import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } // floor(sqrt(a)) long floorSqrt(long a) { import core.bitop : bsr; import std.algorithm : min; long b = a, x = 0, y = 0; for (int e = bsr(a) & ~1; e >= 0; e -= 2) { x <<= 1; y <<= 1; if (b >= (y | 1) << e) { b -= (y | 1) << e; x |= 1; y += 2; } } return x; } // get(floor(N / l)) = \sum_{p<=floor(N/l)} p^K // O(N^(3/4) / log N) time, O(N^(1/2)) space class PrimeSum(T, int K) { long N, sqrtN; bool[] isPrime; T[] small, large; this(long N) { assert(N >= 1, "PrimeSum: N >= 1 must hold"); this.N = N; sqrtN = floorSqrt(N); isPrime = new bool[sqrtN + 1]; small = new T[sqrtN + 1]; large = new T[sqrtN + 1]; isPrime[2 .. $] = true; T powerSum(long n) { static if (K == 0) { return T(n); } else static if (K == 1) { long n0 = n, n1 = n + 1; ((n0 % 2 == 0) ? n0 : n1) /= 2; return T(n0) * T(n1); } else static if (K == 2) { long n0 = n, n1 = n + 1, n2 = 2 * n + 1; ((n0 % 2 == 0) ? n0 : n1) /= 2; ((n0 % 3 == 0) ? n0 : (n1 % 3 == 0) ? n1 : n2) /= 3; return T(n0) * T(n1) * T(n2); } else static if (K == 3) { long n0 = n, n1 = n + 1; ((n0 % 2 == 0) ? n0 : n1) /= 2; return T(n0) * T(n0) * T(n1) * T(n1); } else { static assert(false, "PrimeSum: K is out of range"); } } foreach (n; 1 .. sqrtN + 1) small[n] = powerSum(n); foreach (l; 1 .. sqrtN + 1) large[l] = powerSum(N / l); foreach (p; 2 .. sqrtN + 1) { if (isPrime[p]) { for (long n = p^^2; n <= sqrtN; n += p) isPrime[n] = false; const pk = T(p)^^K, g1 = get(p - 1); foreach (l; 1 .. sqrtN + 1) { const n = N / l; if (n < p^^2) break; large[l] -= pk * (get(n / p) - g1); } foreach_reverse (n; 1 .. sqrtN + 1) { if (n < p^^2) break; small[n] -= pk * (get(n / p) - g1); } } } small[1 .. $] -= T(1); large[1 .. $] -= T(1); } T get(long n) const { return (n <= sqrtN) ? small[n] : large[N / n]; } } long pi(long n) { if (n <= 1) return 0; return new PrimeSum!(long, 0)(n).get(n); } void main() { try { for (; ; ) { const L = readLong(); const R = readLong(); long ans; ans += pi(R); ans -= pi(L - 1); if (L + (L + 1) <= (R - 1) + R) { ans += max(pi((R - 1) + R) - 1, 0); ans -= max(pi(L + (L + 1) - 1) - 1, 0); } writeln(ans); } } catch (EOFException e) { } }