Figurate primes and Hilbert's 8th problem
  In this paper, by using the theory of elliptic curves, we discuss several Diophantine equations related with the so-called figurate primes. Meanwhile, we raise several conjectures related with figurate primes and Hilbert's 8th problem, including Goldbach's conjecture, twin primes conjecture and Catalan's conjecture as well. 
Tianxin Cai, Yong Zhang and Zhongyan Shen
math.NT