NB.                    topcoderfarfromprimeEG.txt

[from http://www.topcoder.com/stat?c=problem_statement&pm=6074&rd=9812]
Problem Statement for FarFromPrimes
Problem Statement

A prime number is an integer greater than 1 that has no positive
divisors other than 1 and itself. The first prime numbers are 2, 3, 5,
7, 11, 13, 17, ...

The number N is considered far from primes if there are no prime
numbers between N-10 and N+10, inclusive, i.e., all numbers N-10, N-9,
..., N-1, N, N+1, ..., N+9, N+10 are not prime.

You are given an int A and an int B. Return the number of far from
primes numbers between A and B, inclusive.

Definition
Class:FarFromPrimes
Method:count
Parameters:int, int
Returns:int
Method signature:int count(int A, int B)
(be sure your methodis public)

Constraints
-A will be between 10 and 100000, inclusive.
-B will be between A and 100000, inclusive.
-(B - A) will be between 0 and 1000, inclusive.

Examples:

0)
3328
4100
Returns: 4
The far from primes numbers are 3480, 3750, 3978 and 4038.

1)
10
1000
Returns: 0

2)
19240
19710
Returns: 53

3)
23659
24065
Returns: 20

4)
97001
97691
Returns: 89


            +.--------------------+.
    Statistics
    ----------
 Problem Name:  	 FarFromPrimes
Used In: 	SRM 291
Used As: 	Division II Level One
Categories: 	Brute Force, Math

 Competitors  	494
Opens 	482
Percent Open 	97.57%
Percent Submitted 	84.44%
Overall Accuracy 	51.82%

 	Java  	C ++  	C#  	VB  	Overall
Problems Submitted 	165 	199 	33 	10 	407
Problems Correct 	99 	135 	16 	6 	256
Submission Accuracy 	60.00% 	67.84% 	48.48% 	60.00% 	62.90%
Problems Failed by Challenge 	24 	21 	5 	0 	50
Problems Failed by System Test 	42 	43 	12 	4 	101
Challenge Attempts Made 	89 	85 	11 	0 	185
Challenge Accuracy 	26.97% 	24.71% 	45.45% 	0.00% 	27.03%
Best Time 	0:03:41.731 	0:02:24.493 	0:03:33.782 	0:10:28.505 	0:02:24.493
High Scorer 	the_real_janski 	fpavetic 	Skipy 	Archimedean1 	fpavetic
Top Submission 	view 	view 	view 	view 	view
Average Correct Time 	0:19:28.695 	0:18:08.615 	0:15:05.521 	0:16:12.882 	0:18:25.179

            +.--------------------+.
 Problem Statistics for Single Round Match 291 > Round 1 > Room 30 > the_real_janski
	Class Name 	Method Name 	Difficulty 	Status 	Points 	
	[ FarFromPrimes ] 	count 	Level One 	Passed System Test 	245.85 	
	Snowflakes 	flareOut 	Level Two 	Passed System Test 	381.58 	
	CrazySwitches 	minimumActions 	Level Three 	Failed System Test 	492.85 	
View FarFromPrimes  Problem Statement
public class FarFromPrimes {
 
  public boolean prime(int n) {
        for (int i = 2; i*i <= n; i++)
          if (n % i == 0)
            return false;
        return true;
  }
  
  public boolean far(int n) { 
    for (int i = n-10; i <= n+10; i++) {
       if (prime(i))
         return false;
    }
    return true;      
  }
  
  public int count(int A, int B) {
    int count = 0;
    for (int i = A; i <= B; i++) {
      if (far(i)) 
        count++;
    }
    return count;
  }
}
 System Test Results
	Test Arguments 		Expected Results 		Success 	
	3328, 4100 		4 		Passed 	
	10, 1000 		0 		Passed 	
	19240, 19710 		53 		Passed 	
	23659, 24065 		20 		Passed 	
...
	3480, 3750 		2 		Passed 	
	9000, 9713 		21 		Passed 	

            +.--------------------+.
 Problem Statistics for Single Round Match 291 > Round 1 > Room 27 > fpavetic
	Class Name 	Method Name 	Difficulty 	Status 	Points 	
	[ FarFromPrimes ] 	count 	Level One 	Passed System Test 	248.21 	
	Snowflakes 	flareOut 	Level Two 	Passed System Test 	360.49 	
	CrazySwitches 	minimumActions 	Level Three 	Opened 	0.00 	
View FarFromPrimes  Problem Statement
#include <iostream>
#include <cstdio>
#include <vector>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <sstream>
#include <functional>
#include <utility>
#include <cstring>
#include <cmath>
#include <cstdlib>

using namespace std; 
 
 class FarFromPrimes { 
 public: 
    int isprime( int a ) {
        if( a < 2 ) return 0;
        if( a == 2 ) return 1;
        if( a % 2 == 0 ) return 0;

        for( int i = 3; i * i <= a; i += 2 )
            if( a % i == 0 )
                return 0;
        return 1;
    }
    int ok( int a ) {
        for( int i = a-10; i <= a+10; ++i )
            if( isprime( i ) )
                return 0;
        return 1;
    }
    int count( int A, int B ) { 
    int c = 0;
     for( int i = A; i <= B; ++i )
        c += ok( i );
        return c;
   } 
     
   
  
 }; 
 
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// Powered by TZTester 1.01 [25-Feb-2003]
// Powered by CodeProcessor
            +.--------------------+.


   qts''
2006 2 24 9 29 28.637

   p: 10
31
   p: i.10
2 3 5 7 11 13 17 19 23 29
   prms=. p: i. 2000
   p: 2000
17393
   prms=. prms#~prms<:10000
   $prms
1229
   difs=. 2-~/\prms
   >./difs
36

   prms=. prmsBtw 3328 4100
   I. 20<difs=. 2-~/\prms
18 53 80 88
   0 1+/I. 20<difs=. 2-~/\prms
18 53 80 88
19 54 81 89
   prms{~0 1+/I. 20<difs=. 2-~/\prms
3469 3739 3967 4027
3491 3761 3989 4049
   -:+/prms{~0 1+/I. 20<difs=. 2-~/\prms
3480 3750 3978 4038
   prms=. prmsBtw 19240 19710

   +/<:-~/10 _10+"(0 1)prms{~0 1+/I. 23<difs=. 2-~/\prms
53
   ffp
3 : '+/_21+-~/prms{~0 1+/I. 22<2-~/\prms=. crnumvec y.'
   ffp=: 3 : '+/<:-~/10 _10+"(0 1)prms{~0 1+/I. 22<2-~/\prms=. crnumvec y.'
   ffp&.>3328 4100;10 1000;19240 19710;23659 24065;97001 97691
+-+-+--+--+--+
|0|0|53|19|87|
+-+-+--+--+--+
   ffp=: 3 : '+/<:-~/10 _10+"(0 1)prms{~0 1+/I. 21<2-~/\prms=. crnumvec y.'
   ffp&.>3328 4100;10 1000;19240 19710;23659 24065;97001 97691
+-+-+--+--+--+
|4|0|53|20|89|
+-+-+--+--+--+

ffp=: 3 : '+/<:-~/10 _10+"(0 1)prms{~0 1+/I. 21<2-~/\prms=. crnumvec y.'

crnumvec=: 3 : '(<./y.),(>./y.),~prmsBtw (<./,>./)y.'

prmsBtw=: 3 : 0
   y.=. (<./,>./)y.
   pt=. p: nt=. >. 1.2*(1{y.)%^.1{y.
   while. pt<1{y. do. pt=. p: nt=. nt+100 end.
   prms=. p: i. nt
   prms=. prms#~(prms>:0{y.)*.prms<:1{y.
)