| Summary: | A conjecture of Cai–Zhang–Shen for figurate primes says that every integer <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula> 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, the Cardano formula for cubic equations, and the contradiction, we prove the conjecture.
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