The 14th Lanqiao Cup Competition Software Competition Final C/C++ University Group B Question B: Gemini Number

[Lanqiao Cup 2023 Country B] Number of Geminis

Test question B: Gemini number

【Problem Description】

If a positive integer $x$ can be expressed as$p^2\times q^2$ , where$p$、$q$ is a prime number and$p\ne q$ , then$x$ is
a "gemini number". Please calculate the interval$[2333,$How many "gemini numbers" are there in$23333333333333$$]\; ?$

Sieve of Ehrlich + brute force enumeration

#include<bits/stdc++.h>
using namespace std;
int main()
{
    
    
	int d=sqrt(23333333333333);
	cout<<d<<endl; //4830458
	
	vector<__int128> primes;
	vector<bool> st(5000010); 
	st[0]=st[1]=1;
	
	for(int i=2;i<=5000000;i++)
	{
    
    
		if(st[i]==0) primes.push_back(i);
		for(int j=0;j<primes.size()&&primes[j]<=5000000/i;j++)
		{
    
    
			st[primes[j]*i]=true;
			if(i%primes[j]==0) break;
		}
	}
	
	auto a=primes;
	int ans=0; 
	for(int i=0;i<a.size();i++)
		for(int j=i+1;j<a.size();j++)
		{
    
    
			if(a[i]*a[i]*a[j]*a[j]<2333) 
				continue;
			if(a[i]*a[i]*a[j]*a[j]>23333333333333) 
				break;
			ans++;
		}
	cout<<ans;//947293 
	
    return 0;
}