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
David Winiecki:
20130313 22:12:29
Diogo's second comment about the Sieve was really helpful. I can't believe how effective that one change was. 

Mukul:
20130313 22:12:29
I think this problem should be solve using Sieve algorithm, otherwise you will get TLE as i got. 

Adrian Kuegel:
20130313 22:12:29
Try this case:


Manuel Meder:
20130313 22:12:29
hi, I'm confused now. I submitted my code 5333234 with "initial error" then I submitted that code again and get "wrong answer" tho if I calculate the Primes from 1 to 1.000.000.000 I get the 50847534 Primes returned. (So if the Primes should be okay, how come it says wrong answer) each set is separated by a blank line and the after the last set theres just a \n.


VICTOR JOHANN CORTEZ:
20130313 22:12:29
10


Dan:
20130313 22:12:29
By definition, a prime number is


:D:
20130313 22:12:29
Please move your code to the forum (probem set archive section). Comments are no place for the whole programs, your spoiling it for others! 

Alca:
20130313 22:12:29
I use MillerRobbin( O(log n) )


superpollo:
20130313 22:12:29
maybe the condition nm<=100000 might be used to increase efficiency... ? 

Rakib Ansary Saikot:
20130313 22:12:29
Another idea is to use an Erathostenes sieve that doesn't store some numbers that are certainly not prime. For example, you can store 30 numbers in one byte: only 30n+1, 30n+n+7, 30n+11, 30n+13, 30n+17, 30n+19, 30n+23 and 30n+29 can be prime. You can expand this idea to 32 bits for maximum performance.

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