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