vsurhuel / goldbatchs-conjecture-in-array

Goldbach’s Conjecture in Array

Implement functions to initialize an array with random natural numbers, determine prime numbers, and find Goldbach's pair for even numbers greater than 4 in the array.

Introduction:

Goldbach’s conjecture, named after German mathematician Christian Goldbach on June 7, 1742, is a problem that states any even positive integer greater than four (4) can be expressed as the sum of two odd prime integers. For example: 10 = 5 + 5, 3 + 7

Although this conjecture holds true up to 4 x 10^18, it remains unproven that all even positive integers above 4 have a Goldbach partition. Therefore, it stands as one of the best-known unsolved problems in number theory and mathematics, remaining open for proof for more than 200 years.

Learning Outcomes:

• Implement an initialization of the array with random natural numbers.
• Implement a function to print the Goldbach’s pair of an even natural number greater than 4 in the array.

Problem Description:

1. void initArrayRandInt(int x[], int s);

   • Initializes array x of size s with random positive integers.

2. bool isPrime(int x);

   • Determines if integer x is a prime number.
   • Return 1 if x is prime, 0 otherwise.

3. bool isEven(int x);

   • Determines if integer x is an even number greater than 4.
   • Return 1 if x is even, 0 otherwise.

4. void printGoldbachsPairInArray(int x[], int s);

   • Prints the Goldbach’s pair (1 pair only) of element(s) in the array (if there are any).
   • Uses the isPrime and isEven functions.

Usage:

Call the printGoldbachsPairInArray function from the main function after initializing the array with random natural numbers using initArrayRandInt. This will display the Goldbach's pair for the even elements in the array (if there are any).

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

// Function prototypes (definitions are provided in the implementation)
void initArrayRandInt(int x[], int s);
bool isPrime(int x);
bool isEven(int x);
void printGoldbachsPairInArray(int x[], int s);

int main() {
    // Set a seed for random number generation
    srand(time(0));

    // Define the size of the array
    const int size = 10;
    
    // Create an array of size 'size'
    int array[size];

    // Initialize the array with random positive integers
    initArrayRandInt(array, size);

    // Print the Goldbach's pair for the even elements in the array
    printGoldbachsPairInArray(array, size);

    return 0;
}

How to Contribute:

Contributions to this project are welcome! If you have any suggestions, bug fixes, or improvements, please follow these steps:

1. Fork this repository.
2. Create a new branch with a descriptive name.
3. Make your changes and commit them with clear commit messages.
4. Push your changes to your forked repository.
5. Submit a pull request explaining the changes you've made.

Credits:

This problem was presented as a C++ Lab Exercise by Sir Michael Jay Anthony Regis.

License:

This project is licensed under the MIT License. See the LICENSE file for more details.