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

By definition, a prime number is
1. Must be bigger than 1
2. The number must be divisible only by one and itself

Actually, the m|n limit was the key for solving the problem (on my end)

Happy thinking everyone :)

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

I use Miller-Robbin( O(log n) )
and I got AC by C++ use 2 secs.
but when I write the Algorithm by Python, I got TLE.. I saw some people use Python and got AC with very short time. How can they do it?

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

maybe the condition n-m<=100000 might be used to increase efficiency... ?

Rakib Ansary Saikot: 2013-03-13 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.

Can someone please elaborate that?

Diogo F. S. Ramos: 2013-03-13 22:12:29

Two main advices from whom who just beat it:

* Runtime errors can be caused by a excessive use of memory. If you are using "sieve of Eratosthenes", just think how much memory would be used.

* If you are using "sieve of Eratosthenes" -- which were my case -- think how the algorithm mark the non-primes and ask yourself: Do I *really* need to find _all_ the primes up to /n/? Is this what the problem asks?

Last edit: 2010-07-14 05:30:41
Jargon: 2013-03-13 22:12:29

@jgomo3
Many psetters will submit solutions by other people with modifications to see if they can solve a bug in the code. (I know I do.) This results in some non-accepted answers by psetters.

Kacper Wikie┬│: 2013-03-13 22:12:29

Chinese Primary test is too slow;
I think Eratosthenes sieve will go faster.

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

abhirut, find the biggest bound (n), and save all the primes from 2 -> n somewhere

you can refer to that collection every time to check for primes.

there is no need to calculate all the primes every time

Last edit: 2009-11-13 07:18:27
Krzysztof Kosi├▒ski: 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.


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