I've been trying to solve Project Euler problem 123  semiprimes
A composite is a number containing at least 2 prime factors. For example, 15 = 3 * 5; 9 = 3 * 3; 12 = 2 * 2 * 3.
There are 10 composites below 30 containing precisely 2, not necessarily distinct, prime factors: 4, 6, 9, 10, 14, 15, 21, 22, 25, 26.
How many composite integers, n < 10^8, have precisely 2, not necessarily distinct, prime factors? 
At first I tried to make a very efficient algorithm, but it gave wrong answer. So I made a brute force algorithm to generate answer for small values of n and then use them to cross check my efficient algorithm and find bugs. I was pretty sure my brute force algorithm would work for all n, but sadly it didn't.
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//Semiprimes
#include<iostream>
#include<fstream>
#include<algorithm>
#include<eku\math\sqrt_uint.h>
using std::cout;
using std::cin;
using std::endl;
void init_pbf(unsigned* pbf,unsigned size)
//fills pbf with primes from a file containing 10^8 primes
{
std::ifstream ifile("E:\\PND\\1e+8.pb32",std::ios::binary);
if(!ifile.is_open()){std::cout<<"Err";return;}
ifile.read((char*)pbf,size*sizeof(unsigned));
}
int main()
{
unsigned i,j,n,size,sqrt_n;
unsigned long long count,prod;
unsigned* pbf;
// unsigned* lb;
cout<<"Enter pbf size: ";
cin>>size;
//Enter 10^8
pbf=new unsigned[size];
init_pbf(pbf,size);
while(true)
{
cout<<"Enter n: ";
cin>>n;
sqrt_n=eku::sqrt_uint<unsigned>(n).first;
count=0;
/*for(i=0;pbf[i]<=sqrt_n;++i)
{
lb=std::upper_bound(pbf,pbf+size,n/pbf[i])1;
count+=lbpbfi+1;
}*/
for(i=0;pbf[i]<=sqrt_n;++i)for(j=i;pbf[j]<=n;++j)
{
prod=pbf[i];
prod*=pbf[j];
if(prod>=n)break;
++count;
}
cout<<count<<endl;
}
return 0;
}
 
Then I found this OEIS page:
http://oeis.org/A066265
This sadly revealed the answer, but I used the values to cross check my brute force approach. It works for n = 10, 100, 1000, 10^4, 10^5, 10^6, 10^7, but not for 10^8. The answer my program displays is one more than the correct answer. I have no idea why this is happening.
The file <eku\math\sqrt_uint.h> is my own and contains a function to calculate square root of an integer. The answer is rounded down if the parameter is not a perfect square.
The file containing the list of primes has never betrayed me in any Project Euler problem before, so there is very little chance that the file is wrong.