Math Problem Statement
Write me Python code that counts the number of primes less than 1000. Make sure your code looks professional.
Solution
Here's a Python script that counts the number of prime numbers less than 1000. The code is written with clarity and professionalism, incorporating good practices like using functions, comments, and meaningful variable names.
pythondef is_prime(n): """ Check if a number is prime. :param n: The number to check. :return: True if the number is prime, False otherwise. """ if n <= 1: return False if n == 2 or n == 3: return True if n % 2 == 0 or n % 3 == 0: return False i = 5 while i * i <= n: if n % i == 0 or n % (i + 2) == 0: return False i += 6 return True def count_primes(limit): """ Count the number of prime numbers less than a given limit. :param limit: The upper limit (exclusive) to count primes. :return: The count of prime numbers less than the limit. """ prime_count = 0 for num in range(2, limit): if is_prime(num): prime_count += 1 return prime_count if __name__ == "__main__": limit = 1000 primes_below_limit = count_primes(limit) print(f"The number of prime numbers less than {limit} is {primes_below_limit}.")
Explanation:
-
is_prime(n)
: A helper function to determine whether a numbern
is prime. It handles special cases for small numbers and then checks divisibility by potential factors up to the square root ofn
. -
count_primes(limit)
: This function counts how many prime numbers exist below the specifiedlimit
. It iterates through all numbers from2
tolimit-1
and uses theis_prime
function to check each one. -
__main__
block: This block runs the script if it is executed directly, setting the limit to 1000 and printing the number of primes found below this limit.
Would you like further details or have any questions about this code? Here are some related questions:
- How can we optimize the prime-checking algorithm for larger limits?
- What is the time complexity of this algorithm?
- How does the Sieve of Eratosthenes compare to this method in efficiency?
- Can we modify this code to list all prime numbers less than 1000?
- What are some real-world applications of prime numbers?
Tip: When dealing with prime numbers in large ranges, consider using the Sieve of Eratosthenes for a more efficient solution.
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Math Problem Analysis
Mathematical Concepts
Number Theory
Prime Numbers
Algorithm Analysis
Formulas
-
Theorems
Prime Number Theorem
Suitable Grade Level
Grades 10-12