Corpus ID: 11630782

Determining Mills' Constant and a Note on Honaker's Problem

@article{Caldwell2005DeterminingMC,
  title={Determining Mills' Constant and a Note on Honaker's Problem},
  author={C. Caldwell and Y. Cheng},
  journal={arXiv: Number Theory},
  year={2005}
}
In 1947 Mills proved that there exists a constant A such that bA 3 n c is a prime for every positive integer n. Determining A requires determining an efiective Hoheisel type result on the primes in short intervals|though most books ignore this di‐culty. Under the Riemann Hypothesis, we show that there exists at least one prime between every pair of consecutive cubes and determine (given RH) that the least possible value of Mills’ constant A does begin with 1:3063778838. We calculate this value… Expand
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