The Piatetski-Shapiro sequences are of the form $[n^c]$, which is an intermediate problem of the conjecture that there exist infinitely many primes of the form $n^2+1$. In this talk, I will introduce the classical results of this topic. I will also show our recent theorem about the infinity of the primes in the intersection of a Piatetski-Shapiro sequence and multiple Beatty sequences with a sketch of our proof. 

海报