Jacob’s Ladder: Prime Numbers in 2D

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00336943" target="_blank" >RIV/68407700:21230/20:00336943 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.3390/mca25010005" target="_blank" >https://doi.org/10.3390/mca25010005</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/mca25010005" target="_blank" >10.3390/mca25010005</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Jacob’s Ladder: Prime Numbers in 2D

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Jacob’s Ladder: Prime Numbers in 2D

Popis výsledku anglicky

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.

Druh

J_ost - Ostatní články v recenzovaných periodicích

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematical and Computational Applications

ISSN

1300-686X

e-ISSN

2297-8747

Svazek periodika

25

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

17

Strana od-do

—

Kód UT WoS článku

000524361400007

EID výsledku v databázi Scopus

2-s2.0-85089761523