SPOJ prime1 wrong answer in python

Question

I am getting Wrong Answer with the following code in python for SPOJ's PRIME1 problem at http://www.spoj.com/problems/PRIME1/. I have tested it on various testcases myself, but cannot find a failing testcase. Can someone please spot the problem in my code?

This code produces nothing for testcases that don't give any prime as output. First i pre-compute primes upto sqrt(1 billion) and then if the requested range has high value less than sqrt(1 billion), i simply print the primes from the pre-computed array, else i run sieve() with usePrimes = True, which uses the pre-computed primes to rule out the non-primes in the given range.

Thanks.

import math
from bisect import bisect_left
from bisect import bisect_right

primes = []
upper_bound = int(math.sqrt(1000000000)) + 1
usePrimes = False
printNL = False
T = 0

def sieve(lo, hi):
    global usePrimes, primes, printNL
    atleast_one = False
    arr = range(lo,hi+1)
    if usePrimes:
        for p in primes:
            if p*p > hi:
                break
            less = int(lo/p) * p
            if less < lo:
                less += p
            while less <= hi:
                arr[less - lo] = 0
                less += p
        for num in arr:
            if num  != 0:
                atleast_one = True
                if printNL:
                    print ''
                    printNL = False
                print num
    else:
        atleast_one = True
        for k in xrange(2,hi):
            if k*k > hi:
                break
            if arr[k] == 0:
                continue
            less = k + k
            while less <= hi:
                arr[less] = 0
                less += k
        for num in arr:
            if num > 1:
                primes.append(num)
    return atleast_one


def printPrimesInRange(lo,hi):
    global primes, printNL
    atleast_one = False
    if hi < upper_bound:
        for p in primes[bisect_left(primes,lo):bisect_right(primes,hi)]:
            atleast_one = True
            if printNL:
                print ''
                printNL = False
            print p
    else:
        atleast_one = sieve(lo,hi)
    return atleast_one

sieve(0, upper_bound)
usePrimes = True

T = input()
while T > 0:
    lo, hi = [eval(y) for y in raw_input().split(' ')]
    atleastOne = printPrimesInRange(lo,hi)
    if atleastOne:
        printNL = True
    T -= 1

Answer 1

If you change the upper_bound to upper_bound = int(math.sqrt(1000000000)) + 123456, then it will pass all the test cases.

Now, can you figure why so? I'll leave it as an exercise to you.