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.

python
def 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:

  1. is_prime(n): A helper function to determine whether a number n is prime. It handles special cases for small numbers and then checks divisibility by potential factors up to the square root of n.

  2. count_primes(limit): This function counts how many prime numbers exist below the specified limit. It iterates through all numbers from 2 to limit-1 and uses the is_prime function to check each one.

  3. __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:

  1. How can we optimize the prime-checking algorithm for larger limits?
  2. What is the time complexity of this algorithm?
  3. How does the Sieve of Eratosthenes compare to this method in efficiency?
  4. Can we modify this code to list all prime numbers less than 1000?
  5. 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

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Theorems

Prime Number Theorem

Suitable Grade Level

Grades 10-12