This is a Python implementation of the Sieve of Atkin, an optimized algorithm for finding all prime numbers up to a given limit.
The Sieve of Atkin is a modern algorithm for finding all prime numbers up to a specified integer. Compared with the older Sieve of Eratosthenes, which marks off multiples of primes, the Sieve of Atkin does some preliminary work and then marks off multiples of squares of primes, thus achieving a better theoretical asymptotic complexity.
This Python program also includes a function to count the number of twin primes (pairs of primes that differ by 2) up to the given limit.
This program requires Python 3.6 or later.
To run the program, save the Python file sieve_of_atkin.py and run it with Python:
python Atkin.py