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
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.


Diogo F. S. Ramos:
20130313 22:12:29
Two main advices from whom who just beat it:


Jargon:
20130313 22:12:29
@jgomo3


Kacper Wikie³:
20130313 22:12:29
Chinese Primary test is too slow;


anonymous:
20130313 22:12:29
abhirut, find the biggest bound (n), and save all the primes from 2 > n somewhere


Krzysztof Kosiñski:
20130313 22:12:29
MillerRabin can do this, but only in compiled languages. Other languages are too slow. You need to use an experimental result described


Muhammad Ridowan:
20130313 22:12:29
Its simple Segmented Sieve(Although implementing not so simple) 

sxpeter:
20130313 22:12:29
Do remember: 1 is NOT a prime number. 
Added by:  Adam Dzedzej 
Date:  20040501 
Time limit:  6s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 