Prime gap graphs and the Riemann hypothesis

I will explain (as gently as possible) how the Riemann hypothesis implies that for every n>1 there exists a simple graph whose vertex degrees are 1 and the first n-1 prime gaps. Moreover, such graphs can be generated recursively by degree preserving steps. Joint work with P. L. Erdős, S. R. Kharel, P. Maga, T. R. Mezei, Z. Toroczkai.