mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 23:11:09 +00:00
98e9d6bdb6
* Fix style of the first ten solutions for Project Euler - Unify the header docstring, and add reference URLs to wikipedia or similar - Fix docstrings to be properly multilined - Add newlines where appropriate - Add doctests where they were missing - Remove doctests that test for the correct solution - fix obvious spelling or grammar mistakes in comments and exception messages - Fix line endings to be UNIX. This makes two of the files seem to have changed completely - no functional changes in any of the solutions were done (except for the spelling fixes mentioned above) * Fix docstrings and main function as per Style Guide
77 lines
1.3 KiB
Python
77 lines
1.3 KiB
Python
"""
|
|
Project Euler Problem 7: https://projecteuler.net/problem=7
|
|
|
|
10001st prime
|
|
|
|
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
|
|
can see that the 6th prime is 13.
|
|
|
|
What is the 10001st prime number?
|
|
|
|
References:
|
|
- https://en.wikipedia.org/wiki/Prime_number
|
|
"""
|
|
|
|
from math import sqrt
|
|
|
|
|
|
def is_prime(num: int) -> bool:
|
|
"""
|
|
Determines whether the given number is prime or not
|
|
|
|
>>> is_prime(2)
|
|
True
|
|
>>> is_prime(15)
|
|
False
|
|
>>> is_prime(29)
|
|
True
|
|
>>> is_prime(0)
|
|
False
|
|
"""
|
|
|
|
if num == 2:
|
|
return True
|
|
elif num % 2 == 0:
|
|
return False
|
|
else:
|
|
sq = int(sqrt(num)) + 1
|
|
for i in range(3, sq, 2):
|
|
if num % i == 0:
|
|
return False
|
|
return True
|
|
|
|
|
|
def solution(nth: int = 10001) -> int:
|
|
"""
|
|
Returns the n-th prime number.
|
|
|
|
>>> solution(6)
|
|
13
|
|
>>> solution(1)
|
|
2
|
|
>>> solution(3)
|
|
5
|
|
>>> solution(20)
|
|
71
|
|
>>> solution(50)
|
|
229
|
|
>>> solution(100)
|
|
541
|
|
"""
|
|
|
|
count = 0
|
|
number = 1
|
|
while count != nth and number < 3:
|
|
number += 1
|
|
if is_prime(number):
|
|
count += 1
|
|
while count != nth:
|
|
number += 2
|
|
if is_prime(number):
|
|
count += 1
|
|
return number
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(f"{solution() = }")
|