素数的python算法

Question

Assume the availability of a function is_prime . Assume a variable n has been associated with positive integer. Write the statements needed to find out how many prime numbers (starting with 2 and going in increasing order with successively higher primes [2,3,5,7,11,13,...]) can be added before exceeding n . Associate this number with the variable k .

 def main():
    n=int(input('n: '))
    k=0
    i=2
    sum=0

    while sum<=n:
        if is_prime(i):
            sum+=i
            i+=1
            k+=1
        print(k)



def is_prime(n):

    for divisor in range(2,int(n**0.5)+1):
        if n/divisor==int(n/divisor):
            return False
    return True

main()

would really appreciate some pointers.

I modified the code a little bit and it is working fine but the program that grades these codes says that I almost certainly should be using a + sign some where. I have no idea. Modified code is:

while sum<=n:

        if is_prime(i):

            sum+=i
            k+=1
            i+=1
    print(k)

output:

n: 10

i: 2

2

i: 3

5

when it should actually go upto i=5 and total =10.

Answer 1

There is actually more efficient why to solve this problem, it is Sieve of Eratosthenes . The basic idea is to generate array of numbers from 2 till n. Then you iterate over this array starting from 2 and replace all numbers, which mod by i == 0 with -1 or delete them.

If you are getting stuck you can check implementation here.

Sieve of Eratosthenes - Finding Primes Python

Answer 2

What you certainly ought to be using is the space character around operators. Also, your alignment is wacky. In Python, alignment indicates structure, and your rewrite will make any interpreter complain (at least, at it's displayed here). If a program (or a robotic TA) is reading and grading your work, and it thinks you need a + sign somewhere, then perhaps it wants to see "sum = sum + i" somewhere. I'll use that. So try this:

def main():
    n = int(input('n: '))
    k = 0
    i = 2
    sum = 0

    while sum <= n:
        if is_prime(i):
            sum = sum + i  # nothing wrong with "sum += i"
            k += 1
        i += 1    # put this inside "if" ==> loop forever 
    print(k)

def is_prime(m):
    for divisor in range(2, int(m**0.5) + 1):
        if m % divisor == 0:
            return False
    return True

main()

Answer 3

if n/divisor==int(n/divisor):

This is wrong. When you divide 2 integers you get integer as a result. So 5/2 = 2. Replace it with

if n%divisor == 0:

EDITED: your modified loop looks almost correct. If I understand your task right it should be

while sum<=n:
    if is_prime(i):
        sum+=i
        k+=1
    i+=1
print(k)

EDITED2: probably you want to stop as soon as sum + next prime is bigger then n and not add another prime value.

while True:
    if is_prime(i):
        if(sum + i > n)
            break;
        else:
            sum += i
            k += 1
    i += 1 
print(k)