While I am studying the famous article [1], in English this is Andrew Granville and Greg Martin, Prime Number Races, The American Mathematical Monthly, vol. 113, (2006), I wondered what about a race of odd semiprimes.
A semiprime is a positive integer that is the product of two prime numbers (see the Wikipedia Semiprime or the article from the encyclopedia MathWorld).
As in the cited article we consider that our race the odd semiprimes separated in two teams, those semiprimes of the form $s=4n+1$ for some positive integer $m$, this is $s\equiv 1\text{ mod }4$ that are our Team 1
$$9,21,25,33,45,49,57,65,69,77,85,93,\ldots,$$
and those semiprimes of the form $s=4n+3$ for some positive integer $m$, that is $s\equiv 3\text{ mod }4$ are our Team 2
$$15 ,35, 39, 51, 55 ,63, 75, 87, 91 ,95, 99\ldots.$$ We denote the corresponding counting functions as $$\#\{\text{semiprimes }4n+1\leq x\}\tag{1}$$ and $$\#\{\text{semiprimes }4n+3\leq x\}.\tag{2}$$
Question. Is it possible to know which team will win the race? I am asking if it is possible to study in a similar way that shows the first section of the mentioned article our race of semiprimes, maybe it is possible to get a similar statement than Hardy's theorem about the difference of previous counting functions $(1)$ and $(2)$, or maybe one can to state a conjecture in the spirit of the conjecture due to Knapowski and Turán but now for the race of semiprimes of the form $4n+1$ versus $4n+3$. Many thanks.
I don't know if this problem is in the literature, feel free to refer the literature and I try to search and read it from the literature to know how does the race end.
References:
[1] Andrew Granville and Greg Martin, Carreras de números primos, La Gaceta de la RSME, Volumen 8, Número 1 (enero-abril, 2005).