Generate a list of n consecutive composite numbers (An interesting method) (original) (raw)

Last Updated : 11 Jul, 2025

Given a number n, generate a list of n composite numbers.
Examples:

Input : 5 Output : 122, 123, 124, 125

Input : 10 Output : 3628802, 3628803, 3628804, 3628805, 3628806, 3628807, 3628808, 3628809, 3628810

The idea here is using the properties of n! . Since n! = 1\times2\times3....(n-1)\times n , then numbers 1, 2, 3..... (n-1), n , all divide n! . Therefore n!+2 is divisible by 2, n!+3 is divisible by 3 ..... n!+n is divisible by n. And by above pattern they are consecutive composites.
We find (n+1)!, then we print numbers (n+1)! + 2, (n+1)! + 3, .... (n+1)! + (n + 1).
Below is the implementation of above approach:

C++ `

// CPP program to print n consecutive composite // numbers. #include using namespace std;

// function to find factorial of given // number unsigned long long int factorial(unsigned int n) {
unsigned long long int res = 1; for (int i=2; i<=n; i++) res *= i; return res; }

// Prints n consecutive numbers. void printNComposite(int n) { unsigned long long int fact = factorial(n+1); for (int i = 2; i <= n+1; ++i) cout << fact + i << " "; }

// Driver program to test above function int main() { int n = 4; printNComposite(n); return 0; }

Java

// Java program to print n consecutive composite // numbers

class GFG {

// function to find factorial of given // number static long factorial(int n) { long res = 1; for (int i = 2; i <= n; i++) { res *= i; } return res; }

// Prints n consecutive numbers. static void printNComposite(int n) { long fact = factorial(n + 1); for (int i = 2; i <= n + 1; ++i) { System.out.print(fact + i + " "); } }

// Driver program to test above function public static void main(String[] args) { int n = 4; printNComposite(n);

}

}

Python3

Python3 program to print n consecutive

composite numbers.

function to find factorial

of given number

def factorial( n):

res = 1;
for i in range(2, n + 1):
    res *= i;
return res;

Prints n consecutive numbers.

def printNComposite(n): fact = factorial(n + 1); for i in range(2, n + 2): print(fact + i, end = " ");

Driver Code

n = 4; printNComposite(n);

This code is contributed by mits

C#

// C# program to print n consecutive composite // numbers using System;

public class Program{

// function to find factorial of given // number static long factorial(int n) { long res = 1; for (int i = 2; i <= n; i++) { res *= i; } return res; }

// Prints n consecutive numbers. static void printNComposite(int n) { long fact = factorial(n + 1); for (int i = 2; i <= n + 1; ++i) { Console.Write(fact + i + " "); } }

// Driver program to test above function public static void Main() { int n = 4; printNComposite(n);

}

}

// This code is contributed by Rajput-Ji

PHP

JavaScript

`

Time Complexity: O(n)
Auxiliary Space: O(1)

The above solution causes overflow very soon (for small values of n). We can use technique to find factorial of large number to avoid overflow.