Prime Eyes: An Observation of Prime Constellations in Grid Arrays

Abstract: This paper explores a special number-theoretic structure arising when natural numbers are arranged in a 7-column grid—namely, center numbers completely surrounded by four adjacent primes. We borrow the Go term “Eye” to name this phenomenon, reveal the modular arithmetic necessity (center numbers are almost exclusively multiples of 30), and identify its connection to Prime Constellations. Finally, the potential infinity of this sequence is discussed using the Hardy-Littlewood conjecture.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-28
DOI
https://doi.org/10.5281/zenodo.23733279
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Prime Eyes: An Observation of Prime Constellations in Grid Arrays

Jingtao Li
3 links
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Prime Eyes: An Observation of Prime Constellations in Grid Arrays

Jingtao Li
preprint en

Abstract

Abstract: This paper explores a special number-theoretic structure arising when natural numbers are arranged in a 7-column grid—namely, center numbers completely surrounded by four adjacent primes. We borrow the Go term “Eye” to name this phenomenon, reveal the modular arithmetic necessity (center numbers are almost exclusively multiples of 30), and identify its connection to Prime Constellations. Finally, the potential infinity of this sequence is discussed using the Hardy-Littlewood conjecture.

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Prime Eyes: An Observation of Prime Constellations in Grid Arrays — Jingtao Li · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS