#define _USE_MATH_DEFINES #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 1000000007; // constexpr int MOD = 998244353; constexpr int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; constexpr int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; // https://github.com/ei1333/library/blob/e4888de51cc691c32057e308cb8a5beb05e78f7b/math/number-theory/kth-root-integer.cpp uint64_t kth_root_integer(uint64_t a, int k) { if(k == 1) return a; auto check = [&](uint32_t x) { uint64_t mul = 1; for(int j = 0; j < k; j++) { if(__builtin_mul_overflow(mul, x, &mul)) return false; } return mul <= a; }; uint64_t ret = 0; for(int i = 31; i >= 0; i--) { if(check(ret | (1u << i))) ret |= 1u << i; } return ret; } // https://github.com/ei1333/library/blob/e4888de51cc691c32057e308cb8a5beb05e78f7b/math/number-theory/prime-table.cpp vector< bool > prime_table(int n) { vector< bool > prime(n + 1, true); if(n >= 0) prime[0] = false; if(n >= 1) prime[1] = false; for(int i = 2; i * i <= n; i++) { if(!prime[i]) continue; for(int j = i * i; j <= n; j += i) { prime[j] = false; } } return prime; } // https://github.com/ei1333/library/blob/e4888de51cc691c32057e308cb8a5beb05e78f7b/math/number-theory/prime-count.cpp template< int64_t LIM = 100000000000LL > struct PrimeCount { private: int64_t sq; vector< bool > prime; vector< int64_t > prime_sum, primes; int64_t p2(int64_t x, int64_t y) { if(x < 4) return 0; int64_t a = pi(y); int64_t b = pi(kth_root_integer(x, 2)); if(a >= b) return 0; int64_t sum = (a - 2) * (a + 1) / 2 - (b - 2) * (b + 1) / 2; for(int64_t i = a; i < b; i++) sum += pi(x / primes[i]); return sum; } int64_t phi(int64_t m, int64_t n) { if(m < 1) return 0; if(n > m) return 1; if(n < 1) return m; if(m <= primes[n - 1] * primes[n - 1]) return pi(m) - n + 1; if(m <= primes[n - 1] * primes[n - 1] * primes[n - 1] && m <= sq) { int64_t sx = pi(kth_root_integer(m, 2)); int64_t ans = pi(m) - (sx + n - 2) * (sx - n + 1) / 2; for(int64_t i = n; i < sx; ++i) ans += pi(m / primes[i]); return ans; } return phi(m, n - 1) - phi(m / primes[n - 1], n - 1); } public: PrimeCount() : sq(kth_root_integer(LIM, 2)), prime_sum(sq + 1) { prime = prime_table(sq); for(int i = 1; i <= sq; i++) prime_sum[i] = prime_sum[i - 1] + prime[i]; primes.reserve(prime_sum[sq]); for(int i = 1; i <= sq; i++) if(prime[i]) primes.push_back(i); } int64_t pi(int64_t n) { if(n <= sq) return prime_sum[n]; int64_t m = kth_root_integer(n, 3); int64_t a = pi(m); return phi(n, a) + a - 1 - p2(n, m); } }; int main() { ll l, r; cin >> l >> r; PrimeCount prime_count; ll ans = prime_count.pi(r) - prime_count.pi(l - 1); if (l < r) ans += prime_count.pi(2 * (r - 1) + 1) - prime_count.pi(2 * l); cout << ans << '\n'; return 0; }