  Dummit, Granville and Kisilevsky have recently shown that the proportion of
semiprimes (products of two primes) not exceeding a given $x$, whose factors
are congruent to $3$ modulo $4$, is more than a quarter when $x$ is
sufficiently large. They have also conjectured that this holds from the very
beginning, that is, for all $x \geq 9$. We give a proof for $x\geq 10^{21}$ via
an explicit approach based on their work. Together with their data for the
remaining $x$, this results in a full proof of the conjecture. Our method
consists of techniques with cancellations of sums over primes with different
remainders. We also rely on classical estimates for prime counting functions,
as well as on very recent explicit improvements by Bennet, Martin, O'Bryant and
Rechnitzer, which have wide applications in essentially any setting involving
estimations of sums over primes.
