# Stormer Numbers

Given a number ‘n’, the task is to generate the first ‘n’ Stormer numbers.

A Stormer Number is a positive integer ‘i’ such that the greatest prime factor of the term is greater than or equal to .
For example, 5 is a Stormer number because the greatest prime factor of 26(i.e 5*5 + 1) is 13 which is greater than or equal to 10(i.e 2*5)

Input : 5
Output : 1 2 4 5 6
Here 3 is not a Stormer number because the greatest prime
factor of 10(i.e 3*3 + 1) is 5, which is not greater than
or equal to 6(i.e 2*3)

Input : 10
Output : 1 2 4 5 6 9 10 11 12 14

Approach:

1. For a number ‘i’, first find the largest prime factor of the number i*i + 1.
2. Next, test whether that prime factor is greater than or equal to 2*i.
3. If it is greater then ‘i’ is a Stormer number.

Below is the implementation of above approach:

## C/C++

 `// C++ program to print  ` `// Stormer numbers  ` `// Function to find  ` `// largest prime factor ` ` `  `#include ` `using` `namespace` `std; ` ` `  ` ``int` `maxPrimeFactors(``int` `n)  ` `{  ` `    ``// Initialize the maximum  ` `    ``// prime factor variable  ` `    ``// with the lowest one  ` `    ``int` `maxPrime = -1;  ` ` `  `    ``// Print the number of  ` `    ``// 2's that divide n  ` `    ``while``(n % 2 == 0)  ` `    ``{  ` `        ``maxPrime = 2;  ` `        ``n /= 2;  ` `    ``}  ` ` `  `    ``// n must be odd at this  ` `    ``// point, thus skip the  ` `    ``// even numbers and iterate  ` `    ``// only for odd integers  ` `    ``for``(``int` `i = 3; i < (``int``)(n * 1 /  ` `                ``2 + 1); i += 2)  ` `        ``while``(n % i == 0)  ` `        ``{  ` `            ``maxPrime = i;  ` `            ``n /= i;  ` `        ``}  ` ` `  `    ``// This condition is to handle  ` `    ``// the case when n is a prime  ` `    ``// number greater than 2  ` `    ``if` `(n > 2)  ` `        ``maxPrime = n;  ` ` `  `    ``return` `(``int``)(maxPrime);  ` `}  ` ` `  `// Function to generate  ` `// Stormer Numbers  ` ` ``int` `stormer(``int` `n)  ` `{  ` `    ``int` `i = 1;  ` `     `  `    ``// Stores the number of  ` `    ``// Stormer numbers found  ` `    ``int` `count = 0;  ` `    ``while``(count < n)  ` `    ``{  ` `        ``int` `t = i * i + 1;  ` `        ``if` `(maxPrimeFactors(t) >= 2 * i)  ` `        ``{  ` `            ``cout << i ; ` `            ``cout <<``" "``;  ` `            ``count += 1;  ` `        ``}  ` `        ``i += 1;  ` `    ``}  ` `    ``return` `i;  ` `}  ` ` `  `    ``// Driver Code  ` `int` `main() { ` ` `  `    ``int` `n = 10;  ` `    ``stormer(n);  ` ` `  `    ``}  `

## Java

 `// Java program to print  ` `// Stormer numbers  ` ` `  `// Function to find  ` `// largest prime factor  ` ` `  `import` `java.io.*; ` ` `  `class` `GFG { ` `static` `int` `maxPrimeFactors(``int` `n)  ` `{  ` `    ``// Initialize the maximum  ` `    ``// prime factor variable  ` `    ``// with the lowest one  ` `    ``int` `maxPrime = -``1``;  ` ` `  `    ``// Print the number of  ` `    ``// 2's that divide n  ` `    ``while``(n % ``2` `== ``0``)  ` `    ``{  ` `        ``maxPrime = ``2``;  ` `        ``n /= ``2``;  ` `    ``}  ` ` `  `    ``// n must be odd at this  ` `    ``// point, thus skip the  ` `    ``// even numbers and iterate  ` `    ``// only for odd integers  ` `    ``for``(``int` `i = ``3``; i < (``int``)(n * ``1` `/  ` `                ``2` `+ ``1``); i += ``2``)  ` `        ``while``(n % i == ``0``)  ` `        ``{  ` `            ``maxPrime = i;  ` `            ``n /= i;  ` `        ``}  ` ` `  `    ``// This condition is to handle  ` `    ``// the case when n is a prime  ` `    ``// number greater than 2  ` `    ``if` `(n > ``2``)  ` `        ``maxPrime = n;  ` ` `  `    ``return` `(``int``)(maxPrime);  ` `}  ` ` `  `// Function to generate  ` `// Stormer Numbers  ` `static` `int` `stormer(``int` `n)  ` `{  ` `    ``int` `i = ``1``;  ` `     `  `    ``// Stores the number of  ` `    ``// Stormer numbers found  ` `    ``int` `count = ``0``;  ` `    ``while``(count < n)  ` `    ``{  ` `        ``int` `t = i * i + ``1``;  ` `        ``if` `(maxPrimeFactors(t) >= ``2` `* i)  ` `        ``{  ` `            ``System.out.print (i +``" "``);  ` `            ``count += ``1``;  ` `        ``}  ` `        ``i += ``1``;  ` `    ``}  ` `    ``return` `i; ` `} ` ` `  `    ``// Driver Code  ` `    ``public` `static` `void` `main (String[] args) { ` `     `  `    ``int` `n = ``10``;  ` `    ``stormer(n);  ` ` `  `    ``} ` `} ` `//This code is contributed akt_mit `

## Python3

 `# Python program to print Stormer numbers ` ` `  `from` `__future__ ``import` `print_function ` ` `  `# Function to find largest prime factor ` ` `  `def` `maxPrimeFactors(n): ` `    ``# Initialize the maximum prime factor ` `    ``# variable with the lowest one ` `    ``maxPrime ``=` `-``1` ` `  `    ``# Print the number of 2's that divide n ` `    ``while` `n ``%` `2` `=``=` `0``: ` `        ``maxPrime ``=` `2` `        ``n ``/``=` `2` ` `  `    ``# n must be odd at this point, thus skip ` `    ``# the even numbers and iterate only for ` `    ``# odd integers ` `    ``for` `i ``in` `range``(``3``, ``int``(n``*``*``0.5``)``+``1``, ``2``): ` `        ``while` `n ``%` `i ``=``=` `0``: ` `            ``maxPrime ``=` `i ` `            ``n ``/``=` `i ` ` `  `    ``# This condition is to handle the case when ` `    ``# n is a prime number greater than 2 ` `    ``if` `n > ``2``: ` `        ``maxPrime ``=` `n ` ` `  `    ``return` `int``(maxPrime) ` ` `  `# Function to generate Stormer Numbers ` ` `  `def` `stormer(n): ` `    ``i ``=` `1` `    ``# Stores the number of Stormer numbers found ` `    ``count ``=` `0` `    ``while``(count < n): ` `        ``t ``=` `i ``*` `i ``+` `1` `        ``if` `maxPrimeFactors(t) >``=` `2` `*` `i: ` `            ``print``(i, end ``=``' '``) ` `            ``count ``+``=` `1` `        ``i ``+``=` `1` ` `  `# Driver Method ` ` `  `if` `__name__``=``=``'__main__'``: ` `    ``n ``=` `10` `    ``stormer(n) `

## C#

 `// C#  program to print  ` `// Stormer numbers  ` `using` `System; ` ` `  `// Function to find  ` `// largest prime factor  ` `public` `class` `GFG{ ` `     `  `    ``static` `int` `maxPrimeFactors(``int` `n)  ` `{  ` `    ``// Initialize the maximum  ` `    ``// prime factor variable  ` `    ``// with the lowest one  ` `    ``int` `maxPrime = -1;  ` ` `  `    ``// Print the number of  ` `    ``// 2's that divide n  ` `    ``while``(n % 2 == 0)  ` `    ``{  ` `        ``maxPrime = 2;  ` `        ``n /= 2;  ` `    ``}  ` ` `  `    ``// n must be odd at this  ` `    ``// point, thus skip the  ` `    ``// even numbers and iterate  ` `    ``// only for odd integers  ` `    ``for``(``int` `i = 3; i < (``int``)(n * 1 /  ` `                ``2 + 1); i += 2)  ` `        ``while``(n % i == 0)  ` `        ``{  ` `            ``maxPrime = i;  ` `            ``n /= i;  ` `        ``}  ` ` `  `    ``// This condition is to handle  ` `    ``// the case when n is a prime  ` `    ``// number greater than 2  ` `    ``if` `(n > 2)  ` `        ``maxPrime = n;  ` ` `  `    ``return` `(``int``)(maxPrime);  ` `}  ` ` `  `// Function to generate  ` `// Stormer Numbers  ` `static` `int` `stormer(``int` `n)  ` `{  ` `    ``int` `i = 1;  ` `     `  `    ``// Stores the number of  ` `    ``// Stormer numbers found  ` `    ``int` `count = 0;  ` `    ``while``(count < n)  ` `    ``{  ` `        ``int` `t = i * i + 1;  ` `        ``if` `(maxPrimeFactors(t) >= 2 * i)  ` `        ``{  ` `            ``Console.Write(i +``" "``);  ` `            ``count += 1;  ` `        ``}  ` `        ``i += 1;  ` `    ``}  ` `    ``return` `i;  ` `}  ` ` `  `    ``// Driver Code  ` `    ``static` `public` `void` `Main (){ ` `            ``int` `n = 10;  ` `            ``stormer(n);  ` ` `  `    ``}  ` `}  ` `//This code is contributed akt_mit  `

## PHP

 ` 2) ` `        ``\$maxPrime` `= ``\$n``; ` ` `  `    ``return` `(int)(``\$maxPrime``); ` `} ` ` `  `// Function to generate ` `// Stormer Numbers ` `function` `stormer(``\$n``) ` `{ ` `    ``\$i` `= 1; ` `     `  `    ``// Stores the number of  ` `    ``// Stormer numbers found ` `    ``\$count` `= 0; ` `    ``while``(``\$count` `< ``\$n``) ` `    ``{ ` `        ``\$t` `= ``\$i` `* ``\$i` `+ 1; ` `        ``if` `(maxPrimeFactors(``\$t``) >= 2 * ``\$i``) ` `        ``{ ` `            ``echo` `\$i``.``" "``; ` `            ``\$count` `+= 1; ` `        ``} ` `        ``\$i` `+= 1; ` `    ``} ` `} ` ` `  `// Driver Code ` `\$n` `= 10; ` `stormer(``\$n``); ` ` `  `// This code is contributed ` `// by mits ` `?> `

Output:

```1 2 4 5 6 9 10 11 12 14
```

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Improved By : Mithun Kumar, jit_t