charAt(i)))``            ``{` `                ``// find first char greater than 2``                ``while` `(i >= ``0` `&& s.charAt(i) <= ``'2'``)``                    ``i--;``                ` `                ``// like 20``                ``if` `(i < ``0``)``                ``{``                    ``i = ``0``;``                    ``decrease(s, i);``                ``}``                ` `                ``// like 7721``                ``else``                    ``decrease(s, i);` `                ``// replace remaining with 7``                ``for` `(``int` `j = i + ``1``; j < s.length(); j++)``                    ``s.setCharAt(j, ``'7'``);``                ``break``;``            ``}``        ``}` `        ``return` `s.toString();``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``StringBuilder s = ``new` `StringBuilder(``"45"``);``        ``System.out.println(primeDigits(s));` `        ``s = ``new` `StringBuilder(``"1000"``);``        ``System.out.println(primeDigits(s));` `        ``s = ``new` `StringBuilder(``"7721"``);``        ``System.out.println(primeDigits(s));` `        ``s = ``new` `StringBuilder(``"7221"``);``        ``System.out.println(primeDigits(s));` `        ``s = ``new` `StringBuilder(``"74545678912345689748593275897894708927680"``);``        ``System.out.println(primeDigits(s));``    ``}``}` `// This code is contributed by``// sanjeev2552`

## Python3

 `# Python3 program to find largest number``# smaller than equal to n with all prime digits.` `# check if character is prime``def` `isPrime(c):``    ``return` `(c ``=``=` `'2'` `or` `c ``=``=` `'3'` `or``            ``c ``=``=` `'5'` `or` `c ``=``=` `'7'``)` `# replace with previous prime character``def` `decrease(s, i):``    ` `    ``# if 2 erase s[i] and replace next with 7``    ``if` `(s[i] <``=` `'2'``):``        ``s.pop(i)``        ``s[i] ``=` `'7'``    ``elif` `(s[i] ``=``=` `'3'``):``        ``s[i] ``=` `'2'``    ``elif` `(s[i] <``=` `'5'``):``        ``s[i] ``=` `'3'``    ``elif` `(s[i] <``=` `'7'``):``        ``s[i] ``=` `'5'``    ``else``:``        ``s[i] ``=` `'7'` `def` `primeDigits(s):``    ``s ``=` `[i ``for` `i ``in` `s]``    ``i ``=` `0` `    ``while` `i < ``len``(s):` `        ``# find first non prime char``        ``if` `(isPrime(s[i]) ``=``=` `False``):` `            ``# find first char greater than 2``            ``while` `(s[i] <``=` `'2'` `and` `i >``=` `0``):``                ``i ``-``=` `1` `            ``# like 20``            ``if` `(i < ``0``):``                ``i ``=` `0``                ``decrease(s, i)``        ` `            ``# like 7721``            ``else``:``                ``decrease(s, i)` `            ``# replace remaining with 7``            ``for` `j ``in` `range``(i ``+` `1``,``len``(s)):``                ``s[j] ``=` `'7'` `            ``break``        ``i ``+``=` `1` `    ``return` `"".join(s)` `# Driver code``s ``=` `"45"``print``(primeDigits(s))` `s ``=` `"1000"``print``(primeDigits(s))` `s ``=` `"7721"``print``(primeDigits(s))` `s ``=` `"7221"``print``(primeDigits(s))` `s ``=` `"74545678912345689748593275897894708927680"``print``(primeDigits(s))` `# This code is contributed by Mohit Kumar`

## C#

 `// C# program to find largest number``// smaller than equal to n with all prime digits.``using` `System;``using` `System.Linq;``using` `System.Collections;``using` `System.Collections.Generic;``class` `HelloWorld {` `    ``// check if character is prime``    ``static` `bool` `isPrime(``char` `c)``    ``{``        ``return` `(c == ``'2'` `|| c == ``'3'` `|| c == ``'5'``                ``|| c == ``'7'``);``    ``}` `    ``// replace with previous prime character``    ``static` `char``[] decrease(``char``[] s, ``int` `i)``    ``{``        ``// if 2 erase s[i] and replace next with 7``        ``if` `(s[i] <= ``'2'``) {``            ``s = s.Where((source, index) => index != i).ToArray();``            ``s[i] = ``'7'``;``        ``}``        ``else` `if` `(s[i] == ``'3'``) {``            ``s[i] = ``'2'``;``        ``}``        ``else` `if` `(s[i] <= ``'5'``) {``            ``s[i] = ``'3'``;``        ``}``        ``else` `if` `(s[i] <= ``'7'``) {``            ``s[i] = ``'5'``;``        ``}``        ``else` `{``            ``s[i] = ``'7'``;``        ``}``        ``return` `s;``    ``}` `    ``static` `string` `primeDigits(``char``[] s)``    ``{``        ``for` `(``int` `i = 0; i < s.Length; i++) {` `            ``// find first non prime char``            ``if` `(isPrime(s[i]) == ``false``) {``                ``// find first char greater than 2``                ``while` `(i >= 0 && s[i] <= ``'2'``) {``                    ``i = i - 1;``                ``}` `                ``// like 20``                ``if` `(i < 0) {``                    ``i = 0;``                    ``s = decrease(s, i);``                ``}` `                ``// like 7721``                ``else` `{``                    ``s = decrease(s, i);``                ``}` `                ``// replace remaining with 7``                ``for` `(``int` `j = i + 1; j < s.Length; j++) {``                    ``s[j] = ``'7'``;``                ``}` `                ``break``;``            ``}``        ``}` `        ``return` `new` `string``(s);``    ``}` `    ``// Driver code``    ``static` `void` `Main()``    ``{` `        ``char``[] s = { ``'4'``, ``'5'` `};``        ``Console.WriteLine(primeDigits(s));` `        ``char``[] s1 = { ``'1'``, ``'0'``, ``'0'``, ``'0'` `};``        ``Console.WriteLine(primeDigits(s1));` `        ``char``[] s2 = { ``'7'``, ``'7'``, ``'2'``, ``'1'` `};``        ``Console.WriteLine(primeDigits(s2));` `        ``char``[] s3 = { ``'7'``, ``'2'``, ``'2'``, ``'1'` `};``        ``Console.WriteLine(primeDigits(s3));` `        ``char``[] s4``            ``= { ``'7'``, ``'4'``, ``'5'``, ``'4'``, ``'6'``, ``'7'``, ``'8'``, ``'9'``,``                ``'1'``, ``'2'``, ``'3'``, ``'4'``, ``'5'``, ``'6'``, ``'8'``, ``'9'``,``                ``'7'``, ``'4'``, ``'8'``, ``'5'``, ``'9'``, ``'3'``, ``'2'``, ``'7'``,``                ``'5'``, ``'8'``, ``'9'``, ``'7'``, ``'8'``, ``'9'``, ``'4'``, ``'7'``,``                ``'0'``, ``'8'``, ``'9'``, ``'2'``, ``'7'``, ``'6'``, ``'8'``, ``'0'` `};``        ``Console.WriteLine(primeDigits(s4));``    ``}``}` `// The code is contributed by Nidhi goel`

## PHP

 `= 0 &&``                   ``\$s``[``\$i``] <= ``'2'``)``                ``--``\$i``;` `            ``// like 20``            ``if` `(``\$i` `< 0)``            ``{``                ``\$i` `= 0;``                ``\$s` `= decrease(``\$s``, ``\$i``);``            ``}` `            ``// like 7721``            ``else``                ``\$s` `= decrease(``\$s``, ``\$i``);` `            ``// replace remaining with 7``            ``for` `(``\$j` `= ``\$i` `+ 1;``                 ``\$j` `< ``strlen``(``\$s``); ``\$j``++)``                ``\$s``[``\$j``] = ``'7'``;    ` `            ``break``;``        ``}``    ``}` `    ``return` `\$s``;``}` `// Driver code``\$s` `= ``"45"``;``echo` `primeDigits(``\$s``) . ``"\n"``;` `\$s` `= ``"1000"``;``echo` `primeDigits(``\$s``) . ``"\n"``;` `\$s` `= ``"7721"``;``echo` `primeDigits(``\$s``) . ``"\n"``;` `\$s` `= ``"7221"``;``echo` `primeDigits(``\$s``) . ``"\n"``;` `\$s` `= ``"74545678912345689748593275897894708927680"``;``echo` `primeDigits(``\$s``);` `// This code is contributed by mits.``?>`

## Javascript

 ``

Output

```37
777
7577
5777
73777777777777777777777777777777777777777
```

The time complexity of the above program is O(N) where N is the length of the string.

My Personal Notes arrow_drop_up