On remarkable properties of primes near factorials and primorials

0551638 - MÚ 2023 RIV CA eng J - Článek v odborném periodiku
Čejchan, Antonín - Křížek, Michal - Somer, L.
On remarkable properties of primes near factorials and primorials.
Journal of Integer Sequences. Roč. 25, č. 1 (2022), č. článku 22.1.4. ISSN 1530-7638
Institucionální podpora: RVO:67985840 ; RVO:68378271
Klíčová slova: factorial prime * Euclidean prime * primorial prime * Fortunate number
Obor OECD: Pure mathematics; Pure mathematics (FZU-D)
Impakt faktor: 0.5, rok: 2022
Způsob publikování: Open access
https://cs.uwaterloo.ca/journals/JIS/VOL25/Krizek/krizek3.html

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.
Trvalý link: http://hdl.handle.net/11104/0326880