TY - JOUR T1 - O rozložení prvočísel v okolí faktoriálů A1 - Čejchan, Antonín A1 - Křížek, Michal A1 - Somer, Lawrence JA - Obzory matematiky, fyziky a informatiky Y1 - 2022 VL - 51 IS - 2 SP - 14 EP - 22 SN - 1335-4981 N2 - The distribution of primes is quite irregular. We prove the following theorem which however allows some regularity: If a prime number p satisfies n! 1 < p < n! r^2 , where r is the smallest prime larger than a given natural number n, then p - n! is also a prime. We state a similar theorem for primes just below n! - 1. Further we prove similar statements also for the case when n! is replaced by q# which is the product of all primes not exceeding a prime q. ER -