project_euler.problem_187.sol1

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?

Functions

benchmark(→ None)	Benchmarks
calculate_prime_numbers(→ list[int])	Returns prime numbers below max_number.
slow_calculate_prime_numbers(→ list[int])	Returns prime numbers below max_number.
slow_solution(→ int)	Returns the number of composite integers below max_number have precisely two,
solution(→ int)	Returns the number of composite integers below max_number have precisely two,
while_solution(→ int)	Returns the number of composite integers below max_number have precisely two,

Module Contents

project_euler.problem_187.sol1.benchmark() → None

Benchmarks

project_euler.problem_187.sol1.calculate_prime_numbers(max_number: int) → list[int]

Returns prime numbers below max_number. See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

>>> calculate_prime_numbers(10)
[2, 3, 5, 7]

>>> calculate_prime_numbers(2)
[]

project_euler.problem_187.sol1.slow_calculate_prime_numbers(max_number: int) → list[int]

Returns prime numbers below max_number. See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

>>> slow_calculate_prime_numbers(10)
[2, 3, 5, 7]

>>> slow_calculate_prime_numbers(2)
[]

project_euler.problem_187.sol1.slow_solution(max_number: int = 10**8) → int

Returns the number of composite integers below max_number have precisely two, not necessarily distinct, prime factors.

>>> slow_solution(30)
10

project_euler.problem_187.sol1.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

project_euler.problem_187.sol1.while_solution(max_number: int = 10**8) → int

Returns the number of composite integers below max_number have precisely two, not necessarily distinct, prime factors.

>>> while_solution(30)
10