Prime-representing functions

: Matomäki Kaisa

Publisher: SPRINGER

: 2010

: Acta Mathematica Hungarica

: ACTA MATHEMATICA HUNGARICA

: ACTA MATH HUNG

: 4

: 128

: 4

: 307

: 314

: 8

: 0236-5294

DOI: https://doi.org/10.1007/s10474-010-9191-x

We construct prime-representing functions. In particular we show that there exist real numbers alpha > 1 such that aOE alpha (2) (n) aOE parts per thousand is prime for all n a a"center dot. Indeed the set consisting of such numbers alpha has the cardinality of the continuum.