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.

hide comments
summerbleach: 2020-05-12 11:22:06

The Osqrt(N) approach took 3.63 sec

sabat_raj3: 2020-05-10 21:50:56

Hey!no need for any complex logic. Use simple logic to traverse from m to n and then check from 2 to root(m) with two loops and it will be accepted. runtime o(nroot(n)).

subratdev: 2020-05-09 20:20:49

Since the range difference is 10^5,we need not create a historical array to save result from 1 - N (MAX - 10^9)
But creating a historical array of size 10^ 5 for every test case can be expensive.Any idea how to go ahead?

Last edit: 2020-05-09 20:21:39
prabhambrose: 2020-05-08 09:18:46

Use segmented Seive guyz ... its meant to be done that way

sarastic_19: 2020-05-05 21:32:42

I got tle error when i use sieveof eratosthenes

sachin954: 2020-04-30 09:14:13

you can use segmented sieve to solve this problem complexity of this is around max (root(n) , n-m)) * loglogn which is always less than o(n) for this problem

Idea is first generate all prime from 1 to root(n) and store that in a list and then check prime for number between range m to n using same like sieve

m_f_h: 2020-04-28 04:03:06

Even with somewhat optimized algorithm (restrict scan to 6k+-1 and primes up to sqrt(n)) it's not possible to avoid timeout in python! That's OK for a challenge but not for a introductory problem.

arpitjha: 2020-04-24 14:13:51

Last edit: 2020-04-24 14:14:55
hks_13: 2020-04-18 15:41:16

sqrt is enough , add 6k+1/6k-1 logic if needed.

Last edit: 2020-04-18 15:47:43
user_666: 2020-04-13 14:48:06

Guys, just use the sqrt and 6k+1 & 6k-1 method and ur solution will be accepted..not need to use the sieve method..All The Best!!

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