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2104fa7aeb
* fixes #5434 * fixes broken solution * removes assert * removes assert * Apply suggestions from code review Co-authored-by: John Law <johnlaw.po@gmail.com> * Update project_euler/problem_003/sol1.py Co-authored-by: John Law <johnlaw.po@gmail.com>
70 lines
1.5 KiB
Python
70 lines
1.5 KiB
Python
"""
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Project Euler Problem 10: https://projecteuler.net/problem=10
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Summation of primes
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The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
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Find the sum of all the primes below two million.
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References:
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- https://en.wikipedia.org/wiki/Prime_number
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"""
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import math
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def is_prime(number: int) -> bool:
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"""Checks to see if a number is a prime in O(sqrt(n)).
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A number is prime if it has exactly two factors: 1 and itself.
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Returns boolean representing primality of given number num (i.e., if the
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result is true, then the number is indeed prime else it is not).
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>>> is_prime(2)
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True
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>>> is_prime(3)
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True
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>>> is_prime(27)
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False
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>>> is_prime(2999)
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True
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>>> is_prime(0)
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False
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>>> is_prime(1)
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False
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"""
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if 1 < number < 4:
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# 2 and 3 are primes
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return True
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elif number < 2 or number % 2 == 0 or number % 3 == 0:
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# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
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return False
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# All primes number are in format of 6k +/- 1
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for i in range(5, int(math.sqrt(number) + 1), 6):
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if number % i == 0 or number % (i + 2) == 0:
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return False
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return True
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def solution(n: int = 2000000) -> int:
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"""
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Returns the sum of all the primes below n.
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>>> solution(1000)
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76127
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>>> solution(5000)
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1548136
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>>> solution(10000)
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5736396
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>>> solution(7)
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10
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"""
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return sum(num for num in range(3, n, 2) if is_prime(num)) + 2 if n > 2 else 0
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if __name__ == "__main__":
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print(f"{solution() = }")
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