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improved prime number generator to check only up to sqrt(n) instead of n (#1984)

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* improved prime number generator to check only up to sqrt(n) instead of n

* added old version as slow_primes() and named new, faster version primes()

* fixed docstring in slow_primes

* Add a timeit benchmark

* Update prime_numbers.py

Co-authored-by: Christian Clauss <cclauss@me.com>
This commit is contained in:
Steven Qu 2020-05-14 18:33:50 -04:00 committed by GitHub
parent 48bb14d4b2
commit c8fbdee229
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1 changed files with 36 additions and 1 deletions
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37
maths/prime_numbers.py
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@ -1,4 +1,32 @@
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]:
@ -21,7 +49,9 @@ def primes(max: int) -> Generator[int, None, None]:
"""
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):
# 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:
@ -32,3 +62,8 @@ 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"))