Almost primes in short intervals (Q5894127)

The author proves that there exists \(x_0>0\) such that \[ |\{x-x^{\frac{101}{232}}<n\leq x:\Omega(n)\leq 2\}|\geq 0.0006\frac{x^{\frac{101}{232}}}{\log x} \] for \(x\geq x_0\), where \(\Omega(n)\) denotes the number of all prime factors of \(n\) counted with multiplicity.