Arbitrarily long strings of consecutive primes in special sets
Let F(x) be a function of the form ∑ri=1dixρi, where d1,…,dr∈R, 0≤ρ1<⋯<ρr, ρr∉Z, ρi∈R for 1≤i≤r and dr≠0. We prove that the sets of the form {n∈N:{F(n)}∈U} for any non-empty open set U⊂[0,1) contain arbitrarily long strings of consecutive primes.
Authors
- Félix Houde
- Maryna Manskova
- Yiqing Wang (ORCID: https://orcid.org/0009-0009-4016-4935)
- Sai Sanjeev Balakrishnan
- Vahagn Hovhannisyan
Institutions
- University of Wisconsin–Madison (US)
- Yerevan State University (AM)
- Graz University of Technology (AT)
- Yerevan State Linguistic University (AM)
- Concordia University (CA)
- University of California, Berkeley (US)
Publication Details
- Journal
- Acta Arithmetica
- Published
- 2025-09-24
- DOI
- https://doi.org/10.4064/aa240201-25-5
- Primary Topic
- Limits and Structures in Graph Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00