Python/maths/prime_numbers.py

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from typing import Generator
import math
def slow_primes(max: 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 + 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: 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 + 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
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)", setup="from __main__ import slow_primes"))
print(timeit("primes(1_000_000)", setup="from __main__ import primes"))