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):
import math

def is_prime(n):
    if n == 1: return False

    for k in range(2, int(math.sqrt(n)) + 1):
        if n % k == 0:
            return False

    return True

number = 10**5+1


q = int(input())
lr = [[int(i) for i in input().split()] for j in range(q)]

ans = [0]*(number)
tmp = False

for i in range(number):
    num = i*2+1
    if num >= number:
        break
    if is_prime(num) and is_prime((num+1)/2):
        ans[i] = 1
    else:
        ans[i] = 0

rui = [0]*(number)



for i in range(1,number):
    rui[i] = rui[i-1] + ans[i-1]



for i in range(q):
    print(rui[lr[i][1]//2+1]-rui[lr[i][0]//2])

Solution (Python):
from sys import stdin
from itertools import combinations
from math import factorial
import numpy as np
import math
import bisect

q = int(stdin.readline().rstrip())
l = [0]*q
r = [0]*q

primes = [3, 5, 13, 37, 61, 73, 157, 193, 277, 313, 397, 421, 457, 541, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2797, 2857, 2917, 3061, 3217, 3253, 3313, 3517, 3733, 4021, 4057, 4177, 4261, 4273, 4357, 4441, 4561, 4621, 4933, 5077, 5101, 5113, 5233, 5413, 5437, 5581, 5701, 6037, 6073, 6121, 6133, 6217, 6337, 6361, 6373, 6637, 6661, 6781, 6997, 7057, 7213, 7393, 7417, 7477, 7537, 7753, 7933, 8053, 8101, 8221, 8317, 8353, 8461, 8521, 8677, 8713, 8893, 9013, 9133, 9181, 9241, 9277, 9601, 9661, 9721, 9817, 9901, 9973, 10333, 10357, 10453, 10837, 10861, 10957, 11113, 11161, 11317, 11497, 11677, 11701, 12073, 12157, 12241, 12301, 12421, 12433, 12457, 12541, 12553, 12601, 12721, 12757, 12841, 12853, 13093, 13381, 13417, 13681, 13921, 13933, 14437, 14593, 14737, 14821, 15013, 15073, 15121, 15241, 15277, 15361, 15373, 15733, 15901, 16033, 16333, 16381, 16417, 16573, 16633, 16657, 16921, 17041, 17053, 17077, 17257, 17293, 17377, 17881, 18013, 18097, 18133, 18181, 18217, 18253, 18301, 18313, 18397, 18481, 18553, 18637, 18793, 19237, 19441, 19477, 19717, 19801, 19813, 19861, 20353, 20533, 20641, 20857, 21001, 21061, 21193, 21277, 21313, 21577, 21661, 21673, 21817, 22093, 22501, 22573, 22621, 22993, 23053, 23173, 23557, 23677, 23773, 23917, 24097, 24421,
24481, 24781, 24841, 25033, 25153, 25237, 25561, 25657, 25933, 26017, 26293, 26317, 26437, 26497, 26821, 26833, 26881, 26953, 27073, 27253, 27337, 27361, 27457, 27997, 28057, 28297, 28393, 28813, 28837, 28921, 29101, 29473, 29641, 30181, 30241, 30517, 30553, 30577, 30637, 30661, 30697, 30781, 30853, 31081, 31237, 31321, 31333, 31357, 31477, 31573, 31873, 31981, 32173, 32377, 32497, 32533, 32833, 33037, 33301, 33457, 33493, 33757, 33961, 34057, 34213, 34273, 34381, 34513, 34897, 34981, 35317, 35521, 35677, 35977, 36097, 36241, 36433, 36457, 36793, 36877, 36901, 36913, 37273, 37321, 37357, 37573, 37717, 37957, 38281, 38461, 38833, 38953, 38977, 39217, 39373, 39397, 39733, 40093, 40177, 40213, 40693, 40813, 41017, 41221, 41281, 41413, 41617, 41893, 42061, 42337, 42373, 42793, 42961, 43117, 43177, 43201, 43321, 43573, 43597, 43633, 43717, 44053, 44101, 44221, 44257, 44293, 44893, 45061, 45337, 45433, 45481, 45553, 45613, 45841, 46021, 46141, 46261, 46861, 46993, 47017, 47161, 47353, 47521, 47533, 47653, 47713, 47737, 47797, 47857, 48121, 48193, 48337, 48673, 48757, 48781, 49033, 49261, 49393, 49417, 49597, 49681, 49957, 50221, 50341, 50377, 50821, 50893, 51157, 51217, 51241, 51481, 51517, 51637, 52057, 52081, 52237, 52321, 52453, 52501, 52813, 52861, 52957, 53077, 53113, 53281, 53401, 53917, 54121, 54133, 54181, 54217, 54421, 54517, 54541, 54673, 54721, 54973, 55057, 55381, 55501, 55633, 55837, 55921, 55933, 56053, 56101, 56113, 56197, 56401, 56437, 56701, 56773, 56821, 56857, 56893, 57073, 57097, 57193, 57241, 57373, 57457, 57853, 58153, 58417, 58441, 58537, 58573, 58693,
59053, 59197, 59221, 59281, 59341, 59833, 60217, 60337, 60373, 60637, 60733, 60937, 61057, 61153, 61261, 61297, 61561, 61657, 61681, 61717, 61861, 62137, 62473, 62497, 62533, 62653, 62773, 63313, 63397, 63541, 63697, 63781, 63913, 64153, 64237, 64381, 64513, 64717, 65173, 65293, 65413, 65437, 65497, 65557, 65677, 65881, 66301, 66361, 66601, 66697, 66853, 66973, 67057, 67153, 67273, 67477, 67537, 67741, 67777, 67933, 67993, 68113, 68281, 68521, 68737, 69001, 69073, 69457, 69493, 69697, 69877, 70117, 70177, 70297, 70501, 70621, 70921, 70981, 71233, 71341, 71353, 71593, 71821, 72073, 72481, 72613, 72901, 72937, 73141, 73417, 73477, 73561, 73693, 74077, 74317, 74377, 74713, 75013, 75133, 75181, 75721, 75793, 75913, 76333, 76561, 76597, 76753, 77137, 77641, 78157, 78193, 78277, 78877, 78901, 79333, 79357, 79537, 79657, 79693, 79801, 79873, 80077, 80173, 80221, 80473, 80701, 80713, 80917, 81013, 81181, 81517, 81637, 81853, 82021, 82153, 82261, 82561, 82981, 83077, 83221, 83233, 83437, 83617, 83701, 83773, 84121, 84313, 84673, 84697, 84793, 84913, 85297, 85333, 85453, 85717, 85933, 86353, 86413, 87181, 87253, 87337, 87421, 87433, 87517, 87553, 87973, 88117, 88177, 88237, 88261, 88513, 88741, 88897, 88993, 89293, 89833, 89917, 90121, 91081, 91381, 91393, 91513, 91957, 92041, 92557, 92761, 92821, 92893, 92941, 93097, 93133, 93493, 93637, 93913, 94033, 94117, 94273, 94321, 94441, 94573, 94777, 94837, 94993, 95257, 95317, 95401, 95581, 95617, 95713, 95737, 96097, 96157, 96181, 96493, 96517, 96973, 97081, 97177, 97501, 97561, 97777, 97813, 98017, 98737, 98953, 99277, 99577, 99661,
99877]

for i in range(q):
    l[i],r[i] = [int(x) for x in stdin.readline().rstrip().split()]

for i in range(q):
    print(bisect.bisect(primes,r[i])-bisect.bisect_left(primes,l[i]))

Solution (Python):
from itertools import accumulate

def my_prime(n):
    if n==1:
        return 0
    for k in range(2, int(n**0.5)+1 ): 
        if n%k ==0:
            return 0
    return 1


Q = int(input())
L = [0]*Q
R = [0]*Q

for i in range(Q):
    L[i], R[i] = list(map(int, input().split()))

min_L = min(L)
max_R = max(R)

ans=[]
for i in range(min_L, max_R +1):
    if i%2 == 1:
        flg = (my_prime(i) and my_prime((i+1)/2) )
    else:
        flg = 0
    ans.append(flg)


ans = [0] + ans
ans = list(accumulate(ans))

for i in range(Q):
    print(ans[R[i] - min_L + 1] - ans[L[i] - min_L])

Solution (Python):
import sys







def primeNums(n):
    from math import floor, sqrt
    sieve = set(range(2, n + 1))
    if 2 in sieve:
        not_prime = set(range(2 * 2, n + 1, 2))
        sieve -= not_prime
    for i in range(3, floor(sqrt(n)) + 1, 2):
        if i in sieve:
            not_prime = set(range(i * 2, n + 1, i))
            sieve -= not_prime
    return sieve

limit = 10 ** 5
prime_table = [0 for _ in range(limit + 1)]
for p in primeNums(limit):
    prime_table[p] = 1

like_2017_table = [0 for _ in range(limit + 1)]
for i in range(3, limit + 1, 2):
    if prime_table[i] and prime_table[(i + 1) // 2]:
            like_2017_table[i] = 1

s = [0 for _ in range(limit + 1)]
for i in range(limit):
    s[i+1] = s[i] + like_2017_table[i+1]

def main():

    q = int(sys.stdin.readline().rstrip())
    m = map(int, sys.stdin.read().split())

    for l, r in zip(m, m):
        res = s[r] - s[l-1]
        print(res)


if __name__ == "__main__":
    main()

Solution (Python):
q = int(input())
    
def is_prime(n):
    if n == 1:
        return False
    for i in range(2,int(n**0.5)+1):
        if n % i == 0:
            return False
    return True

ls = [0]

for i in range(1,100000):
    if is_prime(i) and is_prime((i+1)//2):
        ls.append(ls[i-1]+1)
    else:
        ls.append(ls[i-1])
        
for i in range(q):
    l,r = map(int,input().split())
    if l == r:
        if is_prime(l) and is_prime((l+1)//2):
            print(1)
        else:
          print(ls[r]-ls[l-1])  
    else:
        print(ls[r]-ls[l-1])

Solution (Python):
N = 100000
X = [-1] * (N+1)

k = 2
while k <= N:
    X[k] = 1
    for i in range(k*2, N+1, k):
        X[i] = 0
    while k <= N and X[k] >= 0:
        k += 1
P = [i for i in range(N+1) if X[i] == 1]
Y = [0] * (N+1)

for i in range(3, N+1):
    if X[i] and X[(i+1)//2]:
        Y[i] = Y[i-1] + 1
    else:
        Y[i] = Y[i-1]

Q = int(input())
for _ in range(Q):
    l, r = map(int, input().split())
    print(Y[r] - Y[l-1])

Solution (Python):
import math
lim = int(math.pow(10, 5))
is_prime = [True for _ in range(lim+1)]
is_prime[0], is_prime[1] = False, False
for i in range(2, int(math.sqrt(lim))+1):
    if is_prime[i]:
        for j in range(i*2, lim+1, i):
            is_prime[j] = False


nums = [0 for _ in range(lim+1)]
for i in range(2, lim):
    if is_prime[i] and is_prime[(i+1)//2]:
        nums[i] = nums[i-1] + 1
        
    else:
        nums[i] = nums[i-1]

Q = int(input())
for _ in range(Q):
    l, r = map(int, input().split(' '))
    print(nums[r] - nums[l-1])

Solution (Python):
q = int(input())
p = [False]*(10**5)
c = [0]*(10**5)
temp = [True]*(10**5)
temp[0] = False
temp[1] = False
for i in range(2, 10**5):
  c[i] = c[i-1]
  if temp[i]:
    temp[2*i::i] = [False]*(len(temp[i+i::i]))
    if temp[(i+1)//2] and i%2:
      c[i] += 1

for _ in range(q):
  l, r = map(int, input().split())
  print(c[r] - c[l-1])

Solution (Python):
import sys

sys.setrecursionlimit(10 ** 6)
input = sys.stdin.readline
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")

def main():
    max_r = 10 ** 5 + 5
    prime = [False, True] * (max_r // 2 + 1)
    prime[0] = prime[1] = False
    prime[2] = True
    for x in range(3, max_r):
        if prime[x]:
            for y in range(x ** 2, max_r, x):
                prime[y] = False
    cnt_to_x = [0] * max_r
    p = 0
    for x in range(1, max_r, 2):
        if prime[x] and prime[(x + 1) // 2]:
            cnt_to_x[x] = p = p + 1
        else:
            cnt_to_x[x] = p

    q = int(input())
    for _ in range(q):
        l, r = map(int, input().split())
        print(cnt_to_x[r] - cnt_to_x[l - 2])

main()

Solution (Python):
Q = int(input())
L, R = [], []
F = [False for _ in range(10 ** 5 + 1)]
C = [0 for _ in range(10 ** 5 + 2)]

for _ in range(Q):
	l, r = map(int, input().split())
	L.append(l)
	R.append(r)
	
for i in range(2, 10 ** 5 + 1):
	if not F[i]:
		for j in range(2 * i, 10 ** 5 + 1, i):
			F[j] = True

for i in range(3, 10 ** 5 + 1, 2):
	if F[i] == False and F[(i + 1) // 2] == False:
		C[i] += 1
		
for i in range(1, 10 ** 5 + 1):
	C[i] += C[i - 1]
	
	
for i in range(Q):
	print(C[R[i]] - C[L[i] - 1])

Solution (Python):
import bisect

def primes(n):
    is_prime = [True] * (n + 1)
    is_prime[0] = False
    is_prime[1] = False
    for i in range(2, n + 1):
        for j in range(i * 2, n + 1, i):
            is_prime[j] = False
    return [i for i in range(n + 1) if is_prime[i] and is_prime[(i+1)//2]]

Q = int(input())
p_list = primes(10 ** 5)
for _ in range(Q):
    l, r = map(int, input().split())
    li = bisect.bisect_left(p_list, l)
    ri = bisect.bisect_right(p_list, r)
    print(ri-li)

Solution (Python):
p = [True] * 100010
p[0] = p[1] = False
for i in range(2, 100000):
    if p[i]:
        for j in range(2 * i, 100000, i):
            p[j] = False

s = [0] * 100010
for i in range(100000):
    if p[i] and p[(i + 1) // 2]:
        s[i] = s[i - 1] + 1
    else:
        s[i] = s[i - 1]

q = int(input())
for i in range(q):
    l, r = map(int, input().split())
    print(s[r] - s[l - 1])

Solution (Python):
n=100000
p=[0]*2+[1]*(n-1)
for i in range(2,n+1):
  if p[i]:
    for j in range(i*2,n+1,i):
      p[j]=0
for i in range(1,n+1)[::-1]:
  if p[i]:
    if p[(i+1)//2]:
      continue
    p[i]=0
p[2]=0
c=[0]*(n+1)
for i in range(1,n+1):
  c[i]=c[i-1]+p[i]
q=int(input())
for i in range(q):
  l,r=map(int,input().split())
  print(c[r]-c[l-1])

Solution (Python):
import math
Q=int(input())

def isPrime(num):
    
    if num < 2: return False
    
    elif num == 2: return True
    
    elif num % 2 == 0: return False

    for i in range(3, math.floor(math.sqrt(num))+1, 2):
        if num % i == 0:
            return False

    
    return True


def callIsPrime(input_num=1000):
    numbers = []
    for i in range(1, input_num):
        if isPrime(i):
            numbers.append(i)

    return numbers
A=callIsPrime(100000)
b=[False]*100000
for i in A:
  b[i-1]=True
s=[0]*100000
for i in range(1,100000):
  if b[i]:
    if b[int((i+2)/2)-1]:
      s[i]=s[i-1]+1
    else:s[i]=s[i-1]
  else:
    s[i]=s[i-1]
for i in range(Q):
  l,r=map(int,input().split())
  if l==1:print(s[r-1])
  else:print(s[r-1]-s[l-2])

Solution (Python):
import bisect
q = int(input())
l = []
r = []
for _ in range(q):
    line = list(map(int, input().split()))
    l.append(line[0])
    r.append(line[1])
like2017 = []
pn = [2]
for L in range(3, 10**5):
    chk = True
    for L2 in pn:
        if L%L2 == 0:
            chk = False
            break
    if chk:
        pn.append(L)
def bisect_in(x, line):
    return line[bisect.bisect_left(line, x)] == x
for prime in pn:
    if bisect_in((prime+1)//2, pn):
        like2017.append(prime)
for i in range(q):
    left = bisect.bisect_left(like2017, l[i])
    right = bisect.bisect_right(like2017,r[i])
    print(right - left)

Solution (Python):
import bisect
q = int(input())
l = []
r = []
for _ in range(q):
    line = list(map(int, input().split()))
    l.append(line[0])
    r.append(line[1])
like2017 = []
pn = [2]
for L in range(3, 10**5):
    chk = True
    for L2 in pn:
        if L%L2 == 0:
            chk = False
            break
    if chk:
        pn.append(L)
for prime in pn:
    if (prime+1)//2 in pn:
        like2017.append(prime)
for i in range(q):
    left = bisect.bisect_left(like2017, l[i])
    right = bisect.bisect_right(like2017,r[i])
    print(right - left)

Solution (Python):
import bisect
q = int(input())
l = []
r = []
for _ in range(q):
    line = list(map(int, input().split()))
    l.append(line[0])
    r.append(line[1])
like2017 = [3, 5, 13, 37, 61, 73, 157, 193, 277, 313, 397, 421, 457, 541, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2797, 2857, 2917, 3061, 3217, 3253, 3313, 3517, 3733, 4021, 4057, 4177, 4261, 4273, 4357, 4441, 4561, 4621, 4933, 5077, 5101, 5113, 5233, 5413, 5437, 5581, 5701, 6037, 6073, 6121, 6133, 6217, 6337, 6361, 6373, 6637, 6661, 6781, 6997, 7057, 7213, 7393, 7417, 7477, 7537, 7753, 7933, 8053, 8101, 8221, 8317, 8353, 8461, 8521, 8677, 8713, 8893, 9013, 9133, 9181, 9241, 9277, 9601, 9661, 9721, 9817, 9901, 9973, 10333, 10357, 10453, 10837, 10861, 10957, 11113, 11161, 11317, 11497, 11677, 11701, 12073, 12157, 12241, 12301, 12421, 12433, 12457, 12541, 12553, 12601, 12721, 12757, 12841, 12853, 13093, 13381, 13417, 13681, 13921, 13933, 14437, 14593, 14737, 14821, 15013, 15073, 15121, 15241, 15277, 15361, 15373, 15733, 15901, 16033, 16333, 16381, 16417, 16573, 16633, 16657, 16921, 17041, 17053, 17077, 17257, 17293, 17377, 17881, 18013, 18097, 18133, 18181, 18217, 18253, 18301, 18313, 18397, 18481, 18553, 18637, 18793, 19237, 19441, 19477, 19717, 19801, 19813, 19861, 20353, 20533, 20641, 20857, 21001, 21061, 21193, 21277, 21313, 21577, 21661, 21673, 21817, 22093, 22501, 22573, 22621, 22993, 23053, 23173, 23557, 23677, 23773, 23917, 24097, 24421, 24481, 24781, 24841, 25033, 25153, 25237, 25561, 25657, 25933, 26017, 26293, 26317, 26437, 26497, 26821, 26833, 26881, 26953, 27073, 27253, 27337, 27361, 27457, 27997, 28057, 28297, 28393, 28813, 28837, 28921, 29101, 29473, 29641, 30181, 30241, 30517, 30553, 30577, 30637, 30661, 30697, 30781, 30853, 31081, 31237, 31321, 31333, 31357, 31477, 31573, 31873, 31981, 32173, 32377, 32497, 32533, 32833, 33037, 33301, 33457, 33493, 33757, 33961, 34057, 34213, 34273, 34381, 34513, 34897, 34981, 35317, 35521, 35677, 35977, 36097, 36241, 36433, 36457, 36793, 36877, 36901, 36913, 37273, 37321, 37357, 37573, 37717, 37957, 38281, 38461, 38833, 38953, 38977, 39217, 39373, 39397, 39733, 40093, 40177, 40213, 40693, 40813, 41017, 41221, 41281, 41413, 41617, 41893, 42061, 42337, 42373, 42793, 42961, 43117, 43177, 43201, 43321, 43573, 43597, 43633, 43717, 44053, 44101, 44221, 44257, 44293, 44893, 45061, 45337, 45433, 45481, 45553, 45613, 45841, 46021, 46141, 46261, 46861, 46993, 47017, 47161, 47353, 47521, 47533, 47653, 47713, 47737, 47797, 47857, 48121, 48193, 48337, 48673, 48757, 48781, 49033, 49261, 49393, 49417, 49597, 49681, 49957, 50221, 50341, 50377, 50821, 50893, 51157, 51217, 51241, 51481, 51517, 51637, 52057, 52081, 52237, 52321, 52453, 52501, 52813, 52861, 52957, 53077, 53113, 53281, 53401, 53917, 54121, 54133, 54181, 54217, 54421, 54517, 54541, 54673, 54721, 54973, 55057, 55381, 55501, 55633, 55837, 55921, 55933, 56053, 56101, 56113, 56197, 56401, 56437, 56701, 56773, 56821, 56857, 56893, 57073, 57097, 57193, 57241, 57373, 57457, 57853, 58153, 58417, 58441, 58537, 58573, 58693, 59053, 59197, 59221, 59281, 59341, 59833, 60217, 60337, 60373, 60637, 60733, 60937, 61057, 61153, 61261, 61297, 61561, 61657, 61681, 61717, 61861, 62137, 62473, 62497, 62533, 62653, 62773, 63313, 63397, 63541, 63697, 63781, 63913, 64153, 64237, 64381, 64513, 64717, 65173, 65293, 65413, 65437, 65497, 65557, 65677, 65881, 66301, 66361, 66601, 66697, 66853, 66973, 67057, 67153, 67273, 67477, 67537, 67741, 67777, 67933, 67993, 68113, 68281, 68521, 68737, 69001, 69073, 69457, 69493, 69697, 69877, 70117, 70177, 70297, 70501, 70621, 70921, 70981, 71233, 71341, 71353, 71593, 71821, 72073, 72481, 72613, 72901, 72937, 73141, 73417, 73477, 73561, 73693, 74077, 74317, 74377, 74713, 75013, 75133, 75181, 75721, 75793, 75913, 76333, 76561, 76597, 76753, 77137, 77641, 78157, 78193, 78277, 78877, 78901, 79333, 79357, 79537, 79657, 79693, 79801, 79873, 80077, 80173, 80221, 80473, 80701, 80713, 80917, 81013, 81181, 81517, 81637, 81853, 82021, 82153, 82261, 82561, 82981, 83077, 83221, 83233, 83437, 83617, 83701, 83773, 84121, 84313, 84673, 84697, 84793, 84913, 85297, 85333, 85453, 85717, 85933, 86353, 86413, 87181, 87253, 87337, 87421, 87433, 87517, 87553, 87973, 88117, 88177, 88237, 88261, 88513, 88741, 88897, 88993, 89293, 89833, 89917, 90121, 91081, 91381, 91393, 91513, 91957, 92041, 92557, 92761, 92821, 92893, 92941, 93097, 93133, 93493, 93637, 93913, 94033, 94117, 94273, 94321, 94441, 94573, 94777, 94837, 94993, 95257, 95317, 95401, 95581, 95617, 95713, 95737, 96097, 96157, 96181, 96493, 96517, 96973, 97081, 97177, 97501, 97561, 97777, 97813, 98017, 98737, 98953, 99277, 99577, 99661, 99877]

for i in range(q):
    left = bisect.bisect_left(like2017, l[i])
    right = bisect.bisect_right(like2017,r[i])
    print(right - left)

Solution (Python):
f=[True]*(10**5+1)
like=[False]*(10**5+1)
f[0]=False
f[1]=False
import math
for i in range(2,len(f)):
  if not f[i]:
    continue
  fact=True
  for j in range(2,int(math.sqrt(i))+1):
    if i%j==0:
      fact=False
      break
  
  if fact:
    f[i]=True
    if i*2-1<len(like):
      like[i*2-1]=True
    for p in range(i*2,len(f),i):
      f[p]=False

sums=[0]*(10**5+1)
cur=0
for i in range(len(sums)):
  if f[i] and like[i]:
    sums[i]=cur+1
    cur+=1
  else:
    sums[i]=cur

Q=int(input())
for i in range(Q):
  l,r=map(int,input().split())
  print(sums[r]-sums[l-1])

Solution (Python):
f=[True]*(10**5+1)
like=[False]*(10**5+1)
f[0]=False
f[1]=False
import math
for i in range(2,len(f)):
  fact=True
  for j in range(2,int(math.sqrt(i))+1):
    if i%j==0:
      fact=False
      break
  
  if fact:
    f[i]=True
    if i*2-1<len(like):
      like[i*2-1]=True
    for p in range(i*2,len(f),i):
      f[p]=False

sums=[0]*(10**5+1)
cur=0
for i in range(len(sums)):
  if f[i] and like[i]:
    sums[i]=cur+1
    cur+=1
  else:
    sums[i]=cur

Q=int(input())
for i in range(Q):
  l,r=map(int,input().split())
  if l>0:
    print(sums[r]-sums[l-1])
  else:
    print(sums[r])

Solution (Python):
q = int(input())
list_range = [list(map(int, input().split())) for _ in range(q)]

list_flag_prime = [1 for i in range(10**5+1)]
list_flag_prime[0:2] = [0, 0]
for i in range(2, 10**5+1):
  if list_flag_prime[i] == 1:
    for j in range(2*i, 10**5+1, i):
      list_flag_prime[j] = 0

list_subj = [0 for i in range(10**5+1)]
for i in range(3, 10**5+1, 2):
  if list_flag_prime[i] == 1 & list_flag_prime[int((i+1)/2)] == 1:
    list_subj[i] += 1

list_satisfy = [0 for i in range(10**5+1)]
for i in range(1, 10**5+1):
  list_satisfy[i] += list_satisfy[i-1] + list_subj[i]

for l, r in list_range:
  print(list_satisfy[r] - list_satisfy[l-1])

Solution (Python):
isprimes = [True]*(10**5+1)
isprimes[0] = False
isprimes[1] = False
for i in range(2, 10**5+1):
  if isprimes[i]:
    j = i**2
    while j < 10**5+1:
      isprimes[j] = False
      j += i
islikes = [False]*(10**5+1)
for i in range(3, 10**5+1, 2):
  if isprimes[i] and isprimes[(i+1)//2]:
    islikes[i] = True
ruiseki = [0]*(10**5+1)
for i in range(1, 10**5+1):
  ruiseki[i] = ruiseki[i-1]+(1 if islikes[i] else 0)
Q = int(input())
for _ in range(Q):
  l, r = map(int, input().split())
  print(ruiseki[r]-ruiseki[l-1])

Solution (Python):
import math
def is_prime(n):
    if n == 1: return False
    for k in range(2, int(math.sqrt(n)) + 1):
        if n % k == 0:
            return False
    return True
def near2017(n):
    if is_prime(n):
        return is_prime((n+1)//2)
    else:
        return False

import sys
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
mod = 10**9 + 7
inf = float('inf')

N = 100000
prime = [0]*100001
cur = 0
ans = []
for i in range(1,N+1):
    if near2017(i):
        cur +=1
        prime[i] = cur
    else:
        prime[i] = prime[i-1]

cur = int(0)
Q = I()
for i in range(Q):
    l, r = LI()
    cur = prime[r] - prime[l-1]
    ans.append(cur)

for v in ans:
    print(v)

Solution (Python):
import math
def is_prime(n):
    if n == 1: return False
    for k in range(2, int(math.sqrt(n)) + 1):
        if n % k == 0:
            return False
    return True
def near2017(n):
    if is_prime(n):
        return is_prime((n+1)//2)
    else:
        return False

import sys
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))
mod = 10**9 + 7
inf = float('inf')

N = 100000
prime = [0]*100001
cur = 0
ans = []
for i in range(1,N+1):
    if near2017(i):
        cur +=1
        prime[i] = cur
    else:
        prime[i] = prime[i-1]

cur = int(0)
Q = I()
for i in range(Q):
    l, r = LI()
    cur = prime[r] - prime[l-1]
    ans.append(cur)

for v in ans:
    print(v)

Solution (Python):
import sys
input=sys.stdin.readline
from bisect import bisect_left, bisect_right

Q=int(input())
llr=[]
maxr=1
for i in range(Q):
    l,r=map(int,input().split())
    if r>maxr:
        maxr=r
    llr.append([l,r])
def isprime(n):
    if n==1:
        return 0
    m=int(n**(1/2))
    for i in range(2,m+1):
        if n%i==0:
            return 0
            break
    return 1
l2017=[]
for i in range(1,maxr+1,2):
    if isprime(i) and isprime((i+1)/2):
        l2017.append(i)
for i in range(Q):
    il=bisect_left(l2017,llr[i][0])
    ir=bisect_right(l2017,llr[i][1])
    print(ir-il)

Solution (Python):
import sys
input=sys.stdin.readline
from bisect import bisect_left, bisect_right

Q=int(input())
llr=[]
maxr=1
for i in range(Q):
    l,r=map(int,input().split())
    if r>maxr:
        maxr=r
    llr.append([l,r])
def isprime(n):
    if n==1:
        return 0
    m=int(n**(1/2))
    for i in range(2,m+1):
        if n%i==0:
            return 0
            break
    return 1
l2017=[]
for i in range(1,maxr+1,2):
    if isprime(i) and isprime((i+1)/2):
        l2017.append(i)
for i in range(Q):
    il=bisect_left(l2017,llr[i][0])
    ir=bisect_right(l2017,llr[i][1])
    print(ir-il)

Solution (Python):
def main():
    q=int(input())
    pre=[3, 5, 13, 37, 61, 73, 157, 193, 277, 313, 397, 421, 457, 541, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2797, 2857, 2917,
3061, 3217, 3253, 3313, 3517, 3733, 4021, 4057, 4177, 4261, 4273, 4357, 4441, 4561, 4621, 4933, 5077, 5101, 5113, 5233, 5413, 5437, 5581, 5701, 6037, 6073, 6121, 6133, 6217, 6337, 6361, 6373, 6637, 6661, 6781, 6997, 7057, 7213, 7393, 7417, 7477, 7537, 7753, 7933, 8053, 8101, 8221, 8317, 8353, 8461, 8521, 8677, 8713, 8893, 9013, 9133, 9181, 9241, 9277,
9601, 9661, 9721, 9817, 9901, 9973, 10333, 10357, 10453, 10837, 10861, 10957, 11113, 11161, 11317, 11497, 11677, 11701, 12073, 12157, 12241, 12301, 12421, 12433, 12457, 12541, 12553, 12601, 12721, 12757, 12841, 12853, 13093, 13381, 13417, 13681, 13921, 13933, 14437, 14593, 14737, 14821, 15013, 15073, 15121, 15241, 15277, 15361, 15373, 15733, 15901, 16033, 16333, 16381, 16417, 16573, 16633, 16657, 16921, 17041, 17053, 17077, 17257, 17293, 17377, 17881, 18013, 18097, 18133, 18181, 18217, 18253, 18301, 18313, 18397, 18481, 18553, 18637, 18793, 19237, 19441, 19477, 19717, 19801, 19813, 19861, 20353, 20533, 20641, 20857, 21001, 21061, 21193, 21277, 21313, 21577, 21661, 21673, 21817, 22093, 22501, 22573,
22621, 22993, 23053, 23173, 23557, 23677, 23773, 23917, 24097, 24421, 24481, 24781, 24841, 25033, 25153, 25237, 25561, 25657, 25933, 26017, 26293, 26317, 26437, 26497, 26821, 26833, 26881, 26953, 27073, 27253, 27337, 27361, 27457, 27997, 28057, 28297, 28393, 28813, 28837, 28921, 29101, 29473, 29641, 30181, 30241, 30517, 30553, 30577, 30637, 30661, 30697, 30781, 30853, 31081, 31237, 31321, 31333, 31357, 31477, 31573, 31873, 31981, 32173, 32377, 32497, 32533, 32833, 33037, 33301, 33457, 33493, 33757, 33961, 34057, 34213, 34273, 34381, 34513, 34897, 34981, 35317, 35521, 35677, 35977, 36097, 36241, 36433, 36457, 36793, 36877, 36901, 36913, 37273, 37321, 37357, 37573, 37717, 37957, 38281, 38461, 38833, 38953, 38977, 39217, 39373, 39397, 39733, 40093, 40177, 40213, 40693, 40813, 41017, 41221, 41281, 41413, 41617, 41893,
42061, 42337, 42373, 42793, 42961, 43117, 43177, 43201, 43321, 43573, 43597, 43633, 43717, 44053, 44101, 44221, 44257, 44293, 44893, 45061, 45337, 45433, 45481, 45553, 45613, 45841, 46021, 46141, 46261, 46861, 46993, 47017, 47161, 47353, 47521, 47533, 47653, 47713, 47737, 47797, 47857, 48121, 48193, 48337, 48673, 48757, 48781, 49033, 49261, 49393, 49417, 49597, 49681, 49957, 50221, 50341, 50377, 50821, 50893, 51157, 51217, 51241, 51481, 51517, 51637, 52057, 52081, 52237, 52321, 52453, 52501, 52813, 52861, 52957, 53077, 53113, 53281, 53401, 53917, 54121, 54133, 54181, 54217, 54421, 54517, 54541, 54673, 54721, 54973, 55057, 55381, 55501, 55633, 55837, 55921, 55933, 56053, 56101, 56113, 56197, 56401, 56437, 56701, 56773, 56821, 56857, 56893, 57073, 57097, 57193, 57241, 57373, 57457, 57853, 58153, 58417, 58441, 58537,
58573, 58693, 59053, 59197, 59221, 59281, 59341, 59833, 60217, 60337, 60373, 60637, 60733, 60937, 61057, 61153, 61261, 61297, 61561, 61657, 61681, 61717, 61861, 62137, 62473, 62497, 62533, 62653, 62773, 63313, 63397, 63541, 63697, 63781, 63913, 64153, 64237, 64381, 64513, 64717, 65173, 65293, 65413, 65437, 65497, 65557, 65677, 65881, 66301, 66361, 66601, 66697, 66853, 66973, 67057, 67153, 67273, 67477, 67537, 67741, 67777, 67933, 67993, 68113, 68281, 68521, 68737, 69001, 69073, 69457, 69493, 69697, 69877, 70117, 70177, 70297, 70501, 70621, 70921, 70981, 71233, 71341, 71353, 71593, 71821, 72073, 72481, 72613, 72901, 72937, 73141, 73417, 73477, 73561, 73693, 74077, 74317, 74377, 74713, 75013, 75133, 75181, 75721, 75793, 75913, 76333, 76561, 76597, 76753, 77137, 77641, 78157, 78193, 78277, 78877, 78901, 79333, 79357,
79537, 79657, 79693, 79801, 79873, 80077, 80173, 80221, 80473, 80701, 80713, 80917, 81013, 81181, 81517, 81637, 81853, 82021, 82153, 82261, 82561, 82981, 83077, 83221, 83233, 83437, 83617, 83701, 83773, 84121, 84313, 84673, 84697, 84793, 84913, 85297, 85333, 85453, 85717, 85933, 86353, 86413, 87181, 87253, 87337, 87421, 87433, 87517, 87553, 87973, 88117, 88177, 88237, 88261, 88513, 88741, 88897, 88993, 89293, 89833, 89917, 90121, 91081, 91381, 91393, 91513, 91957, 92041, 92557, 92761, 92821, 92893, 92941, 93097, 93133, 93493, 93637, 93913, 94033, 94117, 94273, 94321, 94441, 94573, 94777, 94837, 94993, 95257, 95317, 95401, 95581, 95617, 95713, 95737, 96097, 96157, 96181, 96493, 96517, 96973, 97081, 97177, 97501, 97561, 97777, 97813, 98017, 98737, 98953, 99277, 99577, 99661, 99877]
    for _ in range(q):
        l,r = map(int,input().split())
        ans=0
        for i in range(len(pre)):
            if pre[i]>r:
                break
            if pre[i]>=l:
                ans+=1
        print(ans)

if __name__ == "__main__":
    main()