Python: Count the number of prime numbers less than a given non-negative number

Last update on April 17 2025 13:05:37 (UTC/GMT +8 hours)

Prime Count Below n

Write a Python program that counts the number of prime numbers that are less than a given non-negative number.

Sample Solution:

Python Code:

# Function to count prime numbers up to a given limit 'n'
def count_Primes_nums(n):
    ctr = 0  # Counter to store the number of prime numbers
    
    # Iterate through numbers up to 'n'
    for num in range(n):
        if num <= 1:  # Numbers less than or equal to 1 are not prime, so skip them
            continue
        
        # Check for factors in the range from 2 to num-1
        for i in range(2, num):
            if (num % i) == 0:  # If num is divisible by i, it's not prime
                break
        else:
            ctr += 1  # If no factors are found, increment the counter (num is prime)

    return ctr  # Return the count of prime numbers

# Print the count of prime numbers up to 10 and 100
print(count_Primes_nums(10))
print(count_Primes_nums(100))

Sample Output:

4
25

Explanation:

Here is a breakdown of the above Python code:

First define a function named "count_Primes_nums()" that takes a limit 'n' as input.
Initialize a counter 'ctr' to store the number of prime numbers.
Use a for loop to iterate through numbers up to 'n'.
Check if the current number is less than or equal to 1; if so, skip it since numbers less than or equal to 1 are not prime.
Use another for loop to check for factors in the range from 2 to 'num-1'.
If a factor is found, break out of the loop; otherwise, increment the counter 'ctr'.
Return the final count of prime numbers.
Print the count of prime numbers up to 10 and 100 using the function.

Visual Presentation:

Python: Count the number of prime numbers less than a given non-negative number

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to count the number of prime numbers less than a given integer using the Sieve of Eratosthenes.
Write a Python program to implement a prime counting function that returns the number of primes below n efficiently.
Write a Python program to count primes below a specified value using a segmented sieve algorithm.
Write a Python program to verify the count of prime numbers less than a given number using iterative methods and compare with sieve results.

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Python Code Editor:

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