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A Variation on Mills-Like Prime-Representing Functions
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László Tóth

Rue des Tanneurs 7

L-6790 Grevenmacher

Grand Duchy of Luxembourg

**Abstract:**

Mills showed that there exists a constant *A* such that
⌊ *A*^{3n} ⌋ is prime for
every positive integer *n*. Kuipers and Ansari generalized
this result to
⌊ *A*^{cn} ⌋
where *c* ∈ **R** and *c* ≥ 2.106.
The main contribution of this paper is a proof
that the function
⌈ *B*^{cn} ⌉
is also a prime-representing function, where
⌈ *X* ⌉
denotes the ceiling or least integer function. Moreover, the first 10
primes in the sequence generated in the case *c* = 3 are calculated.
Lastly, the value of
*B* is approximated to the first 5500 digits and is
shown to begin with 1.2405547052... .

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(Concerned with sequences
A051021
A051254.)

Received June 8 2017; revised versions received September 20 2017; September 26 2017.
Published in *Journal of Integer Sequences*, October 29 2017.

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