The number of rationals determined by large sets of sifted integers

We prove that the number of fractions $$h_1/h_2$$ integers $$h_1,h_2$$ a subset $$\mathcal {A}\subset \mathcal {H}\cap [1,X]$$ is at least $$ \alpha X/(\log X)^{3/2}$$ , where {H}$$ set $$p-1$$ p being prime such $$p+1$$ sum two coprime squares. So, this $$\gg _\varepsilon ^{1+\varepsilon }|\mathcal {A}|^2$$ $$\varepsilon any positive real number. take opportunity to describe geometrical view sieve and its usage study integer sequences.