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
summerbleach:
20200512 11:22:06
The Osqrt(N) approach took 3.63 sec 

sabat_raj3:
20200510 21:50:56
Hey!no need for any complex logic. Use simple logic to traverse from m to n and then check from 2 to root(m) with two loops and it will be accepted. runtime o(nroot(n)). 

subratdev:
20200509 20:20:49
Since the range difference is 10^5,we need not create a historical array to save result from 1  N (MAX  10^9)


prabhambrose:
20200508 09:18:46
Use segmented Seive guyz ... its meant to be done that way


sarastic_19:
20200505 21:32:42
I got tle error when i use sieveof eratosthenes 

sachin954:
20200430 09:14:13
you can use segmented sieve to solve this problem complexity of this is around max (root(n) , nm)) * loglogn which is always less than o(n) for this problem


m_f_h:
20200428 04:03:06
Even with somewhat optimized algorithm (restrict scan to 6k+1 and primes up to sqrt(n)) it's not possible to avoid timeout in python! That's OK for a challenge but not for a introductory problem. 

arpitjha:
20200424 14:13:51
Last edit: 20200424 14:14:55 

hks_13:
20200418 15:41:16
sqrt is enough , add 6k+1/6k1 logic if needed. Last edit: 20200418 15:47:43 

user_666:
20200413 14:48:06
Guys, just use the sqrt and 6k+1 & 6k1 method and ur solution will be accepted..not need to use the sieve method..All The Best!! 
Added by:  Adam Dzedzej 
Date:  20040501 
Time limit:  6s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 