2020/12/25 by Weinstein, I. A.
#11A41 #11N32 #FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2101.00094
The analysis of regularities and randomness in the distribution of prime numbers remains at the research frontiers for many generations of mathematicians from different groups and topical fields. In 2019 D. Fridman et al. (Am. Math. Mon. 2019, 126:1, 70-73) have suggested the constant f1 = 2.9200509773... for generation of the complete sequence of primes with using of a recursive relation for fn such that the floor function \lfloor fn \rfloor = pn, where pn is the nth prime. Here I present the family of constants hn (h1 = 1.2148208055...) such that the ceiling function \lceil hn \rceil = pn. The proposed recursive relation hn=\lceil hn \rceil(hn-1-\lceil hn-1 \rceil+2) generates the sequence of all known prime numbers. I also show that constants hn are irrational.