sol1.py

"""
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?
"""

frommathimportisqrt


defis_prime(number: int) ->bool:
"""
 Determines whether number is prime

 >>> is_prime(3)
 True

 >>> is_prime(4)
 False
 """

returnall(number%divisor!=0fordivisorinrange(2, isqrt(number) +1))


defsolution(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
whileprime_candidate<max_prime:
primes_count+=is_prime(prime_candidate)

cube_index+=1
prime_candidate+=6*cube_index

returnprimes_count


if__name__=="__main__":
print(f"{solution() =}")