Lia is fascinated by anything she considers to be a twin. She calls a pairs of positive integers, $\boldsymbol{i}$ and $j$, twins if:

They are both prime. A prime number is an integer greater than $\mbox{1}$ that has no positive divisors other than $\mbox{1}$ and itself.

Their absolute difference is exactly equal to $2$ (i.e., $|j-i|=2$).

Given an inclusive interval of integers from $n$ to $m$, can you help Lia find the number of pairs of twins there are in the interval (i.e., $[n,m]$)? Note that pairs $(i,j)$ and $(j,i)$ are considered to be the same pair.

Input Format

Two space-separated integers describing the respective values of $n$ and $m$.

Constraints

$1\leq n\leq m\leq10^9$  
$m-n\leq10^6$  

Output Format

Print a single integer denoting the number of pairs of twins.

Sample Input 0
3 13

Sample Output 0
3

Explanation 0

There are three pairs of twins: $(3,5),(5,7)$, and $(11,13)$.

Difficulty: MEDIUM
Tags: Number theory

Starter code:

Solutions:
limit = 1000000
(beg, end) = map(int, input().strip().split(' '))
is_prime = [False] * (limit + 1)
prime = []
for x in range(1, int(limit ** 0.5) + 1):
	for y in range(1, int(limit ** 0.5) + 1):
		n = 4 * x ** 2 + y ** 2
		if n <= limit and (n % 12 == 1 or n % 12 == 5):
			is_prime[n] = not is_prime[n]
		n = 3 * x ** 2 + y ** 2
		if n <= limit and n % 12 == 7:
			is_prime[n] = not is_prime[n]
		n = 3 * x ** 2 - y ** 2
		if x > y and n <= limit and (n % 12 == 11):
			is_prime[n] = not is_prime[n]
for n in range(5, int(limit ** 0.5)):
	if is_prime[n]:
		for k in range(n ** 2, limit + 1, n ** 2):
			is_prime[k] = False
is_prime[2] = is_prime[3] = True
if end <= limit:
	for i in range(beg, end + 1):
		if is_prime[i]:
			prime.append(i)
else:
	d = end - beg
	ans = [True] * (d + 2)
	i = 2
	while i * i <= end:
		if is_prime[i]:
			k = beg // i
			k = k * i
			if k < beg:
				k += i
			if k == i:
				k += i
			while k <= end:
				ans[k - beg] = False
				k += i
		i += 1
	for i in range(d + 1):
		if ans[i]:
			prime.append(beg + i)
count = 0
l = len(prime)
for i in range(l - 1):
	if abs(prime[i] - prime[i + 1]) == 2:
		count += 1
print(count)


(n, m) = map(int, input().split())
table = [1] * (m - n + 1)
if n == 1:
	table[0] = 0
for i in range(2, 40000):
	for j in range(max(i * i, (n + i - 1) // i * i), m // i * i + 1, i):
		table[j - n] = 0
print(len([i for i in range(m - n + 1 - 2) if table[i] and table[i + 2]]))


def potential_primes():
	s = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29)
	for i in s:
		yield i
	s = (1,) + s[3:]
	j = 30
	while True:
		for i in s:
			yield (j + i)
		j += 30

def range_sieve(lo, hi):
	lo = max(2, lo)
	primes = [True] * (hi - lo)
	ihi = int(hi ** 0.5)
	for i in potential_primes():
		if i > ihi:
			break
		ilo = max(i, 1 + (lo - 1) // i) * i
		n = 1 + (hi - ilo - 1) // i
		primes[ilo - lo::i] = n * [False]
	return [i for (i, v) in enumerate(primes, lo) if v]
(n, m) = map(int, input().split())
lst = range_sieve(n, m + 1)
count = 0
for i in range(len(lst) - 1):
	if lst[i + 1] - lst[i] == 2:
		count += 1
print(count)


from math import *

def compute_primes_for(number):
	primes = [2, 3]
	finalnum = int(sqrt(number)) + 1
	for m in range(1, int(finalnum / 6) + 1):
		n = 6 * m - 1
		isPrime = True
		i = 0
		maxi = int(sqrt(n))
		while isPrime == True and primes[i] <= maxi:
			if n % primes[i] == 0:
				isPrime = False
			i += 1
		if isPrime == True:
			primes.append(n)
		n = 6 * m + 1
		isPrime = True
		i = 0
		maxi = int(sqrt(n))
		while isPrime == True and primes[i] <= maxi:
			if n % primes[i] == 0:
				isPrime = False
			i += 1
		if isPrime == True:
			primes.append(n)
	return primes
(x, y) = list(map(int, input().strip().split()))
primes = compute_primes_for(y)
count = 0
is_prime = [True] * (y - x + 1)
for r in range(len(primes)):
	prime = primes[r]
	min_multiplier = int(x / prime)
	min_multiplier = max(2, min_multiplier)
	max_multiplier = int(y / prime)
	for m in range(min_multiplier, max_multiplier + 1):
		index = m * prime - x
		if index < 0:
			continue
		if index >= len(is_prime):
			continue
		is_prime[index] = False
if x <= 3 and y >= 5:
	count += 1
for j in range(int(x / 6), int(y / 6) + 1):
	p = 6 * j - 1
	q = 6 * j + 1
	if p < x or q > y:
		continue
	p_index = p - x
	q_index = q - x
	if is_prime[p_index] and is_prime[q_index]:
		count += 1
print(count)


import math
(n, m) = [int(m) for m in input().strip().split()]

def IsPrime(n):
	if n % 2 == 0:
		return False
	nm1 = n - 1
	s = 0
	while nm1 % 2 == 0:
		nm1 = nm1 // 2
		s += 1
	d = nm1
	nm1 = n - 1
	if n > 251 and n < 4759123141:
		aRng = [2, 7, 61]
	else:
		UpperBound = int(min([n - 1, math.log(n) ** 2 * 2 // 1]))
		aRng = range(2, UpperBound + 1)
	for a in aRng:
		ExpVal = pow(a, d, n)
		if ExpVal != 1:
			CompBool = True
			for r in range(s):
				if r > 0:
					ExpVal = pow(ExpVal, 2, n)
				if ExpVal == nm1:
					CompBool = False
					break
			if CompBool:
				return False
	return True
if n % 2 == 0:
	n += 1
if m % 2 == 0:
	m -= 1
if n == 1:
	n += 2
PrimeList = []
Count = 0
for i in range(n, m + 1, 2):
	if IsPrime(i):
		PrimeList.insert(0, i)
		if len(PrimeList) > 2:
			PrimeList.pop()
		if len(PrimeList) == 2:
			if PrimeList[0] == PrimeList[1] + 2:
				Count += 1
print(Count)


from math import sqrt, ceil

def cross_out(num_prime_list, prime, start):
	begin = max(prime * prime - start, 0)
	i = begin
	while i < len(num_prime_list):
		if (start + i) % prime == 0:
			num_prime_list[i] = False
			i += prime
		else:
			i += 1
(n, m) = [int(s) for s in input().split()]
if m - n < 2:
	print(0)
	exit()
(small_primes, sp_start) = ([True] * (ceil(sqrt(m)) - 1), 2)
(big_primes, bp_start) = ([True] * (m - n + 1), n)
for i in range(0, len(small_primes)):
	p = i + 2
	if small_primes[i] == False:
		continue
	cross_out(small_primes, p, sp_start)
	cross_out(big_primes, p, bp_start)
nm_primes = (bp_start + i for (i, is_prime) in enumerate(big_primes) if is_prime)
(count, prev) = (0, next(nm_primes))
for i in nm_primes:
	if i - prev == 2:
		count += 1
	prev = i
print(count)


(n, m) = input().split()
(n, m) = (int(n), int(m))

def sieve(num):
	ARRAY = [True] * (num + 1)
	ARRAY[0] = ARRAY[1] = False
	for i in range(2, int(num ** 0.5) + 1):
		if ARRAY[i] == True:
			for j in range(2 * i, num + 1, i):
				ARRAY[j] = False
	return [j for (j, i) in enumerate(ARRAY) if i == True]
prime_nums = sieve(int(m ** 0.5) + 1)
prev = -2
count = 0
pos = 0
values = [True for i in range(m - n + 1)]
for i in prime_nums:
	hop = 1
	start = 0
	for pos in range(2 * i + 1):
		if (pos + n) % i == 0 and pos + n != i:
			hop = i
			start = pos
			break
	for j in range(start, m + 1 - n, hop):
		if (j + n) % i == 0:
			values[j] = False
results = [pos + n for (pos, val) in enumerate(values) if val == True]
for i in results:
	if i - prev == 2:
		count += 1
	prev = i
print(count)


import random

def rabinMiller(num):
	s = num - 1
	t = 0
	while s % 2 == 0:
		s = s // 2
		t += 1
	for trials in range(5):
		a = random.randrange(2, num - 1)
		v = pow(a, s, num)
		if v != 1:
			i = 0
			while v != num - 1:
				if i == t - 1:
					return False
				else:
					i = i + 1
					v = v ** 2 % num
	return True

def isPrime(num):
	if num < 2:
		return False
	lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]
	if num in lowPrimes:
		return True
	for prime in lowPrimes:
		if num % prime == 0:
			return False
	return rabinMiller(num)

def generateLargePrime(keysize=1024):
	while True:
		num = random.randrange(2 ** (keysize - 1), 2 ** keysize)
		if isPrime(num):
			return num
(n, m) = [int(x) for x in input().split(' ')]
cnt = 0
a = (n // 6 + 1) * 6 - 1
for i in range(a, m - 1, 6):
	if isPrime(i) and isPrime(i + 2):
		cnt += 1
print(cnt + 1 if n <= 3 and m >= 5 else cnt)


def miller_rabin(n):
	if n < 2:
		return False
	if n == 2:
		return True
	if n == 3:
		return True
	if n & 1 == 0:
		return False
	witness = [2, 3, 5, 7]
	r = 0
	d = n - 1
	while d & 1 == 0:
		d >>= 1
		r += 1
	for a in [w for w in witness if w <= n - 2]:
		x = pow(a, d, n)
		if x == 1 or x == n - 1:
			continue
		for i in range(r):
			x = pow(x, 2, n)
			if x == 1:
				return False
			if x == n - 1:
				break
		else:
			return False
	return True
(n, m) = [int(x) for x in input().split()]
c = 0
for i in range(n, m + 1 - 2):
	if n < 7 or i % 10 == 1 or i % 10 == 7 or (i % 10 == 9):
		if miller_rabin(i) and miller_rabin(i + 2):
			c += 1
print(c)


import sys
(n, m) = map(int, input().split())
if m - n < 2:
	print(0)
	sys.exit()
arr = [1] * (m - n + 1)
left = []
primes = [1] * (int(m ** 0.5) + 1)
for k in range(2, int(m ** 0.5) + 1):
	if primes[k] == 1:
		left.append(k)
		for l in range(k + k, int(m ** 0.5) + 1, k):
			primes[l] = 0
for i in left:
	start = int(n / i) * i
	if start < n:
		start += i
	if start == i:
		start += start
	for j in range(start, m + 1, i):
		arr[j - n] = 0
count = 0
if n == 1:
	arr[0] = 0
if len(arr) < 2:
	print(0)
	sys.exit()
for i in range(2, len(arr)):
	if arr[i] == 1 and arr[i - 2] == 1:
		count += 1
print(count)


def rwh_primes(n):
	sieve = [True] * n
	for i in range(3, int(n ** 0.5) + 1, 2):
		if sieve[i]:
			sieve[i * i::2 * i] = [False] * ((n - i * i - 1) // (2 * i) + 1)
	return [2] + [i for i in range(3, n, 2) if sieve[i]]
top = 31610
primes = set(rwh_primes(top))

def isPrime(n):
	if n < top:
		return n in primes
	else:
		for p in primes:
			if not n % p:
				return False
		return True
(x, y) = map(int, input().split())
xx = x - x % 6 + 6
count = 0
if x <= 3 and y >= 5:
	count = 1
for z in range(xx, y, 6):
	if isPrime(z - 1) and isPrime(z + 1):
		count += 1
print(count)


import mmap
(n, m) = map(int, input().split())

def rwh_primes2(n, m):
	correction = n % 6 > 1
	n = {0: n, 1: n - 1, 2: n + 4, 3: n + 3, 4: n + 2, 5: n + 1}[n % 6]
	sieve = mmap.mmap(-1, n // 3)
	sieve[0] = True
	for i in range(int(n ** 0.5) // 3 + 1):
		if not sieve[i]:
			k = 3 * i + 1 | 1
			kk = k * k
			nd6 = n // 6
			sieve[kk // 3::2 * k] = b'\x01' * ((nd6 - kk // 6 - 1) // k + 1)
			sieve[(kk + 4 * k - 2 * k * (i & 1)) // 3::2 * k] = b'\x01' * ((nd6 - (kk + 4 * k - 2 * k * (i & 1)) // 6 - 1) // k + 1)
	head = []
	if m <= 2:
		head.append(2)
	if m <= 3:
		head.append(3)
	return head + [3 * i + 1 | 1 for i in range(m // 3, n // 3 - correction) if not sieve[i]]
primes = rwh_primes2(m + 1, n)
result = 0
for i in range(len(primes) - 1):
	(p1, p2) = primes[i:i + 2]
	if abs(p1 - p2) == 2:
		result += 1
print(result)


from math import sqrt
primes = []
(n, m) = map(int, input().split())
r = 4 * 10000
arr = [1 for i in range(r)]
for i in range(2, r):
	if arr[i] == 0:
		continue
	else:
		primes.append(i)
		for j in range(i, r, i):
			arr[j] = 0

def t_prime(a):
	for j in primes:
		if j > sqrt(a + 2):
			return True
		if a % j == 0 or (a + 2) % j == 0:
			return False
	return True
count = 1
ans = 0
for i in range(n, m - 1):
	if i == 1 or i == 2:
		continue
	if t_prime(i):
		ans += 1
print(ans)


smallLimit = 320000
(n, m) = map(int, input().split())
smallSieve = [True] * smallLimit
bigSieve = [True] * (m - n + 1)
for i in range(2, smallLimit):
	if smallSieve[i]:
		for k in range(2 * i, smallLimit, i):
			smallSieve[k] = False
		for k in range(max(2 * i, (1 + (n - 1) // i) * i), m + 1, i):
			bigSieve[k - n] = False
primes = [i for i in range(n, m + 1) if bigSieve[i - n]]
print(sum((y - x == 2 for (x, y) in zip(primes, primes[1:]))))


def sieve(m):
	limit = m + 1
	a = list(range(limit))
	a[1] = 0
	sqrtm = int(round(m ** 0.5))
	for i in range(2, sqrtm + 1):
		if a[i]:
			a[i * i:limit:i] = [0] * len(range(i * i, limit, i))
	return filter(None, a)

def bounded_sieve(lo, hi, base_primes):
	a = list(range(lo, hi))
	for p in base_primes:
		lowlim = lo // p * p
		if lowlim < lo:
			lowlim += p
		a[lowlim - lo:hi - lo:p] = [0] * len(range(lowlim - lo, hi - lo, p))
	return list(filter(None, a))
(n, m) = map(int, input().split())
sqrtm = int(round(m ** 0.5))
base_primes = list(sieve(sqrtm))
(lo, hi) = (max(sqrtm + 1, n), m + 1)
bounded_primes = bounded_sieve(lo, hi, base_primes)
primes = base_primes + bounded_primes
count = 0
for i in range(len(primes) - 1):
	if primes[i] >= n and primes[i + 1] <= m and (primes[i + 1] - primes[i] == 2):
		count += 1
print(count)


from math import sqrt
primes = [2]
for i in range(3, 32000, 2):
	isprime = True
	cap = sqrt(i) + 1
	for j in primes:
		if j >= cap:
			break
		if i % j == 0:
			isprime = False
			break
	if isprime:
		primes.append(i)
c = 0
(M, N) = input().split()
M = int(M)
N = int(N)
cap = sqrt(N) + 1
if M < 4 and N > 4:
	c += 1
M = M + (5 - M % 6)
isprime = [True] * 1000001
for i in primes:
	if i >= cap:
		break
	if i >= M:
		start = i * 2
	else:
		start = M + (i - M % i) % i
	falseblock = [False] * len(isprime[start - M:N + 1 - M:i])
	isprime[start - M:N + 1 - M:i] = falseblock
for i in range(M, N):
	if isprime[i - M] and isprime[i - M + 2]:
		c += 1
print(c)


from math import sqrt

def odd_primes(k):
	primes = list(range(3, k + 1, 2))
	for i in range(3, int(sqrt(k)) + 1, 2):
		j = (i - 3) // 2
		if primes[j] == i:
			primes[j::i] = [i] * len(range(j, len(primes), i))
	for (i, p) in enumerate(primes):
		if 3 + 2 * i == p:
			yield p

def twin_primes_range(a, b):
	a = max(a, 3)
	a |= 1
	primes = [True] * len(range(a, b + 1, 2))
	for p in odd_primes(int(sqrt(b)) + 1):
		i = (p - a) // 2 % p
		if p >= a:
			i += p
		primes[i::p] = [False] * len(range(i, len(primes), p))
	return sum((primes[i] and primes[i + 1] for i in range(len(primes) - 1)))
print(twin_primes_range(*map(int, input().split())))


from bisect import bisect_left

def sundaram(max_n):
	numbers = list(range(3, max_n + 1, 2))
	half = max_n // 2
	initial = 4
	for step in range(3, max_n + 1, 2):
		for i in range(initial, half, step):
			numbers[i - 1] = 0
		initial += 2 * (step + 1)
		if initial > half:
			return [2] + list(filter(None, numbers))

def is_prime(n):
	if n <= 31622:
		i = bisect_left(primes_cache, n)
		return i != len(primes_cache) and primes_cache[i] == n
	limit = int(n ** 0.5)
	for p in primes_cache:
		if p > limit:
			return True
		if n % p == 0:
			return False
	for f in range(31627, limit, 6):
		if n % f == 0 or n % (f + 4) == 0:
			return False
	return True

def possible_twins(n, m):
	for base in (i for i in range(n + 1, m) if i % 30 in [0, 12, 18]):
		yield (base - 1, base + 1)
primes_cache = sundaram(31622)
(n, m) = [int(i) for i in input().split()]
twins_num = 0
for i in possible_twins(n, m):
	if all(map(is_prime, i)):
		twins_num += 1
if n <= 3 and m >= 7:
	print(twins_num + 2)
elif 3 < n < 6 and m >= 7 or (n <= 3 and 5 <= m < 7):
	print(twins_num + 1)
else:
	print(twins_num)


prime = []

def update(n, m, k):
	start = n // k * k
	end = m // k * k
	if start < n:
		start += k
	if start == k:
		start += k
	start -= n
	end -= n
	while start <= end:
		prime[start] = False
		start += k
(n, m) = map(int, input().strip().split())
prime = [True for i in range(m - n + 1)]
if 1 == n:
	prime[0] = False
limit = int(m ** (1 / 2) + 1)
if 2 <= limit:
	update(n, m, 2)
if 3 <= limit:
	update(n, m, 3)
step = 2
k = 5
while k <= limit:
	update(n, m, k)
	k += step
	step ^= 6
result = 0
for i in range(len(prime) - 2):
	if prime[i] and prime[i + 2]:
		result += 1
print(result)


import sys
from time import time
import random

def miller_rabin(n, accuracy=10):
	if n < 2:
		return True
	if n < 4:
		return False
	s = 0
	d = n - 1
	while d % 2 == 0:
		s += 1
		d = d // 2
	for _ in range(accuracy):
		a = random.randrange(2, n - 1)
		x = pow(a, d, n)
		if x == 1 or x == n - 1:
			continue
		for _ in range(s - 1):
			x = x ** 2 % n
			if x == 1:
				return True
			if x == n - 1:
				break
		if x != n - 1:
			return True
	return False

def solve(n, m):

	def gen():
		for p in range(n, m + 1):
			if not miller_rabin(p, 3):
				yield p
	aa = list(gen())
	print('primes generated: %d' % len(aa), file=sys.stderr)
	cnt = 0
	for (u, v) in zip(aa, aa[1:]):
		if v - u == 2:
			cnt += 1
	return cnt
tm = time()
(n, m) = map(int, input().split())
print(solve(n, m))
print('time elapsed: %s' % (time() - tm), file=sys.stderr)


import math
import random

def is_prime(num):
	if num % 2 == 0 and num > 2 or num < 2:
		return False
	if num < 4:
		return True
	s = num - 1
	t = 0
	while s % 2 == 0:
		s = s // 2
		t += 1
	for trials in range(5):
		a = random.randrange(2, num - 1)
		v = pow(a, s, num)
		if v != 1:
			i = 0
			while v != num - 1:
				if i == t - 1:
					return False
				else:
					i = i + 1
					v = v ** 2 % num
	return True
(n, m) = map(int, input().split())
twin_primes = []
if n <= 3 and m > 4:
	twin_primes.append(3)
	twin_primes.append(5)
i = (n + 1) // 6 - 1
while 6 * i + 1 <= m:
	if 6 * i + 1 <= m and 6 * i - 1 >= n and is_prime(6 * i - 1) and is_prime(6 * i + 1):
		twin_primes.append(6 * i - 1)
		twin_primes.append(6 * i + 1)
	i += 1
print(len(twin_primes) // 2)


from sys import stderr

def main():
	(lo, hi) = [int(fld) for fld in input().strip().split()]
	print(counttwins(lo, hi))

def counttwins(lo, hi):
	plist = allprimes(int((hi + 1) ** 0.5))
	base = max(3, lo)
	count = hi - base + 1
	seive = [True] * count
	for p in plist:
		start = ((base - 1) // p + 1) * p
		if start == p:
			start += p
		for i in range(start - base, count, p):
			seive[i] = False
	return sum((s1 and s2 for (s1, s2) in zip(seive, seive[2:])))

def allprimes(hi):
	seive = [False, False] + [True] * (hi - 1)
	ans = []
	for (i, isprime) in enumerate(seive):
		if isprime:
			ans.append(i)
			for j in range(i * i, len(seive), i):
				seive[i] = False
	return ans
main()


import math

def get_primes(m, n):
	primes = set(range(m, n + 1))
	primes.discard(1)
	for i in range(2, math.floor(math.sqrt(n)) + 1):
		start_factor = math.ceil(m / i)
		if start_factor == 1:
			start_factor = 2
		start = start_factor * i
		for multiple in range(start, n + 1, i):
			primes.discard(multiple)
	return primes

def count_pairs(primes):
	counter = 0
	last_prime = -1
	for prime in primes:
		if prime - last_prime == 2:
			counter += 1
		last_prime = prime
	return counter
(m, n) = [int(x) for x in input().strip().split(' ')]
primes = get_primes(m, n)
print(count_pairs(primes))


(n, m) = map(int, input().split(' '))

def isPrime(n):
	if n < 2:
		return False
	elif n == n or n == 3:
		return True
	else:
		for i in range(2, int(n ** 0.5) + 1):
			if n % i == 0:
				return False
		return True

def sieveToPrimeList(sieve):
	pList = []
	for (index, value) in enumerate(sieve):
		if value:
			pList += [index]
	return pList

def primes(n):
	sieve = [True] * (n + 1)
	if len(sieve) < 2:
		return []
	else:
		sieve[0] = False
		sieve[1] = False
	for i in range(2, int(len(sieve) ** 0.5) + 1):
		if sieve[i] == False:
			continue
		elif isPrime(i):
			sieve[i] = True
			for j in range(2 * i, len(sieve), i):
				sieve[j] = False
		else:
			sieve[i] = False
	return sieveToPrimeList(sieve)

def getPrimeSegment(factors, start, end):
	sieve = [True] * (end - start + 1)
	shift = start
	for fac in factors:
		firstMultiple = start // fac
		lastMultiple = end // fac
		value = None
		for i in range(max(2, firstMultiple), lastMultiple + 1):
			if value == None:
				value = i * fac
			else:
				value += fac
			if value - shift < len(sieve) and value - shift > -1:
				sieve[value - shift] = False
	return sieveToPrimeList(sieve)

def countPairs(primeList):
	count = 0
	current = None
	for num in primeList:
		if current != None:
			if num - current == 2:
				count += 1
		current = num
	return count
sqPrimeList = primes(int(10000000000.0 ** 0.5) + 1)
primeSegment = getPrimeSegment(sqPrimeList, n, m)
print(countPairs(primeSegment))


def gen_interesting(n, m):
	interesting = {}
	if n <= 3 and 3 <= m:
		interesting[3] = True
	if n <= 5 and 5 <= m:
		interesting[5] = True
	start = n + 1
	while start < 6 or start % 6 != 0:
		start += 1
	for x in range(start, m, 6):
		interesting[x - 1] = True
		interesting[x + 1] = True
	for i in range(3, int(m ** 0.5) + 1):
		if n == i:
			start = n + i
		elif n % i == 0:
			start = n
		else:
			start = i * (n // i + 1)
		for x in range(start, m + 1, i):
			if x == i:
				continue
			if x in interesting:
				del interesting[x]
	return interesting
(n, m) = [int(x) for x in input().strip().split()]
interesting = gen_interesting(n, m)
primes = {}
count = 0
if n <= 3 and 5 <= m:
	count += 1
start = n
while start < 6 or start % 6 != 0:
	start += 1
for x in range(start, m, 6):
	a = x - 1
	b = x + 1
	if a in interesting and b in interesting:
		count += 1
print(count)


(N1, N2) = map(int, input().split())
small_trailing = [i and max((int(not i % 2 ** j) and j for j in range(1, 8))) for i in range(256)]

def trailing(n):
	low_byte = n & 255
	if low_byte:
		return small_trailing[low_byte]
	res = 0
	while not n & 1:
		n //= 2
		res += 1
	return res

def Fermat_test(n, base, s, t):
	b = pow(base, t, n)
	if b == 1 or b == n - 1:
		return True
	else:
		for j in range(1, s):
			b = pow(b, 2, n)
			if b == n - 1:
				return True
			if b == 1:
				return False
	return False

def isprime(n, bases=[336781006125, 9639812373923155]):
	s = trailing(n - 1)
	t = n >> s
	for base in bases:
		if not Fermat_test(n, base, s, t):
			return False
	return True
twins = []
if N1 <= 3 and N2 >= 5:
	twins.append(3)
if N1 <= 5 and N2 >= 7:
	twins.append(5)
for i in range(int(N1 // 30) * 30, N2, 30):
	for j in (11, 17, 29):
		n = i + j
		if n < N1:
			continue
		if n > N2 - 2:
			break
		if isprime(n) and isprime(n + 2):
			twins.append(n)
print(len(twins))


def candidates():
	p = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29)
	yield from p
	p = (1,) + p[3:]
	j = 30
	while True:
		for i in p:
			yield (j + i)
		j += 30

def range_primes(n, m):
	m += 1
	if n < 2:
		n = 2
	primes = [True] * (m - n)
	m_sqrt = int(m ** 0.5)
	for i in candidates():
		if i > m_sqrt:
			break
		lo = max(i, 1 + (n - 1) // i) * i
		num_i = 1 + (m - lo - 1) // i
		primes[lo - n::i] = num_i * [False]
	return [i for (i, is_p) in enumerate(primes, n) if is_p]
(n, m) = map(int, input().split())
last = -2
ans = 0
for p in range_primes(n, m):
	if p - 2 == last:
		ans += 1
	last = p
print(ans)


def isPrime(n):
	if n <= 3:
		return True
	if n % 3 == 0:
		return False
	for d in range(5, int(n ** 0.5) + 1, 6):
		if (n % d == 0) | (n % (d + 2) == 0):
			return False
	return True

def getPrimes(m):
	P = []
	if m == 2:
		P.append(2)
	for m in range(3, m + 1, 2):
		if isPrime(m):
			P.append(m)
	return P

def solve(a, b):
	c = 0
	if a < 5:
		if (a <= 3) & (not b < 5):
			c += 1
	elif a < 11:
		if (a <= 5) & (not b < 7):
			c += 1
		if (a <= 3) & (not b < 5):
			c += 1
	if (a - 5) % 6 == 0:
		a = 5 + (a - 5) // 6 * 6
	else:
		a = 5 + ((a - 5) // 6 + 1) * 6
	P = getPrimes(int(b ** 0.5))
	for n in range(a, b, 6):
		n0 = n
		n1 = n + 2
		if (n0 % 3 == 0) | (n1 % 3 == 0):
			continue
		if (n0 % 2 == 0) | (n1 % 2 == 0):
			continue
		f = False
		l = n1 ** 0.5
		for p in P:
			if p > l:
				break
			if (n0 % p == 0) | (n1 % p == 0):
				f = True
				break
		if f:
			continue
		c += 1
	return c
(A, B) = (int(a) for a in input().split())
print(solve(A, B))


from math import *

def compute_primes_for(number):
	primes = [2, 3]
	finalnum = int(sqrt(number)) + 1
	for m in range(1, int(finalnum / 6) + 1):
		n = 6 * m - 1
		isPrime = True
		i = 0
		maxi = int(sqrt(n))
		while isPrime == True and primes[i] <= maxi:
			if n % primes[i] == 0:
				isPrime = False
			i += 1
		if isPrime == True:
			primes.append(n)
		n = 6 * m + 1
		isPrime = True
		i = 0
		maxi = int(sqrt(n))
		while isPrime == True and primes[i] <= maxi:
			if n % primes[i] == 0:
				isPrime = False
			i += 1
		if isPrime == True:
			primes.append(n)
	return primes
(x, y) = list(map(int, input().strip().split()))
primes = compute_primes_for(y)
count = 0
is_prime = [True] * (y - x + 1)
for r in range(len(primes)):
	prime = primes[r]
	min_multiplier = int(x / prime)
	min_multiplier = max(2, min_multiplier)
	max_multiplier = int(y / prime)
	for m in range(min_multiplier, max_multiplier + 1):
		index = m * prime - x
		if index < 0:
			continue
		if index >= len(is_prime):
			continue
		is_prime[index] = False
if x <= 3 and y >= 5:
	count += 1
for j in range(int(x / 6), int(y / 6) + 1):
	p = 6 * j - 1
	q = 6 * j + 1
	if p < x or q > y:
		continue
	p_index = p - x
	q_index = q - x
	if is_prime[p_index] and is_prime[q_index]:
		count += 1
print(count)


from operator import and_

def ans():
	(n, m) = map(int, input().split())
	if n < 2:
		n = 2
	if m - n < 2:
		return 0
	m += 1
	nm1 = n - 1
	d = m - n
	imax = int(m ** 0.5) + 1
	sieve = [True] * imax
	target = [True] * d
	for i in range(2, imax):
		if sieve[i]:
			for j in range(i * i, imax, i):
				sieve[j] = False
			for j in range(max(nm1 // i * i, i) + i - n, d, i):
				target[j] = False
	return sum(map(and_, target, target[2:]))
print(ans())


boundary = 10 ** 6
is_prime = [True for i in range(boundary + 1)]
(is_prime[0], is_prime[1]) = (False, False)
primes = []
for i in range(2, boundary + 1):
	if is_prime[i]:
		primes.append(i)
		for j in range(i + i, boundary + 1, i):
			is_prime[j] = False
(n, m) = map(int, input().split())
is_prime = [True for i in range(m - n + 3)]
for p in primes:
	start = n if n % p == 0 else n - n % p + p
	for i in range(start, m + 3, p):
		if i != p:
			is_prime[i - n] = False
(is_prime[-1], is_prime[-2]) = (False, False)
if n == 1:
	is_prime[0] = False
count = 0
for i in range(n, m + 1):
	if is_prime[i - n] and is_prime[i - n + 2]:
		count += 1
print(count)


from math import sqrt, ceil
import bisect

def rwh_primes(n):
	sieve = [True] * (n // 2)
	for i in range(3, int(n ** 0.5) + 1, 2):
		if sieve[i // 2]:
			sieve[i * i // 2::i] = [False] * ((n - i * i - 1) // (2 * i) + 1)
	return [2] + [2 * i + 1 for i in range(1, n // 2) if sieve[i]]
_smallp = rwh_primes(1000)

def sieveSegm(stop, start=2, dumpfactor=0.2):
	if n == m:
		return []
	delta = sqrt(stop - start)
	delta = int(ceil(delta * abs(dumpfactor)))
	sep = (stop - start) // delta + 1
	if stop < 1000:
		return _smallp[:bisect.bisect(_smallp, stop) + 1]
	primes = sieveSegm(int(sqrt(stop)) + 1, dumpfactor=0.4)
	primes2 = sieveSegm(int(sqrt(sep) + 1), dumpfactor=0.4)
	q = len(primes2)
	while q > 0 and primes2[0] < start:
		primes2.pop(0)
		q -= 1
	a = start
	while a < stop:
		if a + sep > stop:
			sep = stop - a
		stop2 = int(ceil(sqrt(a + sep)))
		b = [True] * sep
		if a < 2:
			if a == 1:
				b[0] = False
			if a == 0:
				b[:1] = [False, False]
		for c in primes:
			if c > stop2:
				break
			q = a % c
			if q != 0:
				d = a - q + c
			else:
				d = a
			while d < a + sep:
				b[d - a] = False
				d += c
		for c in range(sep):
			if b[c]:
				primes2.append(a + c)
		a += sep
	return sorted(list(set(primes2)))
(n, m) = map(int, input().strip().split(' '))
list_p = sieveSegm(m, n)
l = len(list_p)
cnt = 0
for i in range(l - 1):
	p = list_p[i]
	q = list_p[i + 1]
	if n <= p <= m and n <= q <= m:
		if q == p + 2:
			cnt += 1
print(cnt)


primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997]

def check(a, n):
	d = n - 1
	while ~d & 1:
		d >>= 1
		t = pow(a, d, n)
		if t == n - 1:
			return 1
	if t == 1:
		return 1
	return 0

def f(a, n):
	for i in a:
		if check(i, n) == 0:
			return 0
	return 1

def isprime(n):
	if n < 2:
		return 0
	for i in primes:
		if n == i:
			return 1
		if n > i:
			break
		if n % i == 0:
			return 0
	if n < 1373653:
		a = [2, 3]
		return f(a, n)
	if n < 25326001:
		a = [2, 3, 5]
		return f(a, n)
	if n < 118670087467:
		a = [2, 3, 5, 7]
		if n == 3215031751:
			return 0
		return f(a, n)
	if n < 2152302898747:
		a = [2, 3, 5, 7, 11]
		return f(a, n)
	if n < 3474749660383:
		a = [2, 3, 5, 7, 11, 13]
		return f(a, n)
	a = [2, 3, 5, 7, 11, 13, 17]
	return f(a, n)
(N, M) = [int(x) for x in input().split()]
n = 6 * (N // 6 + 1)
m = 6 * (M // 6 - (M % 6 == 0))
c = 0
a = list(map(isprime, range(n - 1, m, 6)))
b = list(map(isprime, range(n + 1, m + 2, 6)))
for i in range((m - n) // 6 + 1):
	if a[i]:
		if b[i]:
			c += 1
if 3 >= N:
	if 5 <= M:
		c += 1
print(c)


from math import sqrt
(n, m) = map(int, input().split())

def primes_sieve(limit):
	a = [True] * limit
	a[0] = a[1] = False
	for (i, isprime) in enumerate(a):
		if isprime:
			yield i
			for n in range(i * i, limit, i):
				a[n] = False
sieve = list(primes_sieve(int(sqrt(m)) + 1))
non_primes = {1}
for p in sieve:
	rem = n % p
	if rem == 0:
		rem = p
	for i in range(n + p - rem, m + 1, p):
		if i != p:
			non_primes.add(i)
if n % 2 == 0:
	n += 1
primes = [i for i in range(n, m + 1, 2) if i not in non_primes]
print(sum((1 for i in range(len(primes) - 1) if primes[i + 1] - primes[i] == 2)))


from math import sqrt

def all_primes_less_than_n(n):
	n -= 1
	if n < 2:
		return []
	arr = [True] * (n + 1)
	arr[0] = False
	arr[1] = False
	i = 2
	L = int(sqrt(n)) + 1
	while i < L:
		if not arr[i]:
			i += 1
			continue
		j = i * 2
		while j <= n:
			arr[j] = False
			j += i
		i += 1
	res = []
	for i in range(2, n + 1):
		if arr[i]:
			res.append(i)
	return res
(n, m) = [int(i) for i in input().strip().split()]
ps = all_primes_less_than_n(round(sqrt(m)))
arr = [True] * (m - n + 1)
for p in ps:
	for i in range(-n % p, m - n + 1, p):
		arr[i] = False
	if n <= p <= m:
		arr[p - n] = True
if n is 1:
	arr[0] = False
cnt = 0
for i in range((n + 1) % 2, len(arr) - 2, 2):
	if arr[i] and arr[i + 2]:
		cnt += 1
print(cnt)


(n, m) = map(int, input().split())
p = [True for i in range(n, m + 1)]
q = 2
if n == 1:
	p[0] = False
while q ** 2 <= m:
	for j in range(max(2, (n - 1) // q + 1), m // q + 1):
		p[j * q - n] = False
	q += 1
q = 0
for i in range(n, m - 1):
	q += p[i - n] and p[i - n + 2]
print(q)


primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, 17851, 17863, 17881, 17891, 17903, 17909, 17911, 17921, 17923, 17929, 17939, 17957, 17959, 17971, 17977, 17981, 17987, 17989, 18013, 18041, 18043, 18047, 18049, 18059, 18061, 18077, 18089, 18097, 18119, 18121, 18127, 18131, 18133, 18143, 18149, 18169, 18181, 18191, 18199, 18211, 18217, 18223, 18229, 18233, 18251, 18253, 18257, 18269, 18287, 18289, 18301, 18307, 18311, 18313, 18329, 18341, 18353, 18367, 18371, 18379, 18397, 18401, 18413, 18427, 18433, 18439, 18443, 18451, 18457, 18461, 18481, 18493, 18503, 18517, 18521, 18523, 18539, 18541, 18553, 18583, 18587, 18593, 18617, 18637, 18661, 18671, 18679, 18691, 18701, 18713, 18719, 18731, 18743, 18749, 18757, 18773, 18787, 18793, 18797, 18803, 18839, 18859, 18869, 18899, 18911, 18913, 18917, 18919, 18947, 18959, 18973, 18979, 19001, 19009, 19013, 19031, 19037, 19051, 19069, 19073, 19079, 19081, 19087, 19121, 19139, 19141, 19157, 19163, 19181, 19183, 19207, 19211, 19213, 19219, 19231, 19237, 19249, 19259, 19267, 19273, 19289, 19301, 19309, 19319, 19333, 19373, 19379, 19381, 19387, 19391, 19403, 19417, 19421, 19423, 19427, 19429, 19433, 19441, 19447, 19457, 19463, 19469, 19471, 19477, 19483, 19489, 19501, 19507, 19531, 19541, 19543, 19553, 19559, 19571, 19577, 19583, 19597, 19603, 19609, 19661, 19681, 19687, 19697, 19699, 19709, 19717, 19727, 19739, 19751, 19753, 19759, 19763, 19777, 19793, 19801, 19813, 19819, 19841, 19843, 19853, 19861, 19867, 19889, 19891, 19913, 19919, 19927, 19937, 19949, 19961, 19963, 19973, 19979, 19991, 19993, 19997, 20011, 20021, 20023, 20029, 20047, 20051, 20063, 20071, 20089, 20101, 20107, 20113, 20117, 20123, 20129, 20143, 20147, 20149, 20161, 20173, 20177, 20183, 20201, 20219, 20231, 20233, 20249, 20261, 20269, 20287, 20297, 20323, 20327, 20333, 20341, 20347, 20353, 20357, 20359, 20369, 20389, 20393, 20399, 20407, 20411, 20431, 20441, 20443, 20477, 20479, 20483, 20507, 20509, 20521, 20533, 20543, 20549, 20551, 20563, 20593, 20599, 20611, 20627, 20639, 20641, 20663, 20681, 20693, 20707, 20717, 20719, 20731, 20743, 20747, 20749, 20753, 20759, 20771, 20773, 20789, 20807, 20809, 20849, 20857, 20873, 20879, 20887, 20897, 20899, 20903, 20921, 20929, 20939, 20947, 20959, 20963, 20981, 20983, 21001, 21011, 21013, 21017, 21019, 21023, 21031, 21059, 21061, 21067, 21089, 21101, 21107, 21121, 21139, 21143, 21149, 21157, 21163, 21169, 21179, 21187, 21191, 21193, 21211, 21221, 21227, 21247, 21269, 21277, 21283, 21313, 21317, 21319, 21323, 21341, 21347, 21377, 21379, 21383, 21391, 21397, 21401, 21407, 21419, 21433, 21467, 21481, 21487, 21491, 21493, 21499, 21503, 21517, 21521, 21523, 21529, 21557, 21559, 21563, 21569, 21577, 21587, 21589, 21599, 21601, 21611, 21613, 21617, 21647, 21649, 21661, 21673, 21683, 21701, 21713, 21727, 21737, 21739, 21751, 21757, 21767, 21773, 21787, 21799, 21803, 21817, 21821, 21839, 21841, 21851, 21859, 21863, 21871, 21881, 21893, 21911, 21929, 21937, 21943, 21961, 21977, 21991, 21997, 22003, 22013, 22027, 22031, 22037, 22039, 22051, 22063, 22067, 22073, 22079, 22091, 22093, 22109, 22111, 22123, 22129, 22133, 22147, 22153, 22157, 22159, 22171, 22189, 22193, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, 22303, 22307, 22343, 22349, 22367, 22369, 22381, 22391, 22397, 22409, 22433, 22441, 22447, 22453, 22469, 22481, 22483, 22501, 22511, 22531, 22541, 22543, 22549, 22567, 22571, 22573, 22613, 22619, 22621, 22637, 22639, 22643, 22651, 22669, 22679, 22691, 22697, 22699, 22709, 22717, 22721, 22727, 22739, 22741, 22751, 22769, 22777, 22783, 22787, 22807, 22811, 22817, 22853, 22859, 22861, 22871, 22877, 22901, 22907, 22921, 22937, 22943, 22961, 22963, 22973, 22993, 23003, 23011, 23017, 23021, 23027, 23029, 23039, 23041, 23053, 23057, 23059, 23063, 23071, 23081, 23087, 23099, 23117, 23131, 23143, 23159, 23167, 23173, 23189, 23197, 23201, 23203, 23209, 23227, 23251, 23269, 23279, 23291, 23293, 23297, 23311, 23321, 23327, 23333, 23339, 23357, 23369, 23371, 23399, 23417, 23431, 23447, 23459, 23473, 23497, 23509, 23531, 23537, 23539, 23549, 23557, 23561, 23563, 23567, 23581, 23593, 23599, 23603, 23609, 23623, 23627, 23629, 23633, 23663, 23669, 23671, 23677, 23687, 23689, 23719, 23741, 23743, 23747, 23753, 23761, 23767, 23773, 23789, 23801, 23813, 23819, 23827, 23831, 23833, 23857, 23869, 23873, 23879, 23887, 23893, 23899, 23909, 23911, 23917, 23929, 23957, 23971, 23977, 23981, 23993, 24001, 24007, 24019, 24023, 24029, 24043, 24049, 24061, 24071, 24077, 24083, 24091, 24097, 24103, 24107, 24109, 24113, 24121, 24133, 24137, 24151, 24169, 24179, 24181, 24197, 24203, 24223, 24229, 24239, 24247, 24251, 24281, 24317, 24329, 24337, 24359, 24371, 24373, 24379, 24391, 24407, 24413, 24419, 24421, 24439, 24443, 24469, 24473, 24481, 24499, 24509, 24517, 24527, 24533, 24547, 24551, 24571, 24593, 24611, 24623, 24631, 24659, 24671, 24677, 24683, 24691, 24697, 24709, 24733, 24749, 24763, 24767, 24781, 24793, 24799, 24809, 24821, 24841, 24847, 24851, 24859, 24877, 24889, 24907, 24917, 24919, 24923, 24943, 24953, 24967, 24971, 24977, 24979, 24989, 25013, 25031, 25033, 25037, 25057, 25073, 25087, 25097, 25111, 25117, 25121, 25127, 25147, 25153, 25163, 25169, 25171, 25183, 25189, 25219, 25229, 25237, 25243, 25247, 25253, 25261, 25301, 25303, 25307, 25309, 25321, 25339, 25343, 25349, 25357, 25367, 25373, 25391, 25409, 25411, 25423, 25439, 25447, 25453, 25457, 25463, 25469, 25471, 25523, 25537, 25541, 25561, 25577, 25579, 25583, 25589, 25601, 25603, 25609, 25621, 25633, 25639, 25643, 25657, 25667, 25673, 25679, 25693, 25703, 25717, 25733, 25741, 25747, 25759, 25763, 25771, 25793, 25799, 25801, 25819, 25841, 25847, 25849, 25867, 25873, 25889, 25903, 25913, 25919, 25931, 25933, 25939, 25943, 25951, 25969, 25981, 25997, 25999, 26003, 26017, 26021, 26029, 26041, 26053, 26083, 26099, 26107, 26111, 26113, 26119, 26141, 26153, 26161, 26171, 26177, 26183, 26189, 26203, 26209, 26227, 26237, 26249, 26251, 26261, 26263, 26267, 26293, 26297, 26309, 26317, 26321, 26339, 26347, 26357, 26371, 26387, 26393, 26399, 26407, 26417, 26423, 26431, 26437, 26449, 26459, 26479, 26489, 26497, 26501, 26513, 26539, 26557, 26561, 26573, 26591, 26597, 26627, 26633, 26641, 26647, 26669, 26681, 26683, 26687, 26693, 26699, 26701, 26711, 26713, 26717, 26723, 26729, 26731, 26737, 26759, 26777, 26783, 26801, 26813, 26821, 26833, 26839, 26849, 26861, 26863, 26879, 26881, 26891, 26893, 26903, 26921, 26927, 26947, 26951, 26953, 26959, 26981, 26987, 26993, 27011, 27017, 27031, 27043, 27059, 27061, 27067, 27073, 27077, 27091, 27103, 27107, 27109, 27127, 27143, 27179, 27191, 27197, 27211, 27239, 27241, 27253, 27259, 27271, 27277, 27281, 27283, 27299, 27329, 27337, 27361, 27367, 27397, 27407, 27409, 27427, 27431, 27437, 27449, 27457, 27479, 27481, 27487, 27509, 27527, 27529, 27539, 27541, 27551, 27581, 27583, 27611, 27617, 27631, 27647, 27653, 27673, 27689, 27691, 27697, 27701, 27733, 27737, 27739, 27743, 27749, 27751, 27763, 27767, 27773, 27779, 27791, 27793, 27799, 27803, 27809, 27817, 27823, 27827, 27847, 27851, 27883, 27893, 27901, 27917, 27919, 27941, 27943, 27947, 27953, 27961, 27967, 27983, 27997, 28001, 28019, 28027, 28031, 28051, 28057, 28069, 28081, 28087, 28097, 28099, 28109, 28111, 28123, 28151, 28163, 28181, 28183, 28201, 28211, 28219, 28229, 28277, 28279, 28283, 28289, 28297, 28307, 28309, 28319, 28349, 28351, 28387, 28393, 28403, 28409, 28411, 28429, 28433, 28439, 28447, 28463, 28477, 28493, 28499, 28513, 28517, 28537, 28541, 28547, 28549, 28559, 28571, 28573, 28579, 28591, 28597, 28603, 28607, 28619, 28621, 28627, 28631, 28643, 28649, 28657, 28661, 28663, 28669, 28687, 28697, 28703, 28711, 28723, 28729, 28751, 28753, 28759, 28771, 28789, 28793, 28807, 28813, 28817, 28837, 28843, 28859, 28867, 28871, 28879, 28901, 28909, 28921, 28927, 28933, 28949, 28961, 28979, 29009, 29017, 29021, 29023, 29027, 29033, 29059, 29063, 29077, 29101, 29123, 29129, 29131, 29137, 29147, 29153, 29167, 29173, 29179, 29191, 29201, 29207, 29209, 29221, 29231, 29243, 29251, 29269, 29287, 29297, 29303, 29311, 29327, 29333, 29339, 29347, 29363, 29383, 29387, 29389, 29399, 29401, 29411, 29423, 29429, 29437, 29443, 29453, 29473, 29483, 29501, 29527, 29531, 29537, 29567, 29569, 29573, 29581, 29587, 29599, 29611, 29629, 29633, 29641, 29663, 29669, 29671, 29683, 29717, 29723, 29741, 29753, 29759, 29761, 29789, 29803, 29819, 29833, 29837, 29851, 29863, 29867, 29873, 29879, 29881, 29917, 29921, 29927, 29947, 29959, 29983, 29989, 30011, 30013, 30029, 30047, 30059, 30071, 30089, 30091, 30097, 30103, 30109, 30113, 30119, 30133, 30137, 30139, 30161, 30169, 30181, 30187, 30197, 30203, 30211, 30223, 30241, 30253, 30259, 30269, 30271, 30293, 30307, 30313, 30319, 30323, 30341, 30347, 30367, 30389, 30391, 30403, 30427, 30431, 30449, 30467, 30469, 30491, 30493, 30497, 30509, 30517, 30529, 30539, 30553, 30557, 30559, 30577, 30593, 30631, 30637, 30643, 30649, 30661, 30671, 30677, 30689, 30697, 30703, 30707, 30713, 30727, 30757, 30763, 30773, 30781, 30803, 30809, 30817, 30829, 30839, 30841, 30851, 30853, 30859, 30869, 30871, 30881, 30893, 30911, 30931, 30937, 30941, 30949, 30971, 30977, 30983, 31013, 31019, 31033, 31039, 31051, 31063, 31069, 31079, 31081, 31091, 31121, 31123, 31139, 31147, 31151, 31153, 31159, 31177, 31181, 31183, 31189, 31193, 31219, 31223, 31231, 31237, 31247, 31249, 31253, 31259, 31267, 31271, 31277, 31307, 31319, 31321, 31327, 31333, 31337, 31357, 31379, 31387, 31391, 31393, 31397, 31469, 31477, 31481, 31489, 31511, 31513, 31517, 31531, 31541, 31543, 31547, 31567, 31573, 31583, 31601, 31607, 31627]
(n, m) = [int(x) for x in input().split()]
m += 1
is_prime = [True for i in range(m - n)]
if n == 1:
	is_prime[0] = False
for p in primes:
	if p * p > m:
		break
	start = n - n % p
	if n % p != 0:
		start += p
	if start == p:
		start = 2 * p
	for i in range(start, m, p):
		is_prime[i - n] = False
count = 0
i = 0
while i + 2 < m - n:
	if is_prime[i] and is_prime[i + 2]:
		count += 1
	i += 1
print(count)


import math
(n, m) = [int(a) for a in input().strip().split(' ')]
if n == 1:
	n = 3
	if m < 3:
		m = 3
M = int(math.sqrt(m))
P = [0] * (M + 1)
for i in range(2, int(math.sqrt(M)) + 1):
	if P[i] == 0:
		for j in range(2, M // i + 1):
			P[i * j] += 1
I = [0] * (m - n + 1)
for i in range(2, len(P)):
	if P[i] == 0:
		num = m // i - n // i
		if n % i == 0:
			for j in range(-1, num):
				if i - n % i + j * i + n > i:
					I[i - n % i + j * i] += 1
		else:
			for j in range(0, num):
				if i - n % i + j * i + n > i:
					I[i - n % i + j * i] += 1
count = 0
for i in range(0, m - n + 1):
	if i + 2 + n <= m:
		if I[i] == 0 and I[i + 2] == 0:
			count += 1
print(count)


import math

def generatePrimes(a, n):
	primes = list(range(a, n + 1))
	if a > 2:
		el = a % 2
	else:
		el = 2 + a % 2
	for i in range(el, n - a, 2):
		primes[i] = 0
	for x in range(3, int(math.sqrt(n)) + 1, 2):
		if x < a:
			if a % x == 0:
				j = 0
			else:
				j = x - a % x
		else:
			j = x - a
		for i in range(j, len(primes), x):
			if primes[i] == x:
				continue
			else:
				primes[i] = 0
	return filter(lambda x: x is None or x >= a, primes)
(x, y) = [int(i) for i in input().split()]
primes = list(generatePrimes(x, y))
cnt = 0
for i in range(1, len(primes)):
	if primes[i] - primes[i - 1] == 2:
		cnt += 1
print(cnt)


def isqrt(x):
	if x < 0:
		raise ValueError('negative')
	b = x.bit_length() - 1 & -2
	y = 0
	while b >= 0:
		y <<= 1
		z = y + 1
		if z * z <= x >> b:
			y = z
		b -= 2
	return y
(n, m) = map(int, input().split())
primes = []
lim = isqrt(m) + 1
mark = bytearray(lim)
for i in range(3, lim, 2):
	if mark[i]:
		continue
	primes.append(i)
	for j in range(3 * i, lim, 2 * i):
		mark[j] = 1
lim = m - n + 1
mark = bytearray(lim)
for p in primes:
	i = max((n + p - 1) // p | 1, 3)
	for j in range(i * p - n, lim, 2 * p):
		mark[j] = 1
if n == 1:
	mark[0] = 1
count = 0
for i in range(3 - (n & 1), lim, 2):
	if mark[i] == 0 and mark[i - 2] == 0:
		count += 1
print(count)


import math

def prime(n):
	if n <= 1:
		return False
	else:
		for i in range(2, int(n ** 0.5) + 1):
			if n % i == 0:
				return False
				break
		else:
			return True
(n, m) = map(int, input().split(' '))
p = int(m ** 0.5)
primes = []
for i in range(2, p + 1):
	if prime(i):
		primes.append(i)
segment = [True for i in range(n, m + 1)]
for x in primes:
	a = math.ceil(n / x)
	b = math.floor(m / x)
	for i in range(a, b + 1):
		if i != 1:
			segment[x * i - n] = False
if n == 1:
	segment[0] = False
count = 0
for i in range(len(segment)):
	if i + 2 < len(segment):
		if segment[i] == True and segment[i + 2] == True:
			count += 1
print(count)


L = 10 ** 4
isp = [True] * (10 * L)
primes = [0] * L
(i, K) = (2, 0)
while K < L and i < 10 * L:
	if isp[i]:
		j = i
		while i * j < 10 * L:
			isp[i * j] = False
			j += 1
		primes[K] = i
		K += 1
	i += 1
(n, m) = [int(i) for i in input().split()]
npprime = [True] * (m - n + 1)
if n == 1:
	npprime[0] = False
for i in range(K):
	p = primes[i]
	for j in range(max(n + (p - n % p) % p, p ** 2), m + 1, p):
		npprime[j - n] = False
tc = 0
for i in range(n, m - 1):
	if npprime[i - n] and npprime[i + 2 - n]:
		tc += 1
print(tc)


def isProbablePrime(n, ar=None):
	if n <= 1:
		return False
	if n == 2:
		return True
	if n % 2 == 0:
		return False
	if n < 9:
		return True
	if n % 3 == 0:
		return False
	if n % 5 == 0:
		return False
	if not ar:
		if n < 1373653:
			ar = (2, 3)
		elif n < 9080191:
			ar = (31, 73)
		elif n < 4759123141:
			ar = (2, 7, 61)
		elif n < 2152302898747:
			ar = (2, 3, 5, 7, 11)
		elif n < 3474749660383:
			ar = (2, 3, 5, 7, 11, 13)
		elif n < 341550071728321:
			ar = (2, 3, 5, 7, 11, 13, 17)
		else:
			ar = (2, 325, 9375, 28178, 450775, 9780504, 1795265022)
	for a in ar:
		if a == n:
			continue
		(t, u) = (0, n - 1)
		while u & 1 == 0:
			t += 1
			u >>= 1
		xi1 = pow(a, u, n)
		for i in range(0, t):
			xi2 = xi1 * xi1 % n
			if xi2 == 1 and xi1 != 1 and (xi1 != n - 1):
				return False
			xi1 = xi2
		if xi1 != 1:
			return False
	return True
(n, m) = map(int, input().split())
if n % 2 == 0:
	n += 1
(p, count) = (False, 0)
for i in range(n, m + 1, 2):
	if isProbablePrime(i):
		if p:
			count += 1
		p = True
	else:
		p = False
print(count)


import math

def find_all_prime():
	mylist = [0] * 179
	mylist[0] = 1
	mylist[1] = 1
	for i in range(4, 179, 2):
		mylist[i] = 1
	for i in range(3, 14, 2):
		j = i + i
		while j < 179:
			mylist[j] = 1
			j += i
	li = []
	for i in range(179):
		if not mylist[i]:
			li.append(i)
	return li

def find_prime():
	li = find_all_prime()
	mylist = [0] * 31700
	mylist[0] = 1
	mylist[1] = 1
	for i in range(40):
		j = li[i] + li[i]
		while j < 31700:
			mylist[j] = 1
			j += li[i]
	arr = []
	for i in range(31700):
		if not mylist[i]:
			arr.append(i)
	return arr
(start, end) = map(int, input().split())
length = end - start + 1
prime = find_prime()
pr_len = len(prime)
arr = [0] * length
ter_end = end / 2
for i in range(pr_len):
	if ter_end < prime[i]:
		break
	p = start // prime[i]
	r = (p + 1) * prime[i] - start
	if r == prime[i]:
		r -= prime[i]
	if p == 1 and (not r) or (not p and r):
		r += prime[i]
	while r < length:
		arr[r] = 1
		r += prime[i]
if start == 1:
	arr[0] = 1
count = 0
for i in range(length - 2):
	if not arr[i] and (not arr[i + 2]):
		count += 1
print(count)


import math
(n, m) = [int(x) for x in input().split()]

def make_prime_list(n):
	sieve = [False] * 2 + [True] * (n - 2)
	p = 2
	while 2 * p <= n:
		for i in range(2 * p, n, p):
			sieve[i] = False
		p += 1
		while not sieve[p] and 2 * p <= n:
			p += 1
	result = [i for (i, is_prime) in enumerate(sieve) if is_prime]
	return result

def sieve_interval(n, m):
	n = max(n, 2)
	primes = make_prime_list(2 * math.ceil(m ** 0.5))
	sieve = [True] * (m - n + 1)
	for p in primes:
		start = n // p * p
		while start < n or start == p:
			start += p
		for i in range(start, m + 1, p):
			sieve[i - n] = False
	return sieve
sieve = sieve_interval(n, m)
count_twins = 0
for (i, is_prime) in enumerate(sieve[:-2]):
	if is_prime and sieve[i + 2]:
		count_twins += 1
print(count_twins)


from math import sqrt
from itertools import count, islice
(n, m) = input().strip().split()
(n, m) = (int(n), int(m))

def is_prime(n):
	if n == 2:
		return True
	if n % 2 == 0 or n <= 1:
		return False
	if n == 3:
		return True
	sqr = int(sqrt(n)) + 1
	for i in range(3, sqr, 2):
		if n % i == 0:
			return False
	return True

def primes_list(n):
	primes = [2]
	sqr = int(sqrt(n)) + 1
	for i in range(3, sqr, 2):
		if is_prime(i):
			primes.append(i)
	return primes
fin_list = [True] * (m - n + 1)
for i in primes_list(m):
	for j in range(n // i * i + i, m + 1, i):
		fin_list[j - n] = False
for i in primes_list(m):
	if i in range(n, m - n + 1):
		fin_list[i - n] = True
fin_list[0] = is_prime(n)
count = 0
for i in range(len(fin_list) - 2):
	if fin_list[i] and fin_list[i + 2]:
		count += 1
print(count)


def is_prime(n):
	if n <= 61:
		return n in {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61}
	for p in [2, 3, 5, 7, 11]:
		if n % p == 0:
			return False
	bases = set([2, 7, 61])
	(d, s) = (n - 1, 0)
	while d % 2 == 0:
		d //= 2
		s += 1
	for a in bases:
		x = pow(a, d, n)
		if x == 1 or x == n - 1:
			continue
		found = True
		for i in range(s - 1):
			x = x * x % n
			if x == 1:
				return False
			if x == n - 1:
				found = False
				break
		if found:
			return False
	return True

def count_twins(n, m):
	count = 0
	if n <= 3 and m >= 5:
		count += 1
	for k in range(n // 6 + 1, (m - 1) // 6 + 1):
		if is_prime(6 * k - 1) and is_prime(6 * k + 1):
			count += 1
	return count
(n, m) = map(int, input().split())
print(count_twins(n, m))


from collections import defaultdict
(n, m) = map(int, input().split())
mySeive = defaultdict(lambda : True)
mySeive[1] = False
N = int(m ** 0.5)
for i in range(2, N + 1):
	for x in range(2 * i, N + 1, i):
		mySeive[x] = False
L = max(N + 1, n)
for p in filter(lambda x: mySeive[x], range(2, N + 1)):
	for x in range(L - L % p + p if L % p else L, m + 1, p):
		mySeive[x] = False
newP = list(filter(lambda x: mySeive[x], range(n, m + 1)))
print(sum((b - a == 2 for (a, b) in zip(newP[:-1], newP[1:]))))


from fractions import gcd
from operator import mul
import random
import itertools
MAXLOOKUP = 1000000
MAXSMALLPRIME = 300
prime_or_factor = [0] * (MAXLOOKUP + 1)
max_p = int(MAXLOOKUP ** 0.5) + 1
prime_or_factor[4::2] = [2] * len(prime_or_factor[4::2])
prime_or_factor[9::6] = [3] * len(prime_or_factor[9::6])
p = 5
while p <= max_p:
	if prime_or_factor[p] == 0:
		prime_or_factor[p * p::2 * p] = [p] * len(prime_or_factor[p * p::2 * p])
	if p % 6 == 5:
		p += 2
	else:
		p += 4
smallprimes = [p for p in range(2, MAXSMALLPRIME) if prime_or_factor[p] == 0]

def all_factors(x):
	if type(x) == list:
		allf = [1]
		for p in set(x):
			e = x.count(p)
			le = len(allf)
			pn = 1
			for i in range(e):
				pn *= p
				allf.extend([a * pn for a in allf[0:le]])
		return allf
	elif type(x) == int or type(x) == long:
		return all_factors(factorise(x))

def factorise_trial_division(n):
	if n == 1:
		return []
	factors = []
	for p in (2, 3):
		while n % p == 0:
			factors.append(p)
			n //= p
	q = 5
	while q * q <= n:
		for p in (q, q + 2):
			while n % p == 0:
				factors.append(p)
				n //= p
		q += 6
	if n > 1:
		factors.append(n)
	return factors

def factorise_lookup(n):
	i = prime_or_factor[n]
	f = []
	while i:
		f.append(i)
		n //= i
		i = prime_or_factor[n]
	if n > 1:
		f.append(n)
	return f

def brent(N, maxBrentTime=1.0):
	if N % 2 == 0:
		return 2
	(y, c, m) = (random.randint(1, N - 1), random.randint(1, N - 1), 200)
	(g, r, q) = (1, 1, 1)
	while g == 1:
		x = y
		for _ in range(r):
			y = (y * y + c) % N
		k = 0
		while k < r and g == 1:
			ys = y
			for _ in range(min(m, r - k)):
				y = (y * y + c) % N
				q = q * abs(x - y) % N
			g = gcd(q, N)
			k += m
		r = r * 2
	if g == N:
		while True:
			ys = (ys * ys + c) % N
			g = gcd(abs(x - ys), N)
			if g > 1:
				break
	return g

def millerRabin(n, factor=[1]):
	global factorFromMillerRabin
	if n == 2:
		return True
	if n < 2:
		return False
	if n % 2 == 0:
		factor[0] = 2
		return False
	two64 = pow(2, 64)
	if n < 2047:
		P = (2,)
	elif n < 1373653:
		P = (2, 3)
	elif n < 9080191:
		P = (31, 73)
	elif n < 4759123141:
		P = (2, 7, 61)
	elif n < 2152302898747:
		P = (2, 3, 5, 7, 11)
	elif n < 3474749660383:
		P = (2, 3, 5, 7, 11, 13)
	elif n < 341550071728321:
		P = (2, 3, 5, 7, 11, 13, 17)
	elif n < 3825123056546413051:
		P = (2, 3, 5, 7, 11, 13, 17, 19, 23)
	elif n < two64:
		P = (2, 325, 9375, 28178, 450775, 9780504, 1795265022)
	else:
		P = [2, 3, 5, 7, 11, 13, 17, 19, 23] + [random.randint(24, n - 2) for i in range(40)]
	if n < 3825123056546413051 and n in P:
		return True
	d = n - 1 >> 1
	s = 1
	while d & 1 == 0:
		d >>= 1
		s += 1
	for w in P:
		a = pow(w, d, n)
		if a == 1:
			continue
		r = 0
		while r < s:
			if a == n - 1:
				break
			prev_a = a
			a = a * a % n
			if a == 1:
				factor[0] = gcd(prev_a - 1, n)
				return False
			r += 1
		if r == s:
			factor[0] = 1
			return False
	return True

def factorise_large(n, maxBrentTime=1.0):
	brent_failures = 0
	brent_calls = 0
	brent_avoid = 0
	if n <= MAXLOOKUP:
		return factorise_lookup(n)
	millerrabinfactor = [1]
	if millerRabin(n, millerrabinfactor):
		return [n]
	if 1 < millerrabinfactor[0] < n:
		p = millerrabinfactor[0]
		brent_avoid += 1
	else:
		p = brent(n, maxBrentTime)
		brent_calls += 1
	q = n // p
	if p > q:
		(p, q) = (q, p)
	if p == 1:
		if millerRabin(q):
			return [q]
		else:
			brent_failures += 1
			return factorise_large(q, maxBrentTime)
	else:
		return factorise_large(p) + factorise_large(q)

def factorise(n, maxBrentTime=1.0):
	if n <= MAXLOOKUP:
		return factorise_lookup(n)
	factors = []
	for p in smallprimes:
		while n % p == 0:
			factors.append(p)
			n //= p
	if n == 1:
		return factors
	return factors + factorise_large(n, maxBrentTime)

def totient(n):
	f = factorise(n)
	t = 1
	for x in set(f):
		t *= pow(x, f.count(x) - 1) * (x - 1)
	return t

def unfactorise(d):
	return reduce(mul, d, 1)

def radical(d):
	if type(d) == list:
		return reduce(mul, set(d), 1)
	else:
		return reduce(mul, set(factorise(d)), 1)

def is_prime(n):
	if n == 1:
		return False
	if n == 2:
		return True
	t = factorise(n)
	if len(t) == 1:
		return True
	else:
		return False
(a, b) = (int(x) for x in input().split())
d = b - a + 1
poss_prime = [True] * d
for p in [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173]:
	if a % p == 0:
		start = 0
	else:
		start = p - a % p
	if a + start == p:
		start += p
	if start >= d:
		continue
	for i in range(start, d, p):
		poss_prime[i] = False
count = 0
for i in range(d - 2):
	if poss_prime[i] and poss_prime[i + 2]:
		p1 = i + a
		p2 = p1 + 2
		if is_prime(p1) and is_prime(p2):
			count += 1
print(count)


def is_prime(x, L=[]):
	sqrt = int(pow(x, 0.5)) + 1
	PL = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]
	if not L:
		if x < 210:
			if x in PL:
				return True
			else:
				return False
		else:
			for p in PL:
				if x % p == 0:
					return False
			for i in range(1, sqrt // 210 + 1):
				for j in [1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209]:
					if x % (210 * i + j) == 0:
						return False
		return True
	elif x != 0 and x != 1:
		j = 0
		while j < len(L) and L[j] <= sqrt:
			if x % L[j] == 0:
				return False
			j += 1
	else:
		return False
	return True

def is_prime_pair(x, L=[]):
	sqrt = int(pow(x + 2, 0.5)) + 1
	PL = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]
	if not L:
		if x < 210:
			if x in PL:
				return True
			else:
				return False
		else:
			for p in PL:
				if x % p == 0:
					return False
			for i in range(1, sqrt // 210 + 1):
				for j in [1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209]:
					if x % (210 * i + j) == 0:
						return False
		return True
	elif x != 0 and x != 1:
		j = 0
		while j < len(L) and L[j] <= sqrt:
			if x % L[j] == 0 or (x + 2) % L[j] == 0:
				return False
			j += 1
	else:
		return False
	return True

def prime_list(n):
	L = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]
	for k in range(1, n // 210):
		for j in [1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209]:
			if is_prime(210 * k + j, L):
				L.append(210 * k + j)
	k = n // 210
	for j in [1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209]:
		if is_prime(210 * k + j, L) and 210 * k + j <= n:
			L.append(210 * k + j)
	return L

def pair_primes(N, M, prime_list):
	PL = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199]
	RPL = [-1, 1, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101, 103, 107, 109, 137, 139, 149, 151, 167, 169, 179, 181, 191, 193, 197, 199]
	count = 0
	if not N // 210:
		for i in range(0, len(PL) - 1):
			if PL[i] + 2 == PL[i + 1] and PL[i] >= N and (PL[i + 1] <= M):
				count += 1
	for k in range(max(N // 210, 1), M // 210 + 1):
		for j in range(0, len(RPL) // 2):
			if is_prime_pair(210 * k + RPL[2 * j], prime_list) and 210 * k + RPL[2 * j] >= N and (210 * k + RPL[2 * j + 1] <= M):
				count += 1
	return count

def output(L):
	for i in range(0, len(L) // 9):
		s = ''
		for j in range(0, 9):
			s += str(L[9 * i + j]) + ' '
		print(s)
(N, M) = [int(a) for a in input().split()]
prime_list = prime_list(50000)
print(pair_primes(N, M, prime_list))


import sys
from random import randrange

def is_composite(n, accuracy):
	if n == 1:
		return True
	if n < 4:
		return False
	s = 0
	d = n - 1
	while d % 2 == 0:
		s += 1
		d = d // 2
	for _ in range(accuracy):
		a = randrange(2, n - 1)
		x = pow(a, d, n)
		if x == 1 or x == n - 1:
			continue
		for _ in range(s - 1):
			x = x ** 2 % n
			if x == 1:
				return True
			if x == n - 1:
				break
		if x != n - 1:
			return True
	return False

def solve(n, m):
	(pp, trials) = (list(), 8)
	for p in range(n, m + 1):
		if p % 2 == 1 and (not is_composite(p, trials)):
			pp.append(p)
	cnt = 0
	for (p, q) in zip(pp, pp[1:]):
		if q - p == 2:
			cnt += 1
	return cnt
(n, m) = map(int, input().split())
print(solve(n, m))


def primeSieve(n):
	sieve = [True] * (n + 1)
	sieve[0] = sieve[1] = False
	for p in range(2, n + 1):
		if p * p > n:
			break
		if sieve[p]:
			for x in range(p * p, n + 1, p):
				sieve[x] = False
	return [p for p in range(2, n + 1) if sieve[p]]

def sieveInterval(n, m, primes):
	sieve = [True] * (m - n + 1)
	for p in primes:
		if p * p > m:
			break
		np = n // p * p
		if np < n:
			np += p
		if np == p:
			np += p
		for x in range(np, m + 1, p):
			sieve[x - n] = False
	return [p for p in range(n, m + 1) if sieve[p - n]]

def countTwins(primes):
	twins = 0
	for i in range(len(primes) - 1):
		if primes[i + 1] - primes[i] == 2:
			twins += 1
	return twins
(n, m) = map(int, input().split())
primes = primeSieve(min(10 ** 6, m))
intervalPrimes = sieveInterval(n, m, primes)
print(countTwins(intervalPrimes))


import math
primeNo = []
prime_No = []

def simpleSieve(prime, limit):
	for i in range(2, round(math.sqrt(limit)) + 1):
		if prime[i]:
			for j in range(2 * i, limit, i):
				prime[j] = 0
	for i in range(len(prime)):
		if prime[i]:
			primeNo.append(i)

def segmentedSeive(prime_, m, n):
	for i in range(len(primeNo)):
		start = m // primeNo[i] * primeNo[i]
		while start < m or start == primeNo[i]:
			start += primeNo[i]
		for j in range(start, n + 1, primeNo[i]):
			prime_[j - m] = 0
	for i in range(len(prime_)):
		if prime_[i]:
			prime_No.append(i + m)
(m, n) = map(int, input().split())
prime_ = [1] * (n - m + 1)
limit = round(math.sqrt(n)) + 1
prime = [1] * (limit + 1)
prime[0] = prime[1] = 0
simpleSieve(prime, limit)
segmentedSeive(prime_, m, n)
count = 0
for i in range(len(prime_No) - 1):
	if prime_No[i + 1] - prime_No[i] == 2:
		count += 1
print(count)


def prime_sieve(n):
	A = [0, 0] + [1 for i in range(n - 1)]
	for i in range(2, int(n ** 0.5) + 1):
		if A[i] == 1:
			for j in range(i * i, n + 1, i):
				A[j] = 0
	return [i for (i, prime) in enumerate(A) if prime]

def segmented_prime_sieve(a, b):
	a = max(a, 2)
	if a > b:
		return []
	primes = prime_sieve(int(b ** 0.5) + 1)
	A = [1] * (b - a + 1)
	for p in primes:
		i = (a + p - 1) // p * p
		if i == p:
			i += p
		for j in range(i, b + 1, p):
			A[j - a] = 0
	return [i + a for (i, prime) in enumerate(A) if prime]
(n, m) = map(int, input().split())
primes = segmented_prime_sieve(n, m)
count_twins = 0
for i in range(len(primes) - 1):
	if primes[i] + 2 == primes[i + 1]:
		count_twins += 1
print(count_twins)


N = 10 ** 5
p = set(range(3, N, 2))
(m, n) = map(int, input().split())
n += 1
q = set(range(m, n)) - set(range(max(4, m >> 1 << 1), n, 2))
for i in range(3, N, 2):
	if i in p:
		p -= set(range(i * i, N, i))
		q -= set(range(max(i * i, m // i * i), n, i))
q = sorted(q)
print([q[i] - q[i - 1] for i in range(1, len(q))].count(2))


from math import ceil, sqrt

def primes_between(num1, num2):
	is_prime = [True for idx in range(num2 - num1 + 1)]
	for div in range(2, ceil(sqrt(num2)) + 1):
		num = div * max(div, ceil(num1 / div))
		while num <= num2:
			idx = num - num1
			is_prime[idx] = False
			num += div
	res = []
	for idx in range(num2 - num1 + 1):
		if is_prime[idx]:
			num = num1 + idx
			res.append(num)
	return res
(n, m) = map(int, input().strip().split())
primes = primes_between(n, m)
ans = 0
for idx in range(len(primes) - 1):
	prime1 = primes[idx]
	prime2 = primes[idx + 1]
	if prime2 - prime1 == 2:
		ans += 1
print(ans)


(n, m) = input().strip().split()
n = int(n)
m = int(m)
p = [1 for i in range(m - n + 1)]
for i in range(2, 100000):
	k = ((n - 1) // i + 1) * i
	if k == i:
		k += i
	while k <= m:
		p[k - n] = 0
		k += i
ans = 0
for i in range(m - n - 1):
	if p[i] + p[i + 2] == 2:
		ans += 1
if n == 1 and ans > 0:
	ans -= 1
print(ans)


def prime_candidates(n, m):
	if n <= 3:
		raise ValueError
	offset = n % 6
	shift = [1, 0, 3, 2, 1, 0]
	n += shift[offset]
	if n % 6 == 1:
		jump = 4
	elif n % 6 == 5:
		jump = 2
	else:
		raise ValueError
	while n <= m:
		yield n
		n += jump
		jump = 6 - jump

def gcd(a, b):
	while b != 0:
		(a, b) = (b, a % b)
	return a

def powerMod(base, exponent, modulus):
	result = 1
	while exponent > 0:
		if exponent % 2 == 1:
			result = result * base % modulus
		base = base * base % modulus
		exponent //= 2
	return result

def first_twin_prime_candidates(n, m):
	if n <= 3:
		raise ValueError
	offset = n % 6
	n += 5 - offset
	while n <= m:
		yield n
		n += 6

def is_probable_prime(p):
	bases = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]
	if p in bases:
		return True
	if gcd(p, 2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 29 * 31) != 1:
		return False
	for b in [2, 325, 9375, 28178, 450775, 9780504, 1795265022]:
		if b > p:
			break
		result = powerMod(b, (p - 1) / 2, p)
		if result != 1 and result != p - 1:
			return False
	return True

def numberOfTwinPrimesInRange(lower, upper):
	count = 0
	if lower <= 3:
		if upper < 5:
			return 0
		count = 1
		lower = 5
	for p in first_twin_prime_candidates(lower, upper - 2):
		if is_probable_prime(p) and is_probable_prime(p + 2):
			count += 1
	return count
(n, m) = [int(x) for x in input().split()]
print(numberOfTwinPrimesInRange(n, m))


def is_prime(n):
	primes = [2, 7, 61]
	if n <= 1:
		return False
	if n in primes:
		return True
	if not n & 1:
		return False

	def check(a, s, d, n):
		x = pow(a, d, n)
		if x == 1:
			return True
		for i in range(s - 1):
			if x == n - 1:
				return True
			x = pow(x, 2, n)
		return x == n - 1
	s = 0
	d = n - 1
	while not d & 1:
		d >>= 1
		s += 1
	for a in primes:
		if not check(a, s, d, n):
			return False
	return True
(n, m) = map(int, input().split())
lst = [0] * (m - n + 1)
for i in range(n // 2 * 2 + 1, m + 1, 2):
	if is_prime(i):
		lst[i - n] = 1
print(sum((1 for i in range(0, m - n - 1) if lst[i] and lst[i + 2])))


(n, m) = map(int, input().split())
primes = set([2])
for k in range(3, int(m ** 0.5) + 1, 2):
	if not any((k % p == 0 for p in primes)):
		primes.add(k)
candidates = set(range(max(n, 2), m + 1))
for p in primes:
	for k in range(max(2 * p, p * (n // p)), m + 1, p):
		if k in candidates:
			candidates.remove(k)
print(sum((1 for i in candidates if i + 2 in candidates)))


def sieve(n):
	primes = [True] * (n + 1)
	primes[0] = primes[1] = False
	res = []
	for i in range(2, n + 1):
		if primes[i]:
			res.append(i)
			for j in range(i * i, n + 1, i):
				primes[j] = False
	return res

def segmentedSieve(n, m):
	size = m - n + 1
	primes = sieve(int(m ** 0.5))
	isPrime = [True] * size
	for prime in primes:
		for i in range(n // prime * prime, m + 1, prime):
			if i >= n and i > prime:
				isPrime[i - n] = False
	res = 0
	for i in range(0, len(isPrime) - 2):
		if n + i >= 2 and isPrime[i] and isPrime[i + 2]:
			res += 1
	return res
(n, m) = map(int, input().split())
print(segmentedSieve(n, m))


def check_composite(n, s, d, a):
	x = pow(a, d, n)
	if x == 1 or x == n - 1:
		return False
	for y in range(1, s):
		x = x * x % n
		if x == 1:
			return True
		if x == n - 1:
			return False
	return True
small_primes = set([3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37])
small_is_prime = [s in small_primes for s in range(38)]
small_is_prime[2] = True
witnesses_bounds = [(341531, [9345883071009581737]), (716169301, [15, 13393019396194701]), (154639673381, [15, 176006322, 4221622697]), (47636622961201, [2, 2570940, 211991001, 3749873356]), (3770579582154547, [2, 2570940, 880937, 610386380, 4130785767])]
i64_witnesses = [2, 325, 9375, 28178, 450775, 9780504, 1795265022]

def is_prime(n):
	if n < 38:
		return small_is_prime[n]
	for s in small_primes:
		if n % s == 0:
			return False
	d = n - 1
	s = 0
	while not d & 1:
		d >>= 1
		s += 1
	best_witnesses = i64_witnesses
	for (bound, bound_ws) in witnesses_bounds:
		if n < bound:
			best_witnesses = bound_ws
			break
	for a in best_witnesses:
		a %= n
		if a and check_composite(n, s, d, a):
			return False
	return True
(l, r) = map(int, input().split())
cpt = 0
if 3 >= l and 3 <= r and (5 >= l) and (5 <= r):
	cpt = cpt + 1
while l % 6 != 5:
	l = l + 1
for i in range(l, r - 1, 6):
	if is_prime(i):
		if is_prime(i + 2):
			cpt += 1
print(cpt)


import random

def miller_rabin(n, k):
	if n == 1:
		return False
	if n == 2:
		return True
	if n == 3:
		return True
	if n % 2 == 0:
		return False
	(r, s) = (0, n - 1)
	while s % 2 == 0:
		r += 1
		s //= 2
	for _ in range(k):
		a = random.randrange(2, n - 1)
		x = pow(a, s, n)
		if x == 1 or x == n - 1:
			continue
		for _ in range(r - 1):
			x = pow(x, 2, n)
			if x == n - 1:
				break
		else:
			return False
	return True
ans = 0
pr = 0
(n, m) = map(int, input().split())
for t in range(n, m + 1):
	if miller_rabin(t, 5):
		if pr and abs(pr - t) == 2:
			ans += 1
		pr = t
print(ans)


import math

def prime(n):
	prime = [True for i in range(n + 1)]
	pri = []
	p = 2
	while p * p <= n:
		if prime[p]:
			for i in range(p * p, n + 1, p):
				prime[i] = False
		p += 1
	for i in range(2, n + 1):
		if prime[i]:
			pri.append(i)
	return pri

def segment_seive(l, p, n, m):
	count = 0
	len_list = m - n + 1
	primes = [True for i in range(len_list)]
	for i in p:
		b = n // i
		c = b * i
		if c < n:
			c += i
		first_num = c - n
		while first_num < len_list:
			primes[first_num] = False
			first_num += i
	for i in range(len_list):
		if primes[i]:
			l.append(i + n)
	for i in range(1, len(l)):
		if l[i] - l[i - 1] == 2:
			count += 1
	print(count)
(n, m) = map(int, input().split())
p = prime(math.ceil(math.sqrt(m)))
if len(p) == 0:
	print(0)
	exit()
l = []
if n <= int(math.ceil(math.sqrt(m))):
	for i in range(len(p)):
		if p[i] >= n:
			l.append(p[i])
	segment_seive(l, p, p[i - 1] + 1, m)
else:
	segment_seive(l, p, n, m)


from random import randint as r
from math import gcd as g

def isPrime(n, k):
	if n == 1 or n == 4:
		return False
	if n <= 3:
		return True
	while k >= 0:
		a = r(2, n - 1)
		if g(n, a) != 1:
			return False
		if pow(a, n - 1, n) != 1:
			return False
		k -= 1
	return True
(n, m) = map(int, input().split())
k = 9
count = 0
if n % 2:
	i = n
	while True:
		if isPrime(i, k) and isPrime(i + 2, k) and (i + 2 <= m):
			count += 1
		if isPrime(i + 2, k):
			i += 2
		else:
			i += 4
		if i > m:
			break
else:
	i = n + 1
	while True:
		if isPrime(i, k) and isPrime(i + 2, k) and (i + 2 <= m):
			count += 1
		if isPrime(i + 2, k):
			i += 2
		else:
			i += 4
		if i > m:
			break
print(count)