CodeChef PRIME1 problem in Python

import math
max_n=10**9
m = int(math.sqrt(max_n))
arr = [1]*m
arr[0] = arr[1] = 0 
#Calculate primes upto math.sqrt(max_n)
for x in xrange(m):
    for i in xrange(2,int(x**0.5)+1):
        if x%i==0:
            arr[x]=0
            break
list_prime=[]
for i,each in enumerate(arr):
    if each==1:
        list_prime.append(i)

#sieve b/w m and n
for _ in xrange(int(raw_input().strip())):
    m,n = map(int,raw_input().split())
    arr = range(m,n+1) if m>1 else range(2,n+1)
    for each in list_prime:
        firstfactor = (arr[0]/each)*each
        for x in xrange(firstfactor,n+1,each):
            try:
                if x!=each:
                    arr.remove(x)
            except:
                pass
    for each in arr:
        print each
    print

• Using the same variables for different purposes in the same block of code is confusing to the reader. Split the code in 2-3 functions so that they become local variables.

• You use trial division to compute the list of small primes even though you know about sieving. Sieving is faster.

• arr.remove(x) in the innermost loop is slow because it scans through the whole list (to find the element to remove, and to move subsequent elements back). Use a set instead, or a list of boolean values similar to arr in the first part of the code.