/Goldbach-s-Conjecture-Tester

This Python script tests the validity of Goldbach's Conjecture, which states that every even integer greater than 2 can be expressed as the sum of two prime numbers.

Primary LanguagePython

Goldbach's Conjecture Tester

This Python script tests the validity of Goldbach's Conjecture, which states that every even integer greater than 2 can be expressed as the sum of two prime numbers.

How It Works

  1. Prime Number Check (is_prime):

    • The is_prime function efficiently determines if a given number is prime.
    • It uses optimizations for divisibility by 2 and 3, and then checks divisibility by 6k ± 1.

  2. Goldbach's Sum Check (prime_sum):

    • The prime_sum function takes an even number as input.
    • It iterates through potential prime numbers up to half the input number.
    • If it finds two prime numbers that sum up to the input, it returns them.
    • If no such pair is found, it returns None.

  3. Testing Options:

    • The script provides two testing options:
      • Option 1: Tests all even numbers starting from 4 × 10¹⁸, continuing indefinitely. This starting point is chosen because Goldbach's Conjecture has been verified for all even numbers up to 4 × 10¹⁸ through extensive computational efforts.
      • Option 2: Tests even numbers within a user-specified range.

  4. Disproving Goldbach's Conjecture:

    • If the script finds a counterexample (an even number that cannot be expressed as the sum of two primes), it writes that number to a file named "found.txt" and exits.

Usage

  1. Clone or download this repository.
  2. Run the script from your terminal: 
    python goldbach_tester.py
  3. Choose a testing option (1 or 2).
  4. If you choose Option 2, enter the desired start and end even numbers.
  5. Observe the output:
    • If a counterexample is found, it will be printed to the console and written to "found.txt".
    • Otherwise, the script will either continue indefinitely (Option 1) or finish testing the specified range (Option 2).

Disclaimer

This script is a computational tool for testing Goldbach's Conjecture. While it has not been proven false, it's important to note that this script cannot definitively prove the conjecture to be true.

Contributing

Feel free to fork this repository and contribute improvements or optimizations.

License

This project is licensed under the MIT License.

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