在 Python 中找到没有“中断”的第 n 个素数

Question

I'm quite new to coding and I'm being asked to write code to find the nth prime number in Python. I managed to writing the following code:

prime = input("which prime do you want to find?:")

n = 0
for x in range(2, 8000):
    for y in range (2, x):
        if (x % y) == 0:
            break
    else:
        n = n + 1
    if n == prime:
        print(x)
        break

However, I just found out I'm not allowed to use break. They're essentially only allowing me 'for' and 'while' loops. Does anyone have any inkling on how to do this?

Answer 1

Here's how to do this with while loops and no use of break :

# Let's find the first prime equal to or greater than the number input by the user

# Get the user's input
prime = input("which prime do you want to find?:")

found = False
x = 2
# While we haven't found the prime we're looking for and we haven't reached our upper limit...
while not found and x < 8000:
    # See if we can find any factors for 'x', the next number we're considering
    y = 2
    while not found and y < x:
        # While we haven't found a factor and still have more candidates...
        if (x % y) == 0:
            # We found a factor, so note that we have done so.  This will exit the inner
            # while loop that we're in.
            found = True
        else:
            # Not a factor, so try the next factor candidate
            y += 1
    if not found and x >= int(prime):
        # If we didn't find any factors, and the current candidate is equal to or
        # greater than the user's input, then 'x' is the prime we're looking for,
        # so set 'found' to True to exit the outer loop.
        found = True
    else:
        # Otherwise, make sure 'found' is false (it may already be) and move on to the next candidate
        found = False
        x += 1
        
print(x)

I think this version has some value. It shows one reason why having break is valuable. Not being able to use break , this solution is considerably more cumbersome since we have to explicitly keep track of the current values for each loop and we also have to test and set a flag to decide if we should keep iterating. This is NOT the way this problem should be solved in the real world! One should use for loops and break instead.

Answer 2

I'm afraid you'll need to refactor the whole code. Otherwise, with this current code you'll get some errors that are not even related to the prime finding logic.

For instance, the input you are storing in prime variable is by default a string or str data type in python. On the other hand your n variable is an integer or int data type. So these two cannot be compared like you did in if n==prime which can be fixed by replacing it with if n==int(prime) , by converting the prime variable to int data type. You can also convert that while taking the input like this:

prime = int(input("which prime do you want to find?:"))

There is an indentation fault too, but since your post was edited by someone else maybe it wasn't your fault.

However, you could use a better algorithm to find the n-th prime. Nested loops can hurt you so bad because it makes the program too slow, particularly in python. You can checkout some algorithms like Sieve of Eratosthenes , if you don't know them already.