mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-27 23:11:09 +00:00
1400cb86ff
* Fixes (#5434) * Update ciphers.rabin_miller.py maths.miller_rabin.py * Fixing ERROR maths/miller_rabin.py - ModuleNotFoundError and changing project_euler's isPrime to is_prime function names * Update sol1.py * fix: try to change to list * fix pre-commit * fix capital letters * Update miller_rabin.py * Update rabin_miller.py Co-authored-by: John Law <johnlaw.po@gmail.com>
69 lines
1.2 KiB
Python
69 lines
1.2 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 itertools
|
|
import math
|
|
|
|
|
|
def is_prime(number: int) -> bool:
|
|
"""
|
|
Determines whether a given number is prime or not
|
|
|
|
>>> is_prime(2)
|
|
True
|
|
>>> is_prime(15)
|
|
False
|
|
>>> is_prime(29)
|
|
True
|
|
"""
|
|
|
|
if number % 2 == 0 and number > 2:
|
|
return False
|
|
return all(number % i for i in range(3, int(math.sqrt(number)) + 1, 2))
|
|
|
|
|
|
def prime_generator():
|
|
"""
|
|
Generate a sequence of prime numbers
|
|
"""
|
|
|
|
num = 2
|
|
while True:
|
|
if is_prime(num):
|
|
yield num
|
|
num += 1
|
|
|
|
|
|
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
|
|
"""
|
|
return next(itertools.islice(prime_generator(), nth - 1, nth))
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(f"{solution() = }")
|