Python code freezes up my computer - Project Euler 58

Question

I am trying to learn python by solving problems from Project Euler. I am stuck on problem 58. The problem states thus:

Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.
37 36 35 34 33 32 31
38 17 16 15 14 13 30
39 18  5  4  3 12 29
40 19  6  1  2 11 28
41 20  7  8  9 10 27
42 21 22 23 24 25 26
43 44 45 46 47 48 49
It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.
If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?

Here is the code I wrote for solving this problem. I utilize a primesieve to check for primes, but I didn't know what limit to set the primesieve to. So I let the code tell me when I needed to increase the limit. The code runs fine up to limit=10^8, but when I set it to 10^9, the code freezes up my PC and I have to reboot. Not sure what I'm doing wrong. Please let me know if you need additional information. Thanks!

def primesieve(limit):
    primelist=[]
    for i in xrange(limit):
        primelist.append(i)

    primelist[1]=0
    for i in xrange(2,limit):
        if primelist[i]>0:
            ctr=2
            while (primelist[i]*ctr<limit):
                a=primelist[i]*ctr
                primelist[a]=0
                ctr+=1

    primelist=filter(lambda x: x!=0, primelist)
    return primelist

limit=10**7
plist=primesieve(limit)
pset=set(plist)

diagnumbers=5.0
primenumbers=3.0
sidelength=3
lastnumber=9

while (primenumbers/diagnumbers)>=0.1:
    sidelength+=2
    for i in range(3):
        lastnumber+=(sidelength-1)
        if lastnumber in pset:
            primenumbers+=1
    diagnumbers+=4
    lastnumber+=(sidelength-1)
    if lastnumber>plist[-1]:
        print lastnumber,"Need to increase limit"
        break

print "sidelength",sidelength,"  last number",lastnumber,(primenumbers/diagnumbers)

Answer 1

Even though you are using xrange, you are still generating a list of of size 10**9 when making your primesieve. That use a large amount of memory, and is likely your problem.

Instead, you might consider writing a function that checks if a number, N, is prime or not, by checking of any number between (2,N**.5) divide the number evenly. Then, you can go about generating the corner numbers and just perform primality testing.