5 problems

Let ${\mathcal{A}}$ be a primitive Apollonian circle packing. Let $S_{\mathcal{A}}$ be the set of missing curvatures that do not lie in any of the quadratic or quartic obstruction…

Let $\mathcal P$ be a bounded primitive integral Apollonian packing. Define … Here $N_{\mathcal P}(T)$ denotes the relevant circle-counting function. Fuchs–Sanden conjecture. As…

Kissing-prime counting conjecture. As $x\to\infty$,

Prime-curvature counting conjecture. As $x\to\infty$,

Local-to-global principle for Apollonian circle packings. There exists $X_P\in\mathbb Z$ such that every integer $x>X_P$ whose residue modulo $24$ lies in $P_{24}$ is the curvature…