mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 01:00:15 +00:00
bc8df6de31
* [pre-commit.ci] pre-commit autoupdate updates: - [github.com/astral-sh/ruff-pre-commit: v0.2.2 → v0.3.2](https://github.com/astral-sh/ruff-pre-commit/compare/v0.2.2...v0.3.2) - [github.com/pre-commit/mirrors-mypy: v1.8.0 → v1.9.0](https://github.com/pre-commit/mirrors-mypy/compare/v1.8.0...v1.9.0) * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
107 lines
2.5 KiB
Python
107 lines
2.5 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
|
|
"""
|
|
|
|
import math
|
|
|
|
|
|
def is_prime(number: int) -> bool:
|
|
"""Checks to see if a number is a prime in O(sqrt(n)).
|
|
A number is prime if it has exactly two factors: 1 and itself.
|
|
Returns boolean representing primality of given number (i.e., if the
|
|
result is true, then the number is indeed prime else it is not).
|
|
|
|
>>> is_prime(2)
|
|
True
|
|
>>> is_prime(3)
|
|
True
|
|
>>> is_prime(27)
|
|
False
|
|
>>> is_prime(2999)
|
|
True
|
|
>>> is_prime(0)
|
|
False
|
|
>>> is_prime(1)
|
|
False
|
|
"""
|
|
|
|
if 1 < number < 4:
|
|
# 2 and 3 are primes
|
|
return True
|
|
elif number < 2 or number % 2 == 0 or number % 3 == 0:
|
|
# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
|
|
return False
|
|
|
|
# All primes number are in format of 6k +/- 1
|
|
for i in range(5, int(math.sqrt(number) + 1), 6):
|
|
if number % i == 0 or number % (i + 2) == 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
|
|
>>> solution(3.4)
|
|
5
|
|
>>> solution(0)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: Parameter nth must be greater than or equal to one.
|
|
>>> solution(-17)
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: Parameter nth must be greater than or equal to one.
|
|
>>> solution([])
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: Parameter nth must be int or castable to int.
|
|
>>> solution("asd")
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: Parameter nth must be int or castable to int.
|
|
"""
|
|
|
|
try:
|
|
nth = int(nth)
|
|
except (TypeError, ValueError):
|
|
raise TypeError("Parameter nth must be int or castable to int.") from None
|
|
if nth <= 0:
|
|
raise ValueError("Parameter nth must be greater than or equal to one.")
|
|
primes: list[int] = []
|
|
num = 2
|
|
while len(primes) < nth:
|
|
if is_prime(num):
|
|
primes.append(num)
|
|
num += 1
|
|
else:
|
|
num += 1
|
|
return primes[len(primes) - 1]
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(f"{solution() = }")
|