Express a given number as a summation of 4 positive primes. If it is not possible to express then print “-1”.

**Examples:**

Input: 24 Output: 3 11 3 7 Explanation : 3+11+3+7 = 24 and 3, 11, 7 are all prime. Input: 46 Output: 11 11 17 7 explanation : 11+11+17+7 = 46 and 11, 7, 17 are all prime.

**Approach :** Every even integer greater than 2 can be expressed as the sum of two numbers by **Goldbach’s conjecture**.

Below are some facts for expressing a number as sum of 4 primes.

- Number must be greater than or equal to 8 as 2 is the smallest prime
- If given number is even, we can break it as (2 + 2) + x so that x remains even and can broken into two primes.
- If given number is odd, we can break it as (2 + 3) + x so that x remains even and can broken into two primes.

Now we can easily express n as sum of two primes using **link**

## C++

`// CPP program to express n as sum of 4 primes. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// funcion to check if a number is prime or not ` `int` `isPrime(` `int` `x) ` `{ ` ` ` `// does square root of the number ` ` ` `int` `s = ` `sqrt` `(x); ` ` ` ` ` `// traverse from 2 to sqrt(n) ` ` ` `for` `(` `int` `i = 2; i <= s; i++) ` ` ` ` ` `// if any divisor found then non prime ` ` ` `if` `(x % i == 0) ` ` ` `return` `0; ` ` ` ` ` `// if no divisor is found then it is a prime ` ` ` `return` `1; ` `} ` ` ` `void` `Num(` `int` `x, ` `int` `& a, ` `int` `& b) ` `{ ` ` ` `// iterates to check prime or not ` ` ` `for` `(` `int` `i = 2; i <= x / 2; i++) { ` ` ` ` ` `// calls function to check if i and x-i ` ` ` `// is prime or not ` ` ` `if` `(isPrime(i) && isPrime(x - i)) { ` ` ` ` ` `a = i; ` ` ` `b = x - i; ` ` ` ` ` `// if two prime numbers are found, ` ` ` `// then return ` ` ` `return` `; ` ` ` `} ` ` ` `} ` `} ` ` ` `// function to generate 4 prime numbers adding upto n ` `void` `generate(` `int` `n) ` `{ ` ` ` `// if n<=7 then 4 numbers cannot sum to ` ` ` `// get that number ` ` ` `if` `(n <= 7) ` ` ` `cout << ` `"Impossible to form"` `<< endl; ` ` ` ` ` `// a and b stores the last two numbers ` ` ` `int` `a, b; ` ` ` ` ` `// if it is not even then 2 and 3 are first ` ` ` `// two of sequence ` ` ` `if` `(n % 2 != 0) { ` ` ` ` ` `// calls the function to get the other ` ` ` `// two prime numbers considering first two ` ` ` `// primes as 2 and 3 (Note 2 + 3 = 5) ` ` ` `Num(n - 5, a, b); ` ` ` ` ` `// print 2 and 3 as the firsts two prime ` ` ` `// and a and b as the last two. ` ` ` `cout << ` `"2 3 "` `<< a << ` `" "` `<< b << endl; ` ` ` `} ` ` ` ` ` `// if it is even then 2 and 2 are first two ` ` ` `// of sequence ` ` ` `else` `{ ` ` ` ` ` `/// calls the function to get the other ` ` ` `// two prime numbers considering first two ` ` ` `// primes as 2 and 2 (Note 2 + 2 = 4) ` ` ` `Num(n - 4, a, b); ` ` ` ` ` `// print 2 and 2 as the firsts two prime ` ` ` `// and a and b as the last two. ` ` ` `cout << ` `"2 2 "` `<< a << ` `" "` `<< b << endl; ` ` ` `} ` `} ` ` ` `// driver program to test the above function ` `int` `main() ` `{ ` ` ` `int` `n = 28; ` ` ` `generate(n); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java program to express n as sum of ` `// 4 primes. ` `class` `GFG { ` ` ` ` ` `static` `int` `a = ` `0` `, b = ` `0` `; ` ` ` ` ` `// funcion to check if a number ` ` ` `// is prime or not ` ` ` `static` `int` `isPrime(` `int` `x) ` ` ` `{ ` ` ` ` ` `// does square root of the ` ` ` `// number ` ` ` `int` `s = (` `int` `)Math.sqrt(x); ` ` ` ` ` `// traverse from 2 to sqrt(n) ` ` ` `for` `(` `int` `i = ` `2` `; i <= s; i++) ` ` ` ` ` `// if any divisor found ` ` ` `// then non prime ` ` ` `if` `(x % i == ` `0` `) ` ` ` `return` `0` `; ` ` ` ` ` `// if no divisor is found ` ` ` `// then it is a prime ` ` ` `return` `1` `; ` ` ` `} ` ` ` ` ` `static` `void` `Num(` `int` `x) ` ` ` `{ ` ` ` ` ` `// iterates to check prime ` ` ` `// or not ` ` ` `for` `(` `int` `i = ` `2` `; i <= x / ` `2` `; i++) { ` ` ` ` ` `// calls function to check ` ` ` `// if i and x-i is prime ` ` ` `// or not ` ` ` `if` `(isPrime(i) != ` `0` `&& isPrime(x - i) != ` `0` `) { ` ` ` ` ` `a = i; ` ` ` `b = x - i; ` ` ` ` ` `// if two prime numbers ` ` ` `// are found, then return ` ` ` `return` `; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` ` ` `// function to generate 4 prime ` ` ` `// numbers adding upto n ` ` ` `static` `void` `generate(` `int` `n) ` ` ` `{ ` ` ` ` ` `// if n<=7 then 4 numbers cannot ` ` ` `// sum to get that number ` ` ` `if` `(n <= ` `7` `) ` ` ` `System.out.println(` `"Impossible"` ` ` `+ ` `" to form"` `); ` ` ` ` ` `// if it is not even then 2 and 3 ` ` ` `// are first two of sequence ` ` ` `if` `(n % ` `2` `!= ` `0` `) { ` ` ` ` ` `// calls the function to get the ` ` ` `// other two prime numbers ` ` ` `// considering first two primes ` ` ` `// as 2 and 3 (Note 2 + 3 = 5) ` ` ` `Num(n - ` `5` `); ` ` ` ` ` `// print 2 and 3 as the firsts ` ` ` `// two prime and a and b as the ` ` ` `// last two. ` ` ` `System.out.println(` `"2 3 "` `+ a + ` `" "` `+ b); ` ` ` `} ` ` ` ` ` `// if it is even then 2 and 2 are ` ` ` `// first two of sequence ` ` ` `else` `{ ` ` ` ` ` `/// calls the function to get the ` ` ` `// other two prime numbers ` ` ` `// considering first two primes as ` ` ` `// 2 and 2 (Note 2 + 2 = 4) ` ` ` `Num(n - ` `4` `); ` ` ` ` ` `// print 2 and 2 as the firsts ` ` ` `// two prime and a and b as the ` ` ` `// last two. ` ` ` `System.out.println(` `"2 2 "` `+ a + ` `" "` `+ b); ` ` ` `} ` ` ` `} ` ` ` ` ` `// Driver function to test the above ` ` ` `// function ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `int` `n = ` `28` `; ` ` ` ` ` `generate(n); ` ` ` `} ` `} ` ` ` `// This code is contributed by Anant Agarwal. ` |

*chevron_right*

*filter_none*

## Python3

`# Python3 program to express ` `# n as sum of 4 primes. ` `import` `math; ` `# funcion to check if a ` `# number is prime or not ` `def` `isPrime(x): ` ` ` `# does square root ` ` ` `# of the number ` ` ` `s ` `=` `int` `(math.sqrt(x)) ` ` ` ` ` `# traverse from 2 to sqrt(n) ` ` ` `for` `i ` `in` `range` `(` `2` `,s` `+` `1` `): ` ` ` `# if any divisor found ` ` ` `# then non prime ` ` ` `if` `(x ` `%` `i ` `=` `=` `0` `): ` ` ` `return` `0` ` ` `# if no divisor is found ` ` ` `# then it is a prime ` ` ` `return` `1` ` ` `def` `Num(x): ` ` ` `# iterates to check ` ` ` `# prime or not ` ` ` `ab` `=` `[` `0` `]` `*` `2` ` ` `for` `i ` `in` `range` `(` `2` `,` `int` `(x ` `/` `2` `)` `+` `1` `): ` ` ` `# calls function to check ` ` ` `# if i and x-i is prime ` ` ` `# or not ` ` ` `if` `(isPrime(i) !` `=` `0` `and` `isPrime(x ` `-` `i) !` `=` `0` `): ` ` ` `ab[` `0` `] ` `=` `i ` ` ` `ab[` `1` `] ` `=` `x ` `-` `i ` ` ` `# if two prime numbers ` ` ` `# are found, then return ` ` ` `return` `ab ` ` ` `# function to generate 4 prime ` `# numbers adding upto n ` `def` `generate(n): ` ` ` `# if n<=7 then 4 numbers cannot ` ` ` `# sum to get that number ` ` ` `if` `(n <` `=` `7` `): ` ` ` `print` `(` `"Impossible to form"` `) ` ` ` ` ` `# if it is not even then 2 and ` ` ` `# 3 are first two of sequence ` ` ` ` ` `if` `(n ` `%` `2` `!` `=` `0` `): ` ` ` `# calls the function to get ` ` ` `# the other two prime numbers ` ` ` `# considering first two primes ` ` ` `# as 2 and 3 (Note 2 + 3 = 5) ` ` ` `ab` `=` `Num(n ` `-` `5` `) ` ` ` ` ` `# print 2 and 3 as the firsts ` ` ` `# two prime and a and b as the ` ` ` `# last two. ` ` ` `print` `(` `"2 3"` `,ab[` `0` `],ab[` `1` `]) ` ` ` ` ` `# if it is even then 2 and 2 are ` ` ` `# first two of sequence ` ` ` `else` `: ` ` ` `# calls the function to get ` ` ` `# the other two prime numbers ` ` ` `# considering first two primes ` ` ` `# as 2 and 2 (Note 2 + 2 = 4) ` ` ` `ab` `=` `Num(n ` `-` `4` `) ` ` ` ` ` `# print 2 and 2 as the firsts ` ` ` `# two prime and a and b as the ` ` ` `# last two. ` ` ` `print` `(` `"2 2"` `,ab[` `0` `],ab[` `1` `]) ` ` ` `# Driver Code ` `if` `__name__` `=` `=` `'__main__'` `: ` ` ` `n ` `=` `28` ` ` `generate(n) ` ` ` `# This code is contributed by mits. ` |

*chevron_right*

*filter_none*

## C#

`// C# program to express n as sum of ` `// 4 primes. ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `static` `int` `a = 0, b = 0; ` ` ` ` ` `// funcion to check if a number ` ` ` `// is prime or not ` ` ` `static` `int` `isPrime(` `int` `x) ` ` ` `{ ` ` ` ` ` `// does square root of the ` ` ` `// number ` ` ` `int` `s = (` `int` `)Math.Sqrt(x); ` ` ` ` ` `// traverse from 2 to sqrt(n) ` ` ` `for` `(` `int` `i = 2; i <= s; i++) ` ` ` ` ` `// if any divisor found ` ` ` `// then non prime ` ` ` `if` `(x % i == 0) ` ` ` `return` `0; ` ` ` ` ` `// if no divisor is found ` ` ` `// then it is a prime ` ` ` `return` `1; ` ` ` `} ` ` ` ` ` `static` `void` `Num(` `int` `x) ` ` ` `{ ` ` ` ` ` `// iterates to check prime ` ` ` `// or not ` ` ` `for` `(` `int` `i = 2; i <= x / 2; i++) ` ` ` `{ ` ` ` ` ` `// calls function to check ` ` ` `// if i and x-i is prime ` ` ` `// or not ` ` ` `if` `(isPrime(i) != 0 && ` ` ` `isPrime(x - i) != 0) ` ` ` `{ ` ` ` ` ` `a = i; ` ` ` `b = x - i; ` ` ` ` ` `// if two prime numbers ` ` ` `// are found, then return ` ` ` `return` `; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` ` ` `// function to generate 4 prime ` ` ` `// numbers adding upto n ` ` ` `static` `void` `generate(` `int` `n) ` ` ` `{ ` ` ` ` ` `// if n<=7 then 4 numbers cannot ` ` ` `// sum to get that number ` ` ` `if` `(n <= 7) ` ` ` `Console.Write(` `"Impossible"` ` ` `+ ` `" to form"` `); ` ` ` ` ` `// if it is not even then 2 and ` ` ` `// 3 are first two of sequence ` ` ` `if` `(n % 2 != 0) { ` ` ` ` ` `// calls the function to get ` ` ` `// the other two prime numbers ` ` ` `// considering first two primes ` ` ` `// as 2 and 3 (Note 2 + 3 = 5) ` ` ` `Num(n - 5); ` ` ` ` ` `// print 2 and 3 as the firsts ` ` ` `// two prime and a and b as the ` ` ` `// last two. ` ` ` `Console.Write(` `"2 3 "` `+ a + ` `" "` ` ` `+ b); ` ` ` `} ` ` ` ` ` `// if it is even then 2 and 2 are ` ` ` `// first two of sequence ` ` ` `else` `{ ` ` ` ` ` `/// calls the function to get ` ` ` `// the other two prime numbers ` ` ` `// considering first two primes ` ` ` `// as 2 and 2 (Note 2 + 2 = 4) ` ` ` `Num(n - 4); ` ` ` ` ` `// print 2 and 2 as the firsts ` ` ` `// two prime and a and b as the ` ` ` `// last two. ` ` ` `Console.Write(` `"2 2 "` `+ a + ` `" "` ` ` `+ b); ` ` ` `} ` ` ` `} ` ` ` ` ` `// Driver function to test the above ` ` ` `// function ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `int` `n = 28; ` ` ` ` ` `generate(n); ` ` ` `} ` `} ` ` ` `// This code is contributed by nitin mittal. ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// PHP program to express ` `// n as sum of 4 primes. ` `$a` `= 0; ` `$b` `= 0; ` ` ` `// funcion to check if a ` `// number is prime or not ` `function` `isPrime(` `$x` `) ` `{ ` ` ` `// does square root ` `// of the number ` `$s` `= (int)(sqrt(` `$x` `)); ` ` ` `// traverse from 2 to sqrt(n) ` `for` `(` `$i` `= 2; ` `$i` `<= ` `$s` `; ` `$i` `++) ` ` ` `// if any divisor found ` `// then non prime ` `if` `(` `$x` `% ` `$i` `== 0) ` `return` `0; ` ` ` `// if no divisor is found ` `// then it is a prime ` `return` `1; ` `} ` ` ` `function` `Num(` `$x` `) ` `{ ` `global` `$a` `; ` `global` `$b` `; ` ` ` `// iterates to check ` `// prime or not ` `for` `(` `$i` `= 2; ` ` ` `$i` `<= (int)(` `$x` `/ 2); ` `$i` `++) ` `{ ` ` ` `// calls function to check ` `// if i and x-i is prime ` `// or not ` `if` `(isPrime(` `$i` `) != 0 && ` ` ` `isPrime(` `$x` `- ` `$i` `) != 0) ` ` ` `{ ` ` ` `$a` `= ` `$i` `; ` ` ` `$b` `= ` `$x` `- ` `$i` `; ` ` ` ` ` `// if two prime numbers ` ` ` `// are found, then return ` ` ` `return` `; ` ` ` `} ` `} ` `} ` ` ` `// function to generate 4 prime ` `// numbers adding upto n ` `function` `generate(` `$n` `) ` `{ ` `global` `$a` `; ` `global` `$b` `; ` ` ` `// if n<=7 then 4 numbers cannot ` `// sum to get that number ` `if` `(` `$n` `<= 7) ` ` ` `echo` `"Impossible to form"` `; ` ` ` `// if it is not even then 2 and ` `// 3 are first two of sequence ` `if` `(` `$n` `% 2 != 0) ` `{ ` ` ` `// calls the function to get ` ` ` `// the other two prime numbers ` ` ` `// considering first two primes ` ` ` `// as 2 and 3 (Note 2 + 3 = 5) ` ` ` `Num(` `$n` `- 5); ` ` ` ` ` `// print 2 and 3 as the firsts ` ` ` `// two prime and a and b as the ` ` ` `// last two. ` ` ` `echo` `"2 3 $a $b"` `; ` `} ` ` ` `// if it is even then 2 and 2 are ` `// first two of sequence ` `else` `{ ` ` ` `// calls the function to get ` ` ` `// the other two prime numbers ` ` ` `// considering first two primes ` ` ` `// as 2 and 2 (Note 2 + 2 = 4) ` ` ` `Num(` `$n` `- 4); ` ` ` ` ` `// print 2 and 2 as the firsts ` ` ` `// two prime and a and b as the ` ` ` `// last two. ` ` ` `echo` `"2 2 $a $b"` `; ` `} ` `} ` ` ` `// Driver Code ` `$n` `= 28; ` `generate(` `$n` `); ` ` ` `// This code is contributed by mits. ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

2 2 5 19

**Time complexity:** O(n sqrt(n))

**Auxiliary space:** O(1)

This article is contributed by **Raja Vikramaditya** If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.