Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 150 / 4 / a

Let $⟨x⟩$ denote the distance from $x$ to the nearest prime power. For $x\ge 2$ not an integer and $T\ge 2$, the truncated Riemann–von Mangoldt explicit formula isZeros are counted with multiplicity. The constant term comes from $s=0$, the logarithm collects the trivial zeros $-2,-4,\dots$, and the finite sum contains the nontrivial zeros. Enlarging the implied constant covers $1\le T<2$.