Primes of the Form [nc] Original Research Article

A lower bound for πc(x), the number of primes of the form [nc] in [1, x], is given: πc(x) much greater-than x/log x. The significant point here is the longer range of c than formerly, namely 1 < c < image. The sieve method employed is that used by one of the authors in the study of fractional parts of αp, p prime (G. Harman, 1983, J. London Math. Soc.27, 9-18).