Figurate primes and Hilbert's 8th problem
Tianxin Cai, Yong Zhang, Zhongyan Shen
TL;DR
This paper explores the connection between figurate primes and Hilbert's 8th problem using elliptic curves, proposing conjectures related to famous unsolved problems like Goldbach's and twin primes.
Contribution
It introduces new conjectures linking figurate primes with Hilbert's 8th problem and applies elliptic curve theory to Diophantine equations.
Findings
Proposes conjectures connecting figurate primes with classical unsolved problems.
Uses elliptic curves to analyze Diophantine equations involving figurate primes.
Suggests new avenues for research in number theory and prime distributions.
Abstract
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.
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Taxonomy
TopicsAnalytic Number Theory Research · Cryptography and Residue Arithmetic · Algebraic Geometry and Number Theory