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Prime numbers: Added description, removed unnecessary implementation, and improved current #5048

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Prime numbers: Added description, removed unnecessary implementation, and improved current #5048

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54 changes: 16 additions & 38 deletions maths/prime_numbers.py
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Original file line number Diff line number Diff line change
@@ -1,6 +1,13 @@
import math
from typing import Generator

"""
Naive implementation of finding primes by checking if each number
is divisible by 2 or any odd number up to its root.

For a fast implementation see Sieve of Eratosthenes.
"""

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ok to keep an explanation, but state that there are two impls, and you can compre both.


def slow_primes(max: int) -> Generator[int, None, None]:
"""
Expand All @@ -9,8 +16,8 @@ def slow_primes(max: int) -> Generator[int, None, None]:
[]
>>> list(slow_primes(-1))
[]
>>> list(slow_primes(-10))
[]
>>> list(slow_primes(2))
[2]
>>> list(slow_primes(25))
[2, 3, 5, 7, 11, 13, 17, 19, 23]
>>> list(slow_primes(11))
Expand All @@ -22,49 +29,20 @@ def slow_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):
if (i % j) == 0:
break
else:
yield i
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remove these brackets



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
"""
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and keep the tests?

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The tests dont make sense since we removed one of the functions, it just compared the two timings

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I suggest we keep this referential implementation. Please see #1984, #1519.

numbers: Generator = (i for i in range(1, (max + 1)))
for i in (n for n in numbers if n > 1):
if i % 2 == 0:
if i == 2:
yield 2
continue
# 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:
for j in range(3, bound, 2):
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):
for ret in slow_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"))