# Unconditional Prime-Representing Functions, Following Mills

@article{Elsholtz2020UnconditionalPF, title={Unconditional Prime-Representing Functions, Following Mills}, author={Christian Elsholtz}, journal={The American Mathematical Monthly}, year={2020}, volume={127}, pages={639 - 642} }

Abstract Mills proved that there exists a real constant A > 1 such that for all the values are prime numbers. No explicit value of A is known, but assuming the Riemann hypothesis one can choose Here we give a first unconditional variant: is prime, where can be computed to millions of digits. Similarly, is prime, with

## 4 Citations

A Couple of Transcendental Prime-Representing Constants

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Abstract It is well known that the arithmetic nature of Mills’ prime-representing constant is uncertain: we do not know if Mills’ constant is a rational or irrational number. In the case of other…

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Let (ck)k=1∞$(c_k)_{k=1}^\infty$ be a sequence of positive integers. We investigate the set of A>1$A>1$ such that the integer part of Ac1⋯ck$A^{c_1\cdots c_k}$ is always a prime number for every…

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