On remarkable properties of primes near factorials and primorials

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00551638" target="_blank" >RIV/67985840:_____/22:00551638 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68378271:_____/22:00551638

Výsledek na webu

<a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Krizek/krizek3.html" target="_blank" >https://cs.uwaterloo.ca/journals/JIS/VOL25/Krizek/krizek3.html</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On remarkable properties of primes near factorials and primorials

Popis výsledku v původním jazyce

The distribution of primes is quite irregular. However, it is conjectured that if p is the smallest prime greater than n! + 1, then p – n! is also prime. We give a sufficient condition that guarantees when this conjecture is true. In particular, we prove that if a prime number p satisfies n! + 1 > p > n! + r2, where r is the smallest prime larger than a given natural number n, then p – n! is also a prime. Similarly we treat another conjecture: If p is the largest prime smaller than n! – 1, then n! – p is also prime. Then we establish further sufficient conditions also for the case when n! is replaced by q#, which is the product of all primes not exceeding the prime q.

Název v anglickém jazyce

On remarkable properties of primes near factorials and primorials

Popis výsledku anglicky

The distribution of primes is quite irregular. However, it is conjectured that if p is the smallest prime greater than n! + 1, then p – n! is also prime. We give a sufficient condition that guarantees when this conjecture is true. In particular, we prove that if a prime number p satisfies n! + 1 > p > n! + r2, where r is the smallest prime larger than a given natural number n, then p – n! is also a prime. Similarly we treat another conjecture: If p is the largest prime smaller than n! – 1, then n! – p is also prime. Then we establish further sufficient conditions also for the case when n! is replaced by q#, which is the product of all primes not exceeding the prime q.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

10101 - Pure mathematics

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Integer Sequences

ISSN

1530-7638

e-ISSN

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Svazek periodika

25

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

11

Strana od-do

22.1.4

Kód UT WoS článku

000780207300002

EID výsledku v databázi Scopus

2-s2.0-85123451614