PRIME1  Prime Generator
Peter wants to generate some prime numbers for his cryptosystem. Help him! Your task is to generate all prime numbers between two given numbers!
Input
The input begins with the number t of test cases in a single line (t<=10). In each of the next t lines there are two numbers m and n (1 <= m <= n <= 1000000000, nm<=100000) separated by a space.
Output
For every test case print all prime numbers p such that m <= p <= n, one number per line, test cases separated by an empty line.
Example
Input: 2 1 10 3 5 Output: 2 3 5 7 3 5Warning: large Input/Output data, be careful with certain languages (though most should be OK if the algorithm is well designed)
Information
After cluster change, please consider PRINT as a more challenging problem.hide comments
nadstratosfer:
20180409 05:17:35
cobwebs, welcome to SPOJ. While many problems here have idiotic time limits preventing AC with a correct Python solution, this is not one of them. It's a great entry point to this site for a pythonist though, as putting work into AC here will reward you in many other problems. C coders can get away with ridiculous stupidity sometimes as the compiler will straighten it out, we can't; your program *has to* be elegant and efficient. There will be an immense satisfaction in other problems later on when daddy compiler can't help "AC in 1 go" usual suspects while your solution gets a green bar.


cobwebs:
20180408 06:42:02
my python3 algorithm can give the correct answer, but it always exceeds the time. The logic is exactly the same as a friend who coded in C++, but his doesn't exceed. Help.


karan_yadav:
20180330 05:43:07
0.88s :) 

Johnny Nonsense:
20180324 21:19:16
I completed this in C++ without using sieve. You can run these tests faster by retaining a list of primes from one test to the next. Extend the list as necessary, up to and not exceeding sqrt(M). When determining whether a number is prime, you only have to divide it by all prime numbers in the list up to the square root of the test number. If this method doesn't work in some language other than c++, then maybe the tester is too restrictive in the time constraint for that particular language. I hope that this makes sense. 

skandrajmeet:
20180323 10:32:34
please somebody tell me why my code is giving WA .its running perfectly fine for large numbers too.


badasshackme:
20180308 17:58:16
Segmented sieve is the solution, but you need to implement it properly or you will hit TLE. For example, see http://jamiewong.com/2009/11/12/spojproblem2primegenerator/ 

jhanji999:
20180306 15:08:28
what is sc here btw a total noob here


porsamini:
20180305 07:07:47
Yeah, sieve is not necessary 

sky_scraper:
20180302 14:26:12
segmented seive means applying simple seive again on already computed primes(small range) to get primes ahead 

candyzack:
20180219 08:38:46
anyone got AC in python 3? i am using segment sieve... still TLE

Added by:  Adam Dzedzej 
Date:  20040501 
Time limit:  6s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 