Prime values of a sparse polynomial sequence

2021/11/09 by Xiannan Li, Li, Xiannan
Computer Science · Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2111.05403

openalex publication_date 2021/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A distinguishing feature of certain intractable problems in prime number theory is the sparsity of the underlying sequence. Motivated by the general problem of finding primes in sparse polynomial sequences, we give an estimate for the number of primes of the shape x³ + 2y³ where y is small.

Citations

• On the difference between consecutive primes
• Prime Numbers in Short Intervals and a Generalized Vaughan Identity
• Primes represented by x3+2y3

Related

• On the distribution of sparse sequences in prime fields and applications
• On a sequence involving the prime numbers
• Prime polynomial values of linear functions in short intervals
• Polynomial Differences in the Primes
• Computing sparse multiples of polynomials