
    Given a maximum friend-circle size threshold, determine how many indivisible social clusters (represented by prime numbers) exist below this threshold, as these clusters indicate optimal group sizes for friend recommendations. Each prime number represents a naturally forming group size that cannot be broken down into smaller, equally-sized subgroups, making them ideal for maintaining strong social connections.
    

    
def count_Primes_nums(n):
    """
    Given a maximum friend-circle size threshold, determine how many indivisible social clusters (represented by prime numbers) exist below this threshold, as these clusters indicate optimal group sizes for friend recommendations. Each prime number represents a naturally forming group size that cannot be broken down into smaller, equally-sized subgroups, making them ideal for maintaining strong social connections.
    

    """
def count_Primes_nums(n):
    """
    Given a maximum friend-circle size threshold, determine how many indivisible social clusters (represented by prime numbers) exist below this threshold, as these clusters indicate optimal group sizes for friend recommendations. Each prime number represents a naturally forming group size that cannot be broken down into smaller, equally-sized subgroups, making them ideal for maintaining strong social connections.
    

    """
    ctr = 0
    for num in range(n):
        if num <= 1:
            continue
        for i in range(2, num):
            if num % i == 0:
                break
        else:
            ctr += 1
    return ctr