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
Krzysztof KosiƱski: 2013-03-13 22:12:29

Miller-Rabin can do this, but only in compiled languages. Other languages are too slow. You need to use an experimental result described
<a href="http://primes.utm.edu/prove/prove2_3.html">here</a>

If a number is 2-, 7- and 61-SPRP and lower than 4759123141, then it's prime. Combine this with trial division by primes up to 300 to avoid the SPRP test in obvious cases - otherwise it'll be too slow.

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.

Muhammad Ridowan: 2013-03-13 22:12:29

Its simple Segmented Sieve(Although implementing not so simple)

sxpeter: 2013-03-13 22:12:29

Do remember: 1 is NOT a prime number.

seyyed mohammad razavi: 2013-03-13 22:12:29

yes!!!you must divide numbers to 2 part:(1) befor 1000000 (2)after 1000000

Last edit: 2009-04-11 16:33:00
[Trichromatic] XilinX: 2013-03-13 22:12:29

Please make sure that your algorithm is fast enough to handle input cases like 999900000 1000000000.


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