project_euler.problem_007.sol3

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:

Functions

is_prime(→ bool)

Checks to see if a number is a prime in O(sqrt(n)).

prime_generator()

Generate a sequence of prime numbers

solution(→ int)

Returns the n-th prime number.

Module Contents

project_euler.problem_007.sol3.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
project_euler.problem_007.sol3.prime_generator()

Generate a sequence of prime numbers

project_euler.problem_007.sol3.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