diff --git a/DIRECTORY.md b/DIRECTORY.md index 1d3177801..1a641d8ec 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -990,6 +990,8 @@ * [Sol1](project_euler/problem_174/sol1.py) * Problem 180 * [Sol1](project_euler/problem_180/sol1.py) + * Problem 187 + * [Sol1](project_euler/problem_187/sol1.py) * Problem 188 * [Sol1](project_euler/problem_188/sol1.py) * Problem 191 diff --git a/project_euler/problem_187/__init__.py b/project_euler/problem_187/__init__.py new file mode 100644 index 000000000..e69de29bb diff --git a/project_euler/problem_187/sol1.py b/project_euler/problem_187/sol1.py new file mode 100644 index 000000000..12f03e2a7 --- /dev/null +++ b/project_euler/problem_187/sol1.py @@ -0,0 +1,58 @@ +""" +Project Euler Problem 187: https://projecteuler.net/problem=187 + +A composite is a number containing at least two prime factors. +For example, 15 = 3 x 5; 9 = 3 x 3; 12 = 2 x 2 x 3. + +There are ten composites below thirty containing precisely two, +not necessarily distinct, prime factors: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26. + +How many composite integers, n < 10^8, have precisely two, +not necessarily distinct, prime factors? +""" + +from math import isqrt + + +def calculate_prime_numbers(max_number: int) -> list[int]: + """ + Returns prime numbers below max_number + + >>> calculate_prime_numbers(10) + [2, 3, 5, 7] + """ + + is_prime = [True] * max_number + for i in range(2, isqrt(max_number - 1) + 1): + if is_prime[i]: + for j in range(i**2, max_number, i): + is_prime[j] = False + + return [i for i in range(2, max_number) if is_prime[i]] + + +def solution(max_number: int = 10**8) -> int: + """ + Returns the number of composite integers below max_number have precisely two, + not necessarily distinct, prime factors + + >>> solution(30) + 10 + """ + + prime_numbers = calculate_prime_numbers(max_number // 2) + + semiprimes_count = 0 + left = 0 + right = len(prime_numbers) - 1 + while left <= right: + while prime_numbers[left] * prime_numbers[right] >= max_number: + right -= 1 + semiprimes_count += right - left + 1 + left += 1 + + return semiprimes_count + + +if __name__ == "__main__": + print(f"{solution() = }")