On a Conjecture of Cai–Zhang–Shen for Figurate Primes

Junli Zhang and Pengcheng Niu ()
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Junli Zhang: School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an 710021, China
Pengcheng Niu: School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China

Mathematics, 2023, vol. 11, issue 6, 1-13

Abstract: 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, the Cardano formula for cubic equations, and the contradiction, we prove the conjecture.

Keywords: figurate prime; Cai–Zhang–Shen conjecture; extreme value problem; constraint (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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