Buggy python submission (verdict: Time Limit Exceeded):
import random
import numpy as np

def is_prime(q,k=50):
    if q == 2: return 1
    if q < 2 or q&1 == 0: return 0

    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return 0
    return 1
  
chk = np.array([0]*10**5)
for i in range(10**5):
  chk[i] = is_prime(i+1,10)
  
ans = np.array([0]*10**5)
for i in range(2,10**5):
  ans[i] = chk[i]&chk[(i+1)//2]
np.cumsum(ans,out=ans)

q = int(input())
for i in range(q):
  l,s = map(int,input().split())
  print(ans[s-1]-ans[max(0,l-2)])

Fixed submission:
import random
import numpy as np

def is_prime(q,k=50):
    # q = abs(q)
    #計算するまでもなく判定できるものははじく
    if q == 2: return 1
    if q < 2 or q&1 == 0: return 0

    #n-1=2^s*dとし（但しaは整数、dは奇数)、dを求める
    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    #判定をk回繰り返す
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        #[0,s-1]の範囲すべてをチェック
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return 0
    return 1
  
chk = np.array([0]*10**5)
for i in range(10**5):
  chk[i] = is_prime(i+1,15)
  
ans = np.array([0]*10**5)
for i in range(2,10**5):
  ans[i] = chk[i]&chk[(i+1)//2]
np.cumsum(ans,out=ans)

import sys
input = sys.stdin.readline
q = int(input())
for i in range(q):
  l,s = map(int,input().split())
  print(ans[s-1]-ans[max(0,l-2)])

Buggy python submission (verdict: Time Limit Exceeded):
import random
import numpy as np

def is_prime(q,k=50):
    # q = abs(q)
    #計算するまでもなく判定できるものははじく
    if q == 2: return 1
    if q < 2 or q&1 == 0: return 0

    #n-1=2^s*dとし（但しaは整数、dは奇数)、dを求める
    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    #判定をk回繰り返す
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        #[0,s-1]の範囲すべてをチェック
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return 0
    return 1
  
chk = np.array([0]*10**5)
for i in range(10**5):
  chk[i] = is_prime(i+1,20)
  
ans = np.array([0]*10**5)
for i in range(2,10**5):
  ans[i] = chk[i]&chk[(i+1)//2]
np.cumsum(ans,out=ans)

q = int(input())
for i in range(q):
  l,s = map(int,input().split())
  print(ans[s-1]-ans[max(0,l-2)])

Fixed submission:
import random
import numpy as np

def is_prime(q,k=50):
    # q = abs(q)
    #計算するまでもなく判定できるものははじく
    if q == 2: return 1
    if q < 2 or q&1 == 0: return 0

    #n-1=2^s*dとし（但しaは整数、dは奇数)、dを求める
    d = (q-1)>>1
    while d&1 == 0:
        d >>= 1
    
    #判定をk回繰り返す
    for i in range(k):
        a = random.randint(1,q-1)
        t = d
        y = pow(a,t,q)
        #[0,s-1]の範囲すべてをチェック
        while t != q-1 and y != 1 and y != q-1: 
            y = pow(y,2,q)
            t <<= 1
        if y != q-1 and t&1 == 0:
            return 0
    return 1
  
chk = np.array([0]*10**5)
for i in range(10**5):
  chk[i] = is_prime(i+1,15)
  
ans = np.array([0]*10**5)
for i in range(2,10**5):
  ans[i] = chk[i]&chk[(i+1)//2]
np.cumsum(ans,out=ans)

import sys
input = sys.stdin.readline
q = int(input())
for i in range(q):
  l,s = map(int,input().split())
  print(ans[s-1]-ans[max(0,l-2)])