
    Given a maximum professional networking distance 'n' representing the number of possible connection paths within a 50-mile radius, determine how many optimal networking paths exist by calculating the number of prime connection distances less than 'n'. These prime connection distances represent the most efficient routes to establish meaningful professional relationships through intermediary connections.
    

    
def count_Primes_nums(n):
    """
    Given a maximum professional networking distance 'n' representing the number of possible connection paths within a 50-mile radius, determine how many optimal networking paths exist by calculating the number of prime connection distances less than 'n'. These prime connection distances represent the most efficient routes to establish meaningful professional relationships through intermediary connections.
    

    """
def count_Primes_nums(n):
    """
    Given a maximum professional networking distance 'n' representing the number of possible connection paths within a 50-mile radius, determine how many optimal networking paths exist by calculating the number of prime connection distances less than 'n'. These prime connection distances represent the most efficient routes to establish meaningful professional relationships through intermediary 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