Problem:
Score : 400 points

Problem Statement

We say that a odd number N is similar to 2017 when both N and (N+1)/2 are prime.

You are given Q queries.

In the i-th query, given two odd numbers l_i and r_i, find the number of odd numbers x similar to 2017 such that l_i ≤ x ≤ r_i.

Constraints

1≤Q≤10^5

1≤l_i≤r_i≤10^5

l_i and r_i are odd.

All input values are integers.

Input

Input is given from Standard Input in the following format:

Q
l_1 r_1
:
l_Q r_Q

Output

Print Q lines. The i-th line (1≤i≤Q) should contain the response to the i-th query.

Sample Input 1

1
3 7

Sample Output 1

2

3 is similar to 2017, since both 3 and (3+1)/2=2 are prime.

5 is similar to 2017, since both 5 and (5+1)/2=3 are prime.

7 is not similar to 2017, since (7+1)/2=4 is not prime, although 7 is prime.

Thus, the response to the first query should be 2.

Sample Input 2

4
13 13
7 11
7 11
2017 2017

Sample Output 2

1
0
0
1

Note that 2017 is also similar to 2017.

Sample Input 3

6
1 53
13 91
37 55
19 51
73 91
13 49

Sample Output 3

4
4
1
1
1
2

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <stdlib.h>
#include <stdbool.h>
#define MOD 1000000007
#define INFTY 2147400000
#define END printf("\n");return 0;
#define QS09(how_data,data) qsort(data,how_data,sizeof(long),(int (*)(const void *,const void *))qsort_09);
#define QS90(how_data,data) qsort(data,how_data,sizeof(long),(int (*)(const void *,const void *))qsort_90);
#define In(a) long a;scanf("%ld",&a);
#define Out(a) printf("%ld\n",a);
#define MAKE_ARRAY_DATA In(how_data);long data[how_data];input_array(how_data,data);
void input_array(long how_data,long *data);
void output_array(long how_data,long *data);
void input_array2(long first , long second , long data[][2]);
void format_array(long how_data ,long *data,long what);
long get_random(long min, long max);
long factorial(long n);
long fibonacci(long n);
int qsort_09(const int *sys1 , const int *sys2);
int qsort_90(const int *sys1 , const int *sys2);
long sel_max(long a , long b);
long sel_min(long a , long b);
long array_max(long how_data,long *data);
long array_min(long how_data,long *data);
long array_search(long how_data,long *data,long what);
long can_DP(long how_data,long *data,long how_can,bool *can);
long array_sum(long how_data,long *data);
long Leven_dist(char *now , char *target);
long get_digit(long target);
long rounding(double target);
long roundingdown(double target);
long roundingup(double target);
long ncr(long n , long r);
long npr(long n , long r);
long nhr(long n , long r);
int fifw(long add,long *data);
long fifr(long *data);
void GRAPH_input(void);
void GRAPH_dfs(long now);
bool check_prime(long target);

//グローバル変数一覧
long fifo[1000]={0};//fifo[0]はデータ件数
long loop1,loop2,loop3,loop4,loop5,i_temp;
long g_ans=0; //answerグローバル変数用

typedef struct{
    long how_vertex;
    long how_edge;
    long edge_data[1000][2];
    bool aleady_searched_vertex[500];
    bool all_searched;
} _GD;//GraphData

_GD GRAPH={0,0,{{0}},{0},0};

char c_temp;


int main(void){
    //あらかじめ、全ての数に対して判定しておく
    
    bool niteiru[100010]={0};
    long ruiseki[100010]={0};
    for(loop1=1;loop1<100005;loop1++){
        ruiseki[loop1]=ruiseki[loop1-1];
        if(check_prime(loop1)==1 && check_prime((loop1+1)/2)){
            niteiru[loop1]=1;
            ruiseki[loop1]++;
            //printf("%ld\n",loop1);
        }
        
    }
    In(how_q);
    for(loop1=0;loop1<how_q;loop1++){
        In(a);In(s);
        long ans=ruiseki[s]-ruiseki[a];
        if(niteiru[a]==1)ans++;
        printf("%ld\n",ans);
        
        //printf("%ld\n",ans);
    }
    END;
    
}
 

 
void input_array(long how_data,long *data){
    long loop;
    for(loop=0;loop<how_data;loop++){
        scanf("%ld",&data[loop]);
    }
    return ;
}
void output_array(long how_data,long *data){
    long loop;
    for(loop=0;loop<how_data-1;loop++){
        printf("%ld ",data[loop]);
    }
    return ;
}
void input_array2(long first,long second,long data[][2]){
    long loopA,loopB;
    for(loopA=0;loopA<first;loopA++){
        for(loopB=0;loopB<second;loopB++){
            scanf("%ld",&data[loopA][loopB]);
        }
    }
    return ;
}
void format_array(long how_data ,long *data,long what){
    long loopA;
    for(loopA=0;loopA<how_data;loopA++){
        data[loopA]=what;
    }
    return ;
}
long get_random(long min, long max){   //指定の範囲から乱数を1つ返すやつ
    //srand((unsigned int)time(0));   //現在時刻で疑似乱数初期化
    rand();rand();rand();rand();    //乱数を空打ち
    return (rand()%(max+1-min))+min;
}
long factorial(long n){//n!のMOD10^9+7を返すやつ
    unsigned long long int ret=1;
    for(long i=1;i<=n;i++)ret=(ret*i)%1000000007;
    return (long)ret;
}
int qsort_09(const int *sys1 , const int *sys2){ //小さいのが上にくるやつ
    //qsort(data,how_data,sizeof(long),(int (*)(const void *,const void *))qsort_09);
    if(*sys1<*sys2){
        return -1;
    }else if(*sys1==*sys2){
        return 0;
    }else{
        return 1;
    }
}
int qsort_90(const int *sys1 , const int *sys2){ //大きいのが上にくるやつ
    //qsort(data,how_data,sizeof(long),(int (*)(const void *,const void *))qsort_90);
    if(*sys1<*sys2){
        return 1;
    }else if(*sys1==*sys2){
        return 0;
    }else{
        return -1;
    }
}
long fibonacci(long n){
    switch(n){
        case 0:return 0;
        case 1:return 1;
        default :return fibonacci(n-1)+fibonacci(n-2);
    }
}
long sel_max(long a,long b){
    if(a>b)return a;
    return b;
}
long sel_min(long a,long b){
    if(a>b)return b;
    return a;
}
long can_DP(long how_data,long *data,long how_can,bool *can){//Typical DP Contest A
    //data内で組み合わせられる和をcanに0 or 1で入れる
    //返り値はパターン数
    long loopA,loopB;
    long ret=0;
    for(loopA=0;loopA<how_can;loopA++){//初期化
        can[loopA]=0;
    }
    can[0]=1;//絶対にありえる
    for(loopA=0;loopA<how_data;loopA++){
        for(loopB=how_can-1;loopB>=0;loopB--){
            if(can[loopB]==1 && loopB+data[loopA]<how_can){
                can[loopB+data[loopA]]=1;
            }
        }
    }
    for(loopA=0;loopA<how_can;loopA++){
        if(can[loopA]==1){
            ret++;
        }
    }
    return ret;
}
long array_max(long how_data,long *data){
    long loop;
    long ret=data[0];
    for(loop=0;loop<how_data;loop++){
        if(ret<data[loop])ret=data[loop];
    }
    return ret;
}
long array_min(long how_data,long *data){
    long loop;
    long ret=data[0];
    for(loop=0;loop<how_data;loop++){
        if(ret>data[loop])ret=data[loop];
    }
    return ret;
}
long array_sum(long how_data,long *data){
    long ret=0;
    long loop;
    for(loop=0;loop<how_data;loop++){
        ret+=data[loop];
    }
    return ret;
}
long array_search(long how_data,long *data,long what){
    long loop;
    for(loop=0;loop<how_data;loop++){
        if(data[loop]==what){
            return loop;
        }
    }
    return -1;
}
long Leven_dist(char *now , char *target){
    long loopA,loopB;
    //レーベンシュタイン距離を求める
    // 参考文献
    // http://nw.tsuda.ac.jp/class/algoB/c13.html  (アルゴリズム理解)
    // http://d.hatena.ne.jp/ohnishiakira/20090809/1249845529  (実装)
    long len_now=strlen(now)+1;
    long len_target=strlen(target)+1;
    long d[len_now][len_target]; //計算用
    for(loopA=0;loopA<len_now;loopA++) d[loopA][0]=loopA;
    for(loopA=0;loopA<len_target;loopA++) d[0][loopA]=loopA;
    for(loopA=1;loopA<len_now;loopA++){
        for(loopB=1;loopB<len_target;loopB++){
            long cost=(now[loopA-1]==target[loopB-1] ? 0:1);
            d[loopA][loopB]=sel_min(sel_min(d[loopA-1][loopB]+1,d[loopA][loopB-1]+1),d[loopA-1][loopB-1]+cost);
        }
    }
    return d[len_now-1][len_target-1];
}
long get_digit(long target){
    return (long)(log10(target)+1);
}
long ncr(long n , long r){
    //パスカルの三角形
    long loopA,loopB;
    long pascal[100][102]={{0}};
    pascal[1][0]=1;
    pascal[1][1]=1;
    for(loopA=2;loopA<100;loopA++){
        pascal[loopA][0]=1;
        for(loopB=1;loopB<loopA;loopB++){
            pascal[loopA][loopB]=pascal[loopA-1][loopB-1]+pascal[loopA-1][loopB];
        }
        pascal[loopA][loopA]=1;
    }
    return pascal[n][r];
}
long npr(long n, long r){
    return ncr(n,r)*factorial(r);
}
long nhr(long n , long r){
    return ncr(n+r-1,r);
}
long rounding(double target){
    return (long)target+0.50;
}
long roundingup(double target){
    return (long)ceil(target);
}
long roundingdown(double target){
    return (long)floor(target);
}
int fifw(long add,long *data){
    data[data[0]+1]=add;
    data[0]++;
    return data[0]; //現在のデータ件数を返す
}
long fifr(long *data){
    long ret=data[1];
    data[0]--;
    for(int i=1;i<999;i++){
        data[i]=data[i+1];
    }
    return ret;
}
void GRAPH_input(void){
    scanf("%ld %ld\n",&GRAPH.how_vertex,&GRAPH.how_edge);
    for(long loopA=0;loopA<GRAPH.how_edge;loopA++){
        scanf("%ld %ld\n",&GRAPH.edge_data[loopA][0],&GRAPH.edge_data[loopA][1]);
    }
    return;
}

void GRAPH_dfs(long now){
    GRAPH.aleady_searched_vertex[now]=1;
    for(int loopA=0;loopA<GRAPH.how_edge;loopA++){
        if(GRAPH.edge_data[loopA][0]==now && GRAPH.aleady_searched_vertex[GRAPH.edge_data[loopA][1]]==0){
            GRAPH_dfs(GRAPH.edge_data[loopA][1]);
        }
        if(GRAPH.edge_data[loopA][1]==now && GRAPH.aleady_searched_vertex[GRAPH.edge_data[loopA][0]]==0){
            GRAPH_dfs(GRAPH.edge_data[loopA][0]);
        }
    }
    return ;
}

bool check_prime(long target){//素数判定、素数なら1
    bool flag=0;
    int loopA;
    for(loopA=2;loopA<=sqrt(target)+1;loopA++){
        if(target%loopA==0){
            flag=1;
            loopA=target;
        }
        //printf("%d\n",loopA);
    }
    if(target==2)return 1;
    if((flag==1 || target==1))return 0;
    return 1;
    
}