Number of Primes and Twin Primes

This project introduces a formula I developed as a shortcut to determine the number of prime numbers or twin primes between 1 and $P_{n}$#. It simplifies the process, providing an efficient way to calculate these values without relying on traditional, computationally expensive methods.

The included SageMath code allows you to test and validate the formula, making it a practical tool for exploring prime number distributions.

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About the Method

The formula helps calculate:

1. Prime Numbers: The total number of primes in the range [1, $P_{n}$#].
2. Twin Primes: The count of twin prime pairs within the same range.

This method offers a significant shortcut compared to traditional prime-counting techniques.

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SageMath Code

The SageMath code provided is designed to test and demonstrate the formula's accuracy. Use it to experiment with different ranges and explore the behavior of prime numbers and twin primes.

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© My Method :D