最快素数模板

'''

#includeusing namespace std;

typedef long long LL;

const int N = 5e6 + 2;

bool np[N];

int prime[N], pi[N];

int getprime() {

int cnt = 0;

np[0] = np[1] = true;

pi[0] = pi[1] = 0;

for(int i = 2; i < N; ++i) {

if(!np[i]) prime[++cnt] = i;

pi[i] = cnt;

for(int j = 1; j <= cnt && i * prime[j] < N; ++j) {

np[i * prime[j]] = true;

if(i % prime[j] == 0)  break;

}

}

return cnt;

}

const int M = 7;

const int PM = 2 * 3 * 5 * 7 * 11 * 13 * 17;

int phi[PM + 1][M + 1], sz[M + 1];

void init() {

getprime();

sz[0] = 1;

for(int i = 0; i <= PM; ++i)  phi[i][0] = i;

for(int i = 1; i <= M; ++i) {

sz[i] = prime[i] * sz[i - 1];

for(int j = 1; j <= PM; ++j) {

phi[j][i] = phi[j][i - 1] - phi[j / prime[i]][i - 1];

}

}

}

int sqrt2(LL x) {

LL r = (LL)sqrt(x - 0.1);

while(r * r <= x)  ++r;

return int(r - 1);

}

int sqrt3(LL x) {

LL r = (LL)cbrt(x - 0.1);

while(r * r * r <= x)  ++r;

return int(r - 1);

}

LL getphi(LL x, int s) {

if(s == 0)  return x;

if(s <= M)  return phi[x % sz[s]][s] + (x / sz[s]) * phi[sz[s]][s];

if(x <= prime[s]*prime[s])  return pi[x] - s + 1;

if(x <= prime[s]*prime[s]*prime[s] && x < N) {

int s2x = pi[sqrt2(x)];

LL ans = pi[x] - (s2x + s - 2) * (s2x - s + 1) / 2;

for(int i = s + 1; i <= s2x; ++i) {

ans += pi[x / prime[i]];

}

return ans;

}

return getphi(x, s - 1) - getphi(x / prime[s], s - 1);

}

LL getpi(LL x) {

if(x < N)  return pi[x];

LL ans = getphi(x, pi[sqrt3(x)]) + pi[sqrt3(x)] - 1;

for(int i = pi[sqrt3(x)] + 1, ed = pi[sqrt2(x)]; i <= ed; ++i) {

ans -= getpi(x / prime[i]) - i + 1;

}

return ans;

}

LL lehmer_pi(LL x) {

if(x < N)  return pi[x];

int a = (int)lehmer_pi(sqrt2(sqrt2(x)));

int b = (int)lehmer_pi(sqrt2(x));

int c = (int)lehmer_pi(sqrt3(x));

LL sum = getphi(x, a) + LL(b + a - 2) * (b - a + 1) / 2;

for (int i = a + 1; i <= b; i++) {

LL w = x / prime[i];

sum -= lehmer_pi(w);

if (i > c) continue;

LL lim = lehmer_pi(sqrt2(w));

for (int j = i; j <= lim; j++) {

sum -= lehmer_pi(w / prime[j]) - (j - 1);

}

}

return sum;

}

int main() {

ios::sync_with_stdio(false);

init();

LL n;

while(~scanf("%lld", &n)) {

printf("%lld\n", lehmer_pi(n));

}

return 0;

}

'''