Primes of the form [pc] and related questions

Much interest has been shown in determining the range of values of c for which the sequence [n] c contains infinitely many primes. The result is an elementary deduction from the prime number theorem, of course, of 0 c ≤l. In 1953, Piatetski–Shapiro [9] showed that for 1 c c (X) stands for the number of primes in the set {[n c ]n≤x} .