SPOJ Problem Set (classical)

2. Prime Generator

Problem code: PRIME1

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)

Added by:	Adam Dzedzej
Date:	2004-05-01
Time limit:	6s
Source limit:	50000B
Languages:	All except: TECS

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2009-11-22 08:16:56 Arvind S Raj
I solved this problem using sieve's algorithm to find the primes in the given range. It works fine in my machine but generates a sigabrt() when i upload and run it in spoj. what is wrong?

2009-11-13 08:17:53 anonymous
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 08:18:27

2009-10-07 21:09:22 ian
to solve this problem i use the Erathostenes sieve

2009-09-21 07:17:16 小岛
...It's my first time to use Miller-Rabin...But..it isn't work well...

How can I prove use 2,7,61 is Correct?...

2009-09-16 19:54:05 hu la la
Segmented sieve and straight forward implementation !!!
Mine took 0.04s on judge machine, but I'm wondering how this is done under 0.02s...

Last edit: 2009-09-16 20:10:59

2009-09-05 15:36:09 Krzysztof Kosiński
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.

2009-09-01 13:41:50 Muhammad Ridowan
Its simple Segmented Sieve(Although implementing not so simple)

2009-08-29 23:06:01 Abhirut
ok it will take a lot of time if i check from 2 to sqrt(n) every time... any better algos??

2009-08-27 23:05:54 rusbert almonte
lets to resolve problem, i will begin with the more easy, and then i will upgrade...

2009-08-06 16:41:10 Tony Beta Lambda
Naive Miller-Rabin works well, though not very fast.

Last edit: 2009-08-06 16:45:09