查找第 1000 个素数（python）调试

Question

I am attempting to write a code to calculate the 1000th prime number and I'm running into an issue with my loop counter that i don't understand.

prime_test = 1
count=0
for count in range(0,1001):
    for divisor in range(2,prime_test):
        if (prime_test % divisor) == 0:
            break
    else:
        print(prime_test)
        count += 1
    prime_test+=1

Could someone please explain why the above code is dysfunctional? The problem is that the count variable iterates at the same rate as the prime_test variable. How do I separate the two such that count only increases when a new prime is found and not when the loop is engaged?

Answer 1

Don't use for count in range(0, 1001): . That just increments count sequentially, not when it finds a prime. Use a while loop.

prime_test = 2
count = 0
while count < 1000:
    for divisor in range(2,prime_test):
        if (prime_test % divisor) == 0:
            break
    else:
        print(prime_test)
        count += 1
    prime_test += 1

You also should start prime_test at 2 , not 1 , since 1 isn't a prime number, but your algorithm will say it is.

Answer 2

One more answer as the same thing might need to be repeated thousand times before it could be understood.

Setting the value of c before the loop has no effect at all and the new to c within the loop assigned value will be overwritten by next loop loop as c will be set to the next value provided by range() . Python for c in range() loops are not like loops in some other programming languages. So every newbie has to go through this... wondering how it comes.

Following code demonstrates this:

c = 100
for c in range(5):
    print(c, end=' -> ')
    c = c + 5
    print(c)

printing

0 -> 5
1 -> 6
2 -> 7
3 -> 8
4 -> 9

---

---

If you change your code to:

prime_test = 2
counter=0
for count in range(0,11):
    for divisor in range(2, prime_test):
        if (prime_test % divisor) == 0:
            break
    else:
        print(prime_test)
        counter += 1
    prime_test+=1
print(f'{counter=} , {prime_test=} ')

you will get as output:

2
3
5
7
11
counter=5 , prime_test=13