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 (Python):
sosu = 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dp = [False]*(10**5+1);c = 0;check = [False]*(10**5+1)
for i in range(1,10**5+1):
    if i == sosu[c]:dp[i] = True;c+=1
    else:dp[i] = False
for i in range(len(sosu)):
    n = sosu[i]
    if dp[(n+1)//2]:check[n] = True
dp_ios = [0]*(10**5+1)
for i in range(1,10**5+1):
    if check[i]:dp_ios[i] = dp_ios[i-1] + 1
    else:dp_ios[i] = dp_ios[i-1]
q = int(input())
for i in range(q):
    l,r = map(int,input().split())
    print(dp_ios[r]-dp_ios[l-1])