On remarkable properties of primes near factorials and primorials

Result code in 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>
Alternative codes found
RIV/68378271:_____/22:00551638
Result on the web
<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
—

Result language
angličtina
Original language name
On remarkable properties of primes near factorials and primorials
Original language description
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.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)