2018/01/31 by Alberto Fraile, Roberto Martinez, Roberto Martínez +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Field (mathematics) #Prime (order theory) #Prime number #Representation (politics) #Sequence (biology) #Simple (philosophy) #Variety (cybernetics) #math.HO
paper · pdf · doi:10.3390/mca25010005
published in Mathematical and Computational Applications 25(1), 5 (Multidisciplinary Digital Publishing Institute) · 17 pages, 12 figures. v2: Accuracy improved, new results included and references added. v3: Slight clarifications, matches version accepted by journal
openalex created_date 2018/01/12 · openalex publication_date 2020/01/11 · arxiv created 2020/02/02 · arxiv updated 2020/02/04 · openalex updated_date 2026/08/05
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense variety of problems. In this work, we present a simple representation of prime numbers in two dimensions that allows us to formulate a number of conjectures that may lead to important avenues in the field of research on prime numbers. In particular, although the zeroes in our representation grow in a somewhat erratic, hardly predictable way, the gaps between them present a remarkable and intriguing property: a clear exponential decay in the frequency of gaps vs. gap size. The smaller the gaps, the more frequently they appear. Additionally, the sequence of zeroes, despite being non-consecutive numbers, contains a number of primes approximately equal to n / log n , n being the number of terms in the sequence.