Prime Generator (PRIME1) time limit exceeded

I have a problem about a time limit exceeded when my code is submitted though the code runs perfectly on both my IDE and ideone.com. I’ll appreciate any help to speed up my code

from sys import stdin as fp
buffer=fp.readlines()
new_buffer=[]
for i in buffer:
    i=i.strip()
    new_buffer.append(i)
newest_buffer=[]
for i in range(1,len(new_buffer)):
    newest_buffer.append(new_buffer[i].split())
for numlist in newest_buffer:
    start=int(numlist[0])
    stop=int((numlist[1]))+1
    sieve=[i for i in range(1,stop)]
    if sieve[0]==1:
        sieve.pop(0)
    for i in range(0,len(sieve)):
        j=i+1
        while j<len(sieve):
            if sieve[j]%sieve[i]==0:
                sieve.pop(j)
            else:
                j+=1
    for index in range (0,len(sieve)):
        if sieve[0]<start:
            sieve.pop(0)
    for elements in sieve:
        print(elements)
    print()