#pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #pragma GCC optimize("inline") #include using namespace std; template struct cLtraits_identity{ using type = T; } ; template using cLtraits_try_make_signed = typename conditional< is_integral::value, make_signed, cLtraits_identity >::type; template struct cLtraits_common_type{ using tS = typename cLtraits_try_make_signed::type; using tT = typename cLtraits_try_make_signed::type; using type = typename common_type::type; } ; void*wmem; char memarr[96000000]; template inline auto max_L(S a, T b) -> typename cLtraits_common_type::type{ return (typename cLtraits_common_type::type) a >= (typename cLtraits_common_type::type) b ? a : b; } template inline void walloc1d(T **arr, int x, void **mem = &wmem){ static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}; (*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] ); (*arr)=(T*)(*mem); (*mem)=((*arr)+x); } template inline void walloc1d(T **arr, int x1, int x2, void **mem = &wmem){ walloc1d(arr, x2-x1, mem); (*arr) -= x1; } #define ISPRIME_PRE_CALC_SIZE 1000000 char isPrime_prime_table[ISPRIME_PRE_CALC_SIZE]; template inline int isPrime(T n); void isPrime32_init(void); int isPrime32_sub(int b, unsigned n); int isPrime32(unsigned n); int isPrime64_sub(long long b, unsigned long long n); int isPrime64(unsigned long long n); struct Rand{ unsigned x; unsigned y; unsigned z; unsigned w; Rand(void){ x=123456789; y=362436069; z=521288629; w=(unsigned)time(NULL); } Rand(unsigned seed){ x=123456789; y=362436069; z=521288629; w=seed; } inline unsigned get(void){ unsigned t; t = (x^(x<<11)); x=y; y=z; z=w; w = (w^(w>>19))^(t^(t>>8)); return w; } inline double getUni(void){ return get()/4294967296.0; } inline int get(int a){ return (int)(a*getUni()); } inline int get(int a, int b){ return a+(int)((b-a+1)*getUni()); } inline long long get(long long a){ return(long long)(a*getUni()); } inline long long get(long long a, long long b){ return a+(long long)((b-a+1)*getUni()); } inline double get(double a, double b){ return a+(b-a)*getUni(); } inline int getExp(int a){ return(int)(exp(getUni()*log(a+1.0))-1.0); } inline int getExp(int a, int b){ return a+(int)(exp(getUni()*log((b-a+1)+1.0))-1.0); } } ; inline void my_putchar_unlocked(const int k){ putchar_unlocked(k); } inline void wt_L(char a){ my_putchar_unlocked(a); } inline void wt_L(long long x){ int s=0; int m=0; char f[20]; if(x<0){ m=1; x=-x; } while(x){ f[s++]=x%10; x/=10; } if(!s){ f[s++]=0; } if(m){ my_putchar_unlocked('-'); } while(s--){ my_putchar_unlocked(f[s]+'0'); } } inline void wt_L(const char c[]){ int i=0; for(i=0;c[i]!='\0';i++){ my_putchar_unlocked(c[i]); } } template inline T pow2_L(T a){ return a*a; } inline long long Isqrt_f_L(const long long n){ long long r = sqrt(n); r =max_L(r-2, 0); while((pow2_L((r+1)))<= n ){ r++; } return r; } long long llReader(long long mn, long long mx, char nx){ int i; int fg = 0; int m = 1; long long res = 0; double tmp = 0; for(;;){ i = getchar(); if(fg==0 && i=='-'){ fg++; m = -1; } else if('0' <= i && i <= '9'){ fg++; res = 10 * res + i - '0'; tmp = 10 * tmp + i - '0'; assert(tmp < 1e20); } else{ break; } } assert(tmp / 2 <= res); assert((m==1 && fg >= 1) || (m==-1 && fg >= 2)); assert(mn <= m * res && m * res <= mx); assert(i == nx); return m * res; } vector ppp(20000000+1); long long solve1(long long L, long long R){ int i; long long res = 0; for(i=0;i<20000000+1;i++){ if(L<=i && i<=R && ppp[i]){ res++; } } for(i=0;i<20000000+1;i++){ if(2*L+1<=i && i<=2*R-1 && ppp[i]){ res++; } } return res; } long long solve2(long long L, long long R){ long long k; long long a; long long b; long long c; long long res = 0; for(a=(L);a<(R+1);a++){ for(b=(a);b<(R+1);b++){ c = 0; for(k=(a);k<(b+1);k++){ c += k; } if(isPrime(c)){ res++; } } } return res; } int ps; int p[1000000]; long long memo[] = {11078937,21336326,31324703,41146179,50847534,60454705,69985473,79451833,88862422,98222287,107540122,116818447,126062167,135270258,144449537,153600805,162725196,171827136,180906194,189961812,198996103,208013454,217011319,225991743,234954223,243902342,252834065,261751864,270655552,279545368,288422869,297285198,306137611,314977166,323804352,332620900,341426904,350221825,359006517,367783654,376549859,385307831,394055910,402793457,411523195,420243162,428958595,437663672,446362736,455052511,463733626,472408200,481074475,489736021,498388617,507036251,515673696,524309392,532936342,541555851,550170437,558778993,567382703,575978253,584570200,593155089,601735269,610308664,618878615,627440336,635997249,644550922,653099304,661643304,670180516,678714823,687242934,695766925,704286233,712799821,721310048,729813991,738315156,746813071,755305935,763794029,772276773,780756650,789230673,797703398,806169530,814633249,823092766,831548431,840000027,848450250,856895823,865335133,873772692,882206716}; bitset<500000> b; long long solve3sub(long long n){ int i; long long s; long long k; long long res; if(n < 1000000){ for(i=0;i n){ break; } } return i; } s = n / 200000000; if(s){ res = memo[s-1]; s *= 200000000; } else{ res = ps; s = 1000000; } for(;;s+=1000000){ b.set(); for(i=1;;i++){ k = (long long) p[i] * p[i] - s; if(k >= 1000000){ break; } if(k < 0){ k += ((-k+p[i]-1) / p[i]) * p[i]; } if(k % 2 == 0){ k += p[i]; } k /= 2; while(k < 500000){ b.reset(k); k += p[i]; } } if(n-s < 1000000){ for(i=1;i<=n-s;i+=2){ res += b[i/2]; } break; } res += b.count(); } return res; } long long solve3(long long L, long long R){ return solve3sub(2*R) - solve3sub(2*L) + solve3sub(R) - solve3sub(L-1); } long long cntPrime(long long n, void *mem = wmem){ int i; int j; int sn; char*isp; long long*s1; long long*s2; long long x; long long c = -1; if(n <= 1){ return 0; } if(n == 2){ return 1; } sn =Isqrt_f_L(n); walloc1d(&s1, sn+1, &mem); walloc1d(&s2, sn+1, &mem); walloc1d(&isp, sn+1, &mem); s1[0] = 0; for(i=(1);i<(sn+1);i++){ s1[i] = i - 1; } for(i=(1);i<(sn+1);i++){ s2[i] = n/i - 1; } for(i=(2);i<(sn+1);i++){ isp[i] = 1; } for(i=(2);i<(sn+1);i++){ if(isp[i]){ for(j=2*i;j<=sn;j+=i){ isp[j] = 0; } c++; for(j=(1);j<(sn+1);j++){ if((long long)i*i*j > n){ goto gEg5UqEA; } x = n / j / i; if(x <= sn){ s2[j] -= s1[x] - c; } else{ s2[j] -= s2[i*j] - c; } } for(j=(sn+1)-1;j>=((long long)i*i);j--){ s1[j] -= s1[j/i] - c; } } gEg5UqEA:; } return s2[1]; } long long solve4(long long L, long long R){ return cntPrime(2*R) - cntPrime(2*L) + cntPrime(R-1) - cntPrime(L-1); } int main(){ wmem = memarr; { isPrime32_init(); } long long L; long long R; long long res; L = llReader(1, 10000000000LL, ' '); R = llReader(L, 10000000000LL, '\n'); assert(getchar() == EOF); res = solve4(L,R); wt_L(res); wt_L('\n'); return 0; int i; int j; for(i=2;i<20000000+1;i++){ ppp[i] = 1; } for(i=2;i<20000000+1;i++){ if(ppp[i]){ for(j=2*i;j<20000000+1;j+=i){ ppp[j] = 0; } } } p[2] = 1; for(i=3;i<1000000;i+=2){ p[i] = 1; } for(i=3;i<1000;i+=2){ if(p[i]){ for(j=i*i;j<1000000;j+=i){ p[j] = 0; } } } for(i=0;i<1000000;i++){ if(p[i]){ p[ps++] = i; } } if(1){ int xtzQOlbs; long long L; long long R; long long r1; long long r2; long long r3; long long r4; Rand rnd; puts(""); for(L=(1);L<(30);L++){ for(R=(L);R<(30);R++){ r1 = solve1(L,R); r2 = solve2(L,R); r3 = solve3(L,R); r4 = solve4(L,R); wt_L(L); wt_L(' '); wt_L(R); wt_L(' '); wt_L(":"); wt_L(' '); wt_L(r1); wt_L(' '); wt_L(r2); wt_L(' '); wt_L(r3); wt_L(' '); wt_L(r4); wt_L('\n'); assert(r1==r2 && r2==r3 && r3==r4); } } for(xtzQOlbs=(0);xtzQOlbs<(100);xtzQOlbs++){ L = rnd.get(1LL, 10000000000LL); R = rnd.get(1LL, 10000000000LL); if(L > R){ swap(L, R); } ; r3 = solve3(L,R); r4 = solve4(L,R); wt_L(L); wt_L(' '); wt_L(R); wt_L(' '); wt_L(":"); wt_L(' '); wt_L(r3); wt_L(' '); wt_L(r4); wt_L('\n'); assert(r3==r4); } } return 0; } template inline int isPrime(T n){ T i; if(n<=1){ return 0; } if(n <= (1ULL<<32) - 1){ return isPrime32(n); } if(n <= (1ULL<<63) - 1 + (1ULL<<63)){ return isPrime64(n); } if(n<=3){ return 1; } if(n%2==0){ return 0; } for(i=3;i*i<=n;i+=2){ if(n%i==0){ return 0; } } return 1; } int isPrime32_sub(int b, unsigned n){ unsigned i; unsigned t = 0; unsigned u = n-1; unsigned long long nw; unsigned long long nx; while(!(u&1)){ t++; u >>= 1; } nw = 1; nx = b % n; while(u){ if(u&1){ nw = (nw * nx) % n; } nx = (nx * nx) % n; u >>= 1; } for(i=(0);i<(t);i++){ nx = (nw * nw) % n; if(nx == 1 && nw != 1 && nw != n-1){ return 0; } nw = nx; } if(nw == 1){ return 1; } return 0; } int isPrime32(unsigned n){ if(n < 100000){ return isPrime_prime_table[n]; } if(n % 2 == 0){ return 0; } if(!isPrime32_sub(2,n)){ return 0; } if(n<=1000000){ if(!isPrime32_sub(3,n)){ return 0; } } else{ if(!isPrime32_sub(7,n)){ return 0; } if(!isPrime32_sub(61,n)){ return 0; } } return 1; } int isPrime64_sub(long long b, unsigned long long n){ unsigned long long i; unsigned long long t = 0; unsigned long long u = n-1; __uint128_t nw; __uint128_t nx; while(!(u&1)){ t++; u >>= 1; } nw = 1; nx = b % n; while(u){ if(u&1){ nw = (nw * nx) % n; } nx = (nx * nx) % n; u >>= 1; } for(i=(0);i<(t);i++){ nx = (nw * nw) % n; if(nx == 1 && nw != 1 && nw != n-1){ return 0; } nw = nx; } if(nw == 1){ return 1; } return 0; } int isPrime64(unsigned long long n){ if(n < 100000){ return isPrime_prime_table[n]; } if(n < (1ULL<<32)){ return isPrime32(n); } if(n % 2 == 0){ return 0; } if(!isPrime64_sub(2,n)){ return 0; } if(n <= 21652684502221ULL){ if(!isPrime64_sub(1215,n)){ return 0; } if(!isPrime64_sub(34862,n)){ return 0; } if(!isPrime64_sub(574237825,n)){ return 0; } } else{ if(!isPrime64_sub(325,n)){ return 0; } if(!isPrime64_sub(9375,n)){ return 0; } if(!isPrime64_sub(28178,n)){ return 0; } if(!isPrime64_sub(450775,n)){ return 0; } if(!isPrime64_sub(9780504,n)){ return 0; } if(!isPrime64_sub(1795265022,n)){ return 0; } } return 1; } void isPrime32_init(void){ int i; int j; int k; k =Isqrt_f_L(ISPRIME_PRE_CALC_SIZE); for(i=(2);i<(ISPRIME_PRE_CALC_SIZE);i++){ isPrime_prime_table[i] = 1; } for(i=(2);i<(k+1);i++){ if(isPrime_prime_table[i]){ for(j=(i*i);j<(ISPRIME_PRE_CALC_SIZE);j+=(i)){ isPrime_prime_table[j] = 0; } } } } // cLay version 20210717-1 [beta] // --- original code --- // ll llReader(ll mn, ll mx, char nx){ // int i, fg = 0, m = 1; // ll res = 0; double tmp = 0; // // for(;;){ // i = getchar(); // if(fg==0 && i=='-'){ // fg++; // m = -1; // } else if('0' <= i <= '9'){ // fg++; // res = 10 * res + i - '0'; // tmp = 10 * tmp + i - '0'; // assert(tmp < 1e20); // } else { // break; // } // } // assert(tmp / 2 <= res); // assert((m==1 && fg >= 1) || (m==-1 && fg >= 2)); // assert(mn <= m * res <= mx); // assert(i == nx); // return m * res; // } // // // vector ppp(2d7+1); // ll solve1(ll L, ll R){ // int i; // ll res = 0; // for(i=0;i<2d7+1;i++) if(L<=i<=R && ppp[i]) res++; // for(i=0;i<2d7+1;i++) if(2*L+1<=i<=2*R-1 && ppp[i]) res++; // return res; // } // // ll solve2(ll L, ll R){ // ll k, a, b, c, res = 0; // rep(a,L,R+1) rep(b,a,R+1){ // c = 0; // rep(k,a,b+1) c += k; // if(isPrime(c)) res++; // } // return res; // } // // // int ps, p[1000000]; // ll memo[] = {11078937,21336326,31324703,41146179,50847534,60454705,69985473,79451833,88862422,98222287,107540122,116818447,126062167,135270258,144449537,153600805,162725196,171827136,180906194,189961812,198996103,208013454,217011319,225991743,234954223,243902342,252834065,261751864,270655552,279545368,288422869,297285198,306137611,314977166,323804352,332620900,341426904,350221825,359006517,367783654,376549859,385307831,394055910,402793457,411523195,420243162,428958595,437663672,446362736,455052511,463733626,472408200,481074475,489736021,498388617,507036251,515673696,524309392,532936342,541555851,550170437,558778993,567382703,575978253,584570200,593155089,601735269,610308664,618878615,627440336,635997249,644550922,653099304,661643304,670180516,678714823,687242934,695766925,704286233,712799821,721310048,729813991,738315156,746813071,755305935,763794029,772276773,780756650,789230673,797703398,806169530,814633249,823092766,831548431,840000027,848450250,856895823,865335133,873772692,882206716}; // bitset<500000> b; // // ll solve3sub(ll n){ // int i; // ll s, k, res; // // if(n < 1000000){ // for(i=0;i n) break; // return i; // } // // s = n / 200000000; // if(s){ // res = memo[s-1]; // s *= 200000000; // } else { // res = ps; // s = 1000000; // } // // for(;;s+=1000000){ // b.set(); // for(i=1;;i++){ // k = (ll) p[i] * p[i] - s; // if(k >= 1000000) break; // if(k < 0) k += ((-k+p[i]-1) / p[i]) * p[i]; // if(k % 2 == 0) k += p[i]; // k /= 2; // while(k < 500000) b.reset(k), k += p[i]; // } // if(n-s < 1000000){ // for(i=1;i<=n-s;i+=2) res += b[i/2]; // break; // } // res += b.count(); // } // // return res; // } // // ll solve3(ll L, ll R){ // return solve3sub(2*R) - solve3sub(2*L) + solve3sub(R) - solve3sub(L-1); // } // // ll cntPrime(ll n, void *mem = wmem){ // int i, j, sn; // char *isp; // ll *s1, *s2, x, c = -1; // if(n <= 1) return 0; // if(n == 2) return 1; // // sn = Isqrt_f(n); // walloc1d(&s1, sn+1, &mem); // walloc1d(&s2, sn+1, &mem); // walloc1d(&isp, sn+1, &mem); // // s1[0] = 0; // rep(i,1,sn+1) s1[i] = i - 1; // rep(i,1,sn+1) s2[i] = n/i - 1; // rep(i,2,sn+1) isp[i] = 1; // // rep(i,2,sn+1) if(isp[i]){ // for(j=2*i;j<=sn;j+=i) isp[j] = 0; // c++; // // rep(j,1,sn+1){ // if((ll)i*i*j > n) break_continue; // x = n / j / i; // if(x <= sn) s2[j] -= s1[x] - c; // else s2[j] -= s2[i*j] - c; // } // rrep(j,(ll)i*i,sn+1){ // s1[j] -= s1[j/i] - c; // } // } // // return s2[1]; // } // // ll solve4(ll L, ll R){ // return cntPrime(2*R) - cntPrime(2*L) + cntPrime(R-1) - cntPrime(L-1); // } // // { // ll L, R, res; // L = llReader(1, 1d10, ' '); // R = llReader(L, 1d10, '\n'); // assert(getchar() == EOF); // // res = solve4(L,R); // wt(res); // return 0; // // int i, j; // for(i=2;i<2d7+1;i++) ppp[i] = 1; // for(i=2;i<2d7+1;i++) if(ppp[i]) for(j=2*i;j<2d7+1;j+=i) ppp[j] = 0; // // p[2] = 1; // for(i=3;i<1000000;i+=2) p[i] = 1; // for(i=3;i<1000;i+=2) if(p[i]) for(j=i*i;j<1000000;j+=i) p[j] = 0; // for(i=0;i<1000000;i++) if(p[i]) p[ps++] = i; // // if(1){ // ll L, R; // ll r1, r2, r3, r4; // Rand rnd; // // puts(""); // rep(L,1,30) rep(R,L,30){ // r1 = solve1(L,R); // r2 = solve2(L,R); // r3 = solve3(L,R); // r4 = solve4(L,R); // wt(L,R,":",r1,r2,r3,r4); // assert(r1==r2==r3==r4); // } // // rep(100){ // L = rnd.get(1LL, 1d10); // R = rnd.get(1LL, 1d10); // sortE(L,R); // r3 = solve3(L,R); // r4 = solve4(L,R); // wt(L,R,":",r3,r4); // assert(r3==r4); // } // } // // }