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!


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.


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.


1 10
3 5


Warning: large Input/Output data, be careful with certain languages (though most should be OK if the algorithm is well designed)


After cluster change, please consider PRINT as a more challenging problem.

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yemyelcee: 2018-04-10 15:58:36

What does runtime error NZEC mean?

nadstratosfer: 2018-04-09 05:17:35

cobwebs, welcome to SPOJ. While many problems here have idiotic time limits preventing AC with a correct Python solution, this is not one of them. It's a great entry point to this site for a pythonist though, as putting work into AC here will reward you in many other problems. C coders can get away with ridiculous stupidity sometimes as the compiler will straighten it out, we can't; your program *has to* be elegant and efficient. There will be an immense satisfaction in other problems later on when daddy compiler can't help "AC in 1 go" usual suspects while your solution gets a green bar.

Got a tad sentimental as it's been almost a year when I came here, an old man trying to relearn things I gave up many years ago. Passed this one with miserable 0.99s after a fierce battle but have taken advantage of this experience in hundreds of other problems. Finally came back a month ago armed with an enlightement I had while brushing my teeth and got my katharsis with a 0.06s. Good luck to every Python enthusiast banging his head against the wall this one problem is, it might just be a begin of a great adventure for you all =)

cobwebs: 2018-04-08 06:42:02

my python3 algorithm can give the correct answer, but it always exceeds the time. The logic is exactly the same as a friend who coded in C++, but his doesn't exceed. Help.

^ this shows the unfairness in timings

Last edit: 2018-04-08 07:21:40
karan_yadav: 2018-03-30 05:43:07

0.88s :)

Johnny Nonsense: 2018-03-24 21:19:16

I completed this in C++ without using sieve. You can run these tests faster by retaining a list of primes from one test to the next. Extend the list as necessary, up to and not exceeding sqrt(M). When determining whether a number is prime, you only have to divide it by all prime numbers in the list up to the square root of the test number. If this method doesn't work in some language other than c++, then maybe the tester is too restrictive in the time constraint for that particular language. I hope that this makes sense.

skandrajmeet: 2018-03-23 10:32:34

please somebody tell me why my code is giving WA .its running perfectly fine for large numbers too.
please suggest some sample test cases to try .code <script src="" type="text/javascript" ></script>

badasshackme: 2018-03-08 17:58:16

Segmented sieve is the solution, but you need to implement it properly or you will hit TLE. For example, see

jhanji999: 2018-03-06 15:08:28

what is sc here btw a total noob here

porsamini: 2018-03-05 07:07:47

Yeah, sieve is not necessary

sky_scraper: 2018-03-02 14:26:12

segmented seive means applying simple seive again on already computed primes(small range) to get primes ahead

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