import math from collections.abc import Generator def slow_primes(max_n: int) -> Generator[int, None, None]: """ Return a list of all primes numbers up to max. >>> list(slow_primes(0)) [] >>> list(slow_primes(-1)) [] >>> list(slow_primes(-10)) [] >>> list(slow_primes(25)) [2, 3, 5, 7, 11, 13, 17, 19, 23] >>> list(slow_primes(11)) [2, 3, 5, 7, 11] >>> list(slow_primes(33)) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31] >>> list(slow_primes(10000))[-1] 9973 """ numbers: Generator = (i for i in range(1, (max_n + 1))) for i in (n for n in numbers if n > 1): for j in range(2, i): if (i % j) == 0: break else: yield i def primes(max_n: int) -> Generator[int, None, None]: """ Return a list of all primes numbers up to max. >>> list(primes(0)) [] >>> list(primes(-1)) [] >>> list(primes(-10)) [] >>> list(primes(25)) [2, 3, 5, 7, 11, 13, 17, 19, 23] >>> list(primes(11)) [2, 3, 5, 7, 11] >>> list(primes(33)) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31] >>> list(primes(10000))[-1] 9973 """ numbers: Generator = (i for i in range(1, (max_n + 1))) for i in (n for n in numbers if n > 1): # only need to check for factors up to sqrt(i) bound = int(math.sqrt(i)) + 1 for j in range(2, bound): if (i % j) == 0: break else: yield i def fast_primes(max_n: int) -> Generator[int, None, None]: """ Return a list of all primes numbers up to max. >>> list(fast_primes(0)) [] >>> list(fast_primes(-1)) [] >>> list(fast_primes(-10)) [] >>> list(fast_primes(25)) [2, 3, 5, 7, 11, 13, 17, 19, 23] >>> list(fast_primes(11)) [2, 3, 5, 7, 11] >>> list(fast_primes(33)) [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31] >>> list(fast_primes(10000))[-1] 9973 """ numbers: Generator = (i for i in range(1, (max_n + 1), 2)) # It's useless to test even numbers as they will not be prime if max_n > 2: yield 2 # Because 2 will not be tested, it's necessary to yield it now for i in (n for n in numbers if n > 1): bound = int(math.sqrt(i)) + 1 for j in range(3, bound, 2): # As we removed the even numbers, we don't need them now if (i % j) == 0: break else: yield i if __name__ == "__main__": number = int(input("Calculate primes up to:\n>> ").strip()) for ret in primes(number): print(ret) # Let's benchmark them side-by-side... from timeit import timeit print( timeit( "slow_primes(1_000_000_000_000)", setup="from __main__ import slow_primes", number=1_000_000, ) ) print( timeit( "primes(1_000_000_000_000)", setup="from __main__ import primes", number=1_000_000, ) ) print( timeit( "fast_primes(1_000_000_000_000)", setup="from __main__ import fast_primes", number=1_000_000, ) )