from math import*
c=1
x=3
p=2

n=20 #I changed this to a smaller number. Increase it as you work out some of the bugs!

logsum=log(2)

while x<n:  #I think you want c<n here because you want to find the 1000th prime right?
    prime=True
    #divisor=3
    #while divisor<(x/2):
    #Maybe combine these last two statements into a 'for' statement. Along these lines:
    for divisor in range(3, x/2):   #basically the same idea but more concise...

###This next section is where you are running into trouble. I would suggest
###simplifying these tests...
        if x%divisor>0:
            divisor=divisor+2
        else:
            prime=False
            divisor=x

        if prime==True:
            c=c+1
            p=x
            logsum=logsum+log(p)
    x=x+2 #Indent was wrong here, moved it left so you aren't stuck in an infinite loop.

#I added these print statements so you can maybe see how it is running off track in
#your first if statement. The p values are not the correct prime numbers,
#and c is not right either. See if you can fix it...it isn't very far off.
    print 'x=',x
    print 'p=',p
    print 'c=',c

print logsum
print n