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Open AccessFeature PaperArticle

Jacob’s Ladder: Prime Numbers in 2D

1
Advanced Materials Group, Department of Control Engineering, Czech Technical University in Prague, Karlovo Náměstí 13, 2 Prague, Czech Republic
2
Euskal Herriko Unibertsitatea, Universidad del País Vasco, Barrio Sarriena, s/n 48940 Leioa, Spain
3
Science Institute, University of Iceland, Dunhaga 3, 107 Reykjavík, Iceland
*
Author to whom correspondence should be addressed.
Math. Comput. Appl. 2020, 25(1), 5; https://doi.org/10.3390/mca25010005
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.

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