Python/project_euler/problem_131/sol1.py

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"""
Project Euler Problem 131: https://projecteuler.net/problem=131
There are some prime values, p, for which there exists a positive integer, n,
such that the expression n^3 + n^2p is a perfect cube.
For example, when p = 19, 8^3 + 8^2 x 19 = 12^3.
What is perhaps most surprising is that for each prime with this property
the value of n is unique, and there are only four such primes below one-hundred.
How many primes below one million have this remarkable property?
"""
from math import isqrt
def is_prime(number: int) -> bool:
"""
Determines whether number is prime
>>> is_prime(3)
True
>>> is_prime(4)
False
"""
for divisor in range(2, isqrt(number) + 1):
if number % divisor == 0:
return False
return True
def solution(max_prime: int = 10**6) -> int:
"""
Returns number of primes below max_prime with the property
>>> solution(100)
4
"""
primes_count = 0
cube_index = 1
prime_candidate = 7
while prime_candidate < max_prime:
primes_count += is_prime(prime_candidate)
cube_index += 1
prime_candidate += 6 * cube_index
return primes_count
if __name__ == "__main__":
print(f"{solution() = }")