5783

This number is a prime.

In graph theory, 5783 is the number of distinct simple, connected, 20-vertex, degree-3 graphs with a girth of at least 5. To understand this more fully, recall these graph theory definitions:

- A "simple" graph has no multiple edges or loops. 

- A "connected" graph has a path (succession of edges) between any two vertices. 

- The "degree" of a vertex is the number of edges connected to it, and the 
  degree of a graph is its highest vertex degree.

- A "cycle" is a path that starts and ends at the same vertex V and never 
  visits the same vertex twice (except for V). 

- The "girth" of a graph is the length (number of edges) of its shortest cycle.