Geodesic
Prime numbers of the form [nc]
Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 237-254

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In 1953, Pjateckii ̆-S ̆apiro has proved that there are infinitely many primes of the form [n^c] for 1 [less than] c [less than] {12\over11} (with an asymptotic result). This range, which measures our progress in the technique of exponential sums, has been improved by many authors. In this paper we obtain 1 [less than] c\leq{243\over205}. 
Rivat, J.; Wu, J. Prime numbers of the form [nc]. Glasgow mathematical journal, Tome 43 (2001) no. 2, pp. 237-254. doi: 10.1017/S0017089501020080
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