  A conjecture of Cai-Zhang-Shen for figurate primes says that every integer
$k>1$ is the sum of two figurate primes. In this paper we give an equivalent
proposition to the conjecture. By considering extreme value problems with
constraints about the conjecture in the cases of odd and even integers and
using the method of Lagrange multipliers, Cardano formula for cubic equations
and the contradiction, we prove the conjecture.
