2023/11/22 by Anand Bhardwaj, Bhardwaj, Anand, Luisa Degen +5
Engineering · Mathematics · #11A41 #11B50 #11N13 #11P32 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2311.13375
openalex publication_date 2023/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If p is prime, a sequence of prime numbers \p, 2p+1, 4p+3,...,2n-1(p+1)-1\ is called a Cunningham chain. These are finite sequences of prime numbers, for which each element but the last is a Sophie Germain prime. It is conjectured that there are arbitrarily large such Cunningham chains, and these chains form an essential part of the study of Sophie Germain primes. In this paper, we aim to significantly improve existing bounds for the length of Cunningham chains by considering their behaviour in the framework of what we will define as rogueness.