TheAlgorithms-Python
86 строк · 1.8 Кб
1"""
2Project Euler Problem 7: https://projecteuler.net/problem=7
3
410001st prime
5
6By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
7can see that the 6th prime is 13.
8
9What is the 10001st prime number?
10
11References:
12- https://en.wikipedia.org/wiki/Prime_number
13"""
14
15import itertools
16import math
17
18
19def is_prime(number: int) -> bool:
20"""Checks to see if a number is a prime in O(sqrt(n)).
21A number is prime if it has exactly two factors: 1 and itself.
22Returns boolean representing primality of given number (i.e., if the
23result is true, then the number is indeed prime else it is not).
24
25>>> is_prime(2)
26True
27>>> is_prime(3)
28True
29>>> is_prime(27)
30False
31>>> is_prime(2999)
32True
33>>> is_prime(0)
34False
35>>> is_prime(1)
36False
37"""
38
39if 1 < number < 4:
40# 2 and 3 are primes
41return True
42elif number < 2 or number % 2 == 0 or number % 3 == 0:
43# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
44return False
45
46# All primes number are in format of 6k +/- 1
47for i in range(5, int(math.sqrt(number) + 1), 6):
48if number % i == 0 or number % (i + 2) == 0:
49return False
50return True
51
52
53def prime_generator():
54"""
55Generate a sequence of prime numbers
56"""
57
58num = 2
59while True:
60if is_prime(num):
61yield num
62num += 1
63
64
65def solution(nth: int = 10001) -> int:
66"""
67Returns the n-th prime number.
68
69>>> solution(6)
7013
71>>> solution(1)
722
73>>> solution(3)
745
75>>> solution(20)
7671
77>>> solution(50)
78229
79>>> solution(100)
80541
81"""
82return next(itertools.islice(prime_generator(), nth - 1, nth))
83
84
85if __name__ == "__main__":
86print(f"{solution() = }")
87