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

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Merged
merged 5 commits into from
May 14, 2020
Merged

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

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8a123b9
improved prime number generator to check only up to sqrt(n) instead of n
steven7214 May 14, 2020
33e375d
added old version as slow_primes() and named new, faster version prim…
steven7214 May 14, 2020
f7fb16e
fixed docstring in slow_primes
steven7214 May 14, 2020
a694615
Add a timeit benchmark
cclauss May 14, 2020
de8da46
Update prime_numbers.py
cclauss May 14, 2020
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29 changes: 28 additions & 1 deletion maths/prime_numbers.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2,6 +2,33 @@
import math


def slow_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):
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.
Expand All @@ -23,7 +50,7 @@ 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):
# only need to check for factors up to sqrt(i)
bound = int(math.sqrt(i))+1
bound = int(math.sqrt(i)) + 1
for j in range(2, bound):
if (i % j) == 0:
break
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