PYTHON CODE FOR PRIME NUMBER AND C CODE

                         PRIME NUMBER

This function takes a number n as input and returns True if the number is prime and False otherwise. The function first checks if the number is less than or equal to 1, in which case it is not prime. Then it checks whether the number is divisible by any integer between 2 and the square root of the number (inclusive). If it is divisible by any integer in that range, it is not prime; otherwise, it is prime.

You can call this function with a number like this:

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number is a number that is only divisible by 1 and itself.

For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31 are all prime numbers. However, 4, 6, 8, 9, 10, 12, and 15 are not prime numbers because they have other factors besides 1 and themselves.

Prime numbers are important in mathematics because they have unique properties that make them useful in many applications, including cryptography, number theory, and computer science. For example, many encryption algorithms rely on the fact that it is difficult to factor large numbers into their prime factors. Additionally, prime numbers are used in generating random numbers and in testing the efficiency of algorithms.

Here are 20 examples of prime numbers:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71

These are all positive integers greater than 1 that have no positive integer divisors other than 1 and themselves.

It is not feasible to list 10000 examples of prime numbers, but here's a Python code that generates a list of the first 10000 prime numbers:

def is_prime(n):
    if n <= 1:
        return False
    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            return False
    return True

print(is_prime(17))  # Output: True
print(is_prime(21))  # Output: False

...................................................................................

def generate_primes(n):

    primes = []

    num = 2

    while len(primes) < n:

        is_prime = True

        for i in range(2, int(num ** 0.5) + 1):

            if num % i == 0:

                is_prime = False

                break

        if is_prime:

            primes.append(num)

        num += 1

    return primes

print(generate_primes(10000))

This code generates a list of the first 10000 prime numbers using a simple algorithm that checks each number up to the square root of the number to see if it is divisible by any smaller number. The resulting list of prime numbers is returned by the `generate_primes` function and printed to the console.

Note that generating large prime numbers can be computationally expensive and may require more advanced algorithms for efficiency.

 C CODE FOR PRIME NUMBERS

Certainly! Here's a C code snippet that checks whether a given number is prime or not:

```c

#include <stdio.h>

int is_prime(int num) {

    if (num <= 1) {

        return 0; // Numbers less than or equal to 1 are not prime

    }

    if (num <= 3) {

        return 1; // 2 and 3 are prime

    }

    if (num % 2 == 0 || num % 3 == 0) {

        return 0; // Numbers divisible by 2 or 3 are not prime

    }

    for (int i = 5; i * i <= num; i += 6) {

        if (num % i == 0 || num % (i + 2) == 0) {

            return 0; // Numbers divisible by i or i+2 are not prime

        }

    }

    return 1; // If none of the above conditions are met, the number is prime

}

int main() {

    int number;

    printf("Enter an integer: ");

    scanf("%d", &number);

    if (is_prime(number)) {

        printf("%d is a prime number.\n", number);

    } else {

        printf("%d is not a prime number.\n", number);

    }

    return 0;

}

```

In this code:

1. We define a function `is_prime` that takes an integer `num` as input and returns `1` if it's prime and `0` if it's not.

2. Inside the `is_prime` function, we handle the special cases where `num` is less than or equal to `1`, `2`, or `3`.

3. We use a loop to check divisibility by numbers starting from `5` up to the square root of `num`. This loop is optimized to reduce the number of iterations compared to checking divisibility by all numbers up to `num`.

4. In the `main` function, we take user input, call the `is_prime` function, and print the result.

Compile and run this C code, and it will tell you whether the entered number is prime or not.