Explicit bounds for prime gaps and graphic sequence

Abstract: A prime gap graph is defined to be a graph on $n$ vertices with respective degrees $1$ and the $n-1$ first prime gaps. In a recent paper of P. Erdős, G. Harcos, S. Kharel, P. Maga, T. Mezei, Z. Toroczkai, they proved that under RH, prime gap graphs exist for every $n$. Also they exist unconditionally for $n$ large enough. Moreover, it is possible to give an iterative construction of these graphs.

The ideas in this result lie between elementary number theory, graph theory and combinatorics. In this talk, I will explain how to obtain this result in its unconditional form, while trying to find explicitly how large $n$ should be to get a graphic sequence.

This talk is based on the aforementioned paper, and a joint work with Keshav Aggarwal.

Mathematics

Audience: researchers in the topic

Greek Algebra & Number Theory Seminar