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Jacob's Ladder: Prime numbers in 2d
- Source :
- Math. Comput. Appl. 2020, 25, 5
- Publication Year :
- 2017
-
Abstract
- 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) , being n the number of terms in the sequence.<br />Comment: 17 pages, 12 figures. v2: Accuracy improved, new results included and references added. v3: Slight clarifications, matches version accepted by journal
- Subjects :
- Mathematics - History and Overview
Subjects
Details
- Database :
- arXiv
- Journal :
- Math. Comput. Appl. 2020, 25, 5
- Publication Type :
- Report
- Accession number :
- edsarx.1801.01540
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.3390/mca25010005