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, n-m<=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
5
Warning: 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
karate_25: 2018-09-24 01:21:10

I wanna know why i get a wrong answer , could I know how u test inputs , do u test it as a collection of input or every input separately ?!!

julkas: 2018-09-23 15:41:35

@kire85 I have tested sieve-of-atkin from geeksforgeeks on ideone.com with your modification for limit=10**6 (without printing primes) with PyPy. It's very slow - 0.17s. My PyPy implementations of SE (sieve of Etatosthenes), OSE (odd sieve of Etatosthenes), SS (sieve of Sundaram) for limit=10**6 give 0.04s.
For this problem I use precomputed primes below (10**9)**0.5 with non orthodoxal Sundaram algorithm and then sieve interval for each query (my PyPy time - 0.02s).
You can make custom and random tests on ideone.com or https://www.spoj.com/problems/BACTERIA/.
If you want good Python time you must optimize I/O also.

Last edit: 2018-09-23 16:41:22
kire85: 2018-09-23 09:53:33

in c++ i get a 0.4 solution with first sieve-ing the primes below 32000 (sqrt of 1 000 000 000) and then using those primes with modolus to check if each number is prime in the range for each testcase. I have coded the same solution i python but TLE. i used https://www.geeksforgeeks.org/sieve-of-atkin/ as sieve. The python code as a flaw. It is missing r =r+1 in the last while loop. I have pointed this out in the comments.

marcobw1: 2018-09-09 19:01:16

Use complexity O(n^2) , check up division until squared(n), it shall work

y17prashant: 2018-09-09 09:05:55

using seive will cause lot of memory for very large numbers . Just read the question we have to only output the prime numbers simply go by traditional sqrt(n) method or use segmented seive.

joe_erwaa: 2018-09-08 18:35:18

would anyone please tell me what sieve is? i'm new for SPOJ

noob_101: 2018-09-07 20:07:10

finally got the solution in python

aj_254: 2018-09-04 19:38:18

finally got AC!! after 23 TLE.same logic of python works in c++ and in python its tle .

anant6025: 2018-09-03 22:19:53

I tried Sieve of Eratosthenes--->TLE
Then tried Sieve of Atkins--->TLE
Then tried the basic less then sqrt(upper limit) approach---->Still wondering how did i get an AC

Last edit: 2018-09-03 22:20:14
contrevien: 2018-09-03 15:59:11

Description says "between", however the second sample test case contradicts this.


Added by:Adam Dzedzej
Date:2004-05-01
Time limit:6s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6