Next Article in Journal
Acknowledgement to Reviewers of MCA in 2019
Previous Article in Journal
Cost Efficiency Evaluation Based on a Data Envelopment Analysis Approach by Considering Undesirable Outputs on the Basis of the Semi-Disposability Assumption
Open AccessFeature PaperArticle

Jacob’s Ladder: Prime Numbers in 2D

Advanced Materials Group, Department of Control Engineering, Czech Technical University in Prague, Karlovo Náměstí 13, 2 Prague, Czech Republic
Euskal Herriko Unibertsitatea, Universidad del País Vasco, Barrio Sarriena, s/n 48940 Leioa, Spain
Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavík, Iceland
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2020, 25(1), 5;
Received: 17 December 2019 / Revised: 7 January 2020 / Accepted: 8 January 2020 / Published: 11 January 2020
(This article belongs to the Section Natural Sciences)
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.
Keywords: prime numbers; number theory; number sequences prime numbers; number theory; number sequences
MDPI and ACS Style

Fraile, A.; Martínez, R.; Fernández, D. Jacob’s Ladder: Prime Numbers in 2D. Math. Comput. Appl. 2020, 25, 5.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop