  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 $f_1 =
2.9200509773...$ for generation of the complete sequence of primes with using
of a recursive relation for $f_n$ such that the floor function $\lfloor f_n
\rfloor = p_n$, where $p_n$ is the nth prime. Here I present the family of
constants $h_n (h_1 = 1.2148208055...)$ such that the ceiling function $\lceil
h_n \rceil = p_n$. The proposed recursive relation $h_n=\lceil h_n
\rceil(h_{n-1}-\lceil h_{n-1} \rceil+2)$ generates the sequence of all known
prime numbers. I also show that constants $h_n$ are irrational.
