#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template void print_tuple(ostream&, const T&) {} template void print_tuple(ostream& os, const T& t) { if (i) os << ','; os << get(t); print_tuple(os, t); } template ostream& operator<<(ostream& os, const tuple& t) { os << '{'; print_tuple<0, tuple, Args...>(os, t); return os << '}'; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); } int popcount(signed t) { return __builtin_popcount(t); } int popcount(long long t) { return __builtin_popcountll(t); } bool ispow2(int i) { return i && (i & -i) == i; } template T ceil(T x, T y) { assert(y >= 1); return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, T y) { assert(y >= 1); return (x > 0 ? x / y : (x - y + 1) / y); } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } #pragma endregion typedef pair P; #define stop \ char nyaa; \ cin >> nyaa; #define rep(i, n) for (int i = 0; i < n; i++) #define per(i, n) for (int i = n - 1; i >= 0; i--) #define Rep(i, sta, n) for (int i = sta; i < n; i++) #define rep1(i, n) for (int i = 1; i <= n; i++) #define per1(i, n) for (int i = n; i >= 1; i--) #define Rep1(i, sta, n) for (int i = sta; i <= n; i++) #define all(v) (v).begin(), (v).end() typedef pair LP; typedef long double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acos(-1.0); bool isp[25000001]; vector ps; void init(int sup = 25000000) { fill(isp + 2, isp + sup + 1, true); for (int i = 2; i <= sup; i++) { if (!isp[i]) continue; ps.push_back(i); for (int j = 2 * i; j <= sup; j += i) { isp[j] = false; } } } ll count_prime(ll n) { if (n < 10) { ll res = 0; for (int i = 2; i <= n; i++) if (isp[i]) res++; return res; } ll t = 1; while (t * t * t <= n) { t++; } t--; int loc = 0; rep(i, ps.size()) if (ps[i] > t) { loc = i; break; } // cout << "! " << t <<" "< used(t * t + 1, false); vector> ids(loc); rep(i, loc) { for (int j = ps[i]; j <= t * t; j += ps[i]) { if (!used[j]) { used[j] = true; ids[i].push_back(j); } } } function calc = [&](ll n, ll m) -> ll { if (m == 0) return n; if (n <= t * t) { ll res = n; rep(i, m) { res -= upper_bound(all(ids[i]), n) - ids[i].begin(); } return res; } else { return calc(n, m - 1) - calc(n / ps[m - 1], m - 1); } }; ll ans = calc(n, loc) + loc; ans--; int las = ps.size(); rep(i, ps.size()) { if ((ll)ps[i] * ps[loc] > n) { las = i; break; } } while (true) { while (loc < las && (ll)ps[loc] * ps[las - 1] > n) { las--; } if (loc >= las) break; // cout << ps[loc] << " " << ps[las - 1] << "\n"; ans -= las - loc; loc++; } return ans; } const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; const long long MOD = 1000000007; // const long long MOD = 998244353; int main() { cin.tie(0); ios::sync_with_stdio(false); init(); ll L, R; cin >> L >> R; auto calc = [&](ll n) { return count_prime(n); }; // number of primes lower than n ll ans = 0; ans += calc(R) - calc(L - 1); if (L + 1 <= R) ans += calc((R - 1) + R) - calc(L + (L + 1) - 1); cout << ans << '\n'; return 0; }