# Program to find first N Fermat Numbers

Fermat numbers are non-negative odd numbers which is valid for all values of k>=0. Only the first seven terms of the sequence are known till date. First, five terms of the series are prime but rest of them are not. The kth term of Fermat number is represented as

The sequence:

3, 5, 17, 257, 65537, 4294967297, 18446744073709551617

For a given N, the task is to find the first N Fermat numbers.

Examples:

Input: N = 4
Output: 3, 5, 17, 257

Input: N = 7
Output : 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617

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

Approach :
Using the above-mentioned formula we will find the Nth term of the series.

Below is the implementation of the above approach :

## C++

 `// CPP program to print fermat numbers ` `#include ` `#include ` `using` `namespace` `boost::multiprecision; ` `#define llu int128_t ` `using` `namespace` `std; ` ` `  `/* Iterative Function to calculate (x^y) in O(log y) */` `llu power(llu x, llu y) ` `{ ` `    ``llu res = 1; ``// Initialize result ` ` `  `    ``while` `(y > 0) { ` `        ``// If y is odd, multiply x with the result ` `        ``if` `(y & 1) ` `            ``res = res * x; ` ` `  `        ``// n must be even now ` `        ``y = y >> 1; ``// y = y/2 ` `        ``x = x * x; ``// Change x to x^2 ` `    ``} ` `    ``return` `res; ` `} ` ` `  `// Function to find nth fermat number  ` `llu Fermat(llu i) ` `{ ` `    ``// 2 to the power i ` `    ``llu power2_i = power(2, i); ` ` `  `    ``// 2 to the power 2^i ` `    ``llu power2_2_i = power(2, power2_i); ` ` `  `    ``return` `power2_2_i + 1; ` `} ` ` `  `// Function to find first n Fermat numbers ` `void` `Fermat_Number(llu n) ` `{ ` `     `  `    ``for` `(llu i = 0; i < n; i++) { ` `         `  `        ``// Calculate 2^2^i ` `        ``cout << Fermat(i); ` `         `  `        ``if``(i!=n-1) ` `            ``cout << ``", "``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``llu n = 7; ` `     `  `    ``// Function call ` `    ``Fermat_Number(n); ` ` `  `    ``return` `0; ` `} `

## Python3

 `# Python3 program to print fermat numbers ` ` `  `# Iterative Function to calculate (x^y) in O(log y)  ` `def` `power(x, y): ` ` `  `    ``res ``=` `1` `# Initialize result ` ` `  `    ``while` `(y > ``0``): ` `         `  `        ``# If y is odd,  ` `        ``# multiply x with the result ` `        ``if` `(y & ``1``): ` `            ``res ``=` `res ``*` `x ` ` `  `        ``# n must be even now ` `        ``y ``=` `y >> ``1` `# y = y/2 ` `        ``x ``=` `x ``*` `x ``# Change x to x^2 ` `    ``return` `res ` ` `  `# Function to find nth fermat number ` `def` `Fermat(i): ` `     `  `    ``# 2 to the power i ` `    ``power2_i ``=` `power(``2``, i) ` ` `  `    ``# 2 to the power 2^i ` `    ``power2_2_i ``=` `power(``2``, power2_i) ` ` `  `    ``return` `power2_2_i ``+` `1` ` `  `# Function to find first n Fermat numbers ` `def` `Fermat_Number(n): ` ` `  `    ``for` `i ``in` `range``(n): ` ` `  `        ``# Calculate 2^2^i ` `        ``print``(Fermat(i), end ``=` `"") ` ` `  `        ``if``(i !``=` `n ``-` `1``): ` `            ``print``(end ``=` `", "``) ` ` `  `# Driver code ` `n ``=` `7` ` `  `# Function call ` `Fermat_Number(n) ` ` `  `# This code is contributed by Mohit Kumar `

output:

```3, 5, 17, 257, 65537, 4294967297, 18446744073709551617
```

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Second year Department of Information Technology Jadavpur University

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