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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home | Author index | Key index | Search ]
- CC2005
- C. Caldwell and Y. Cheng, "Determining Mills' constant and a note on Honaker's problem," J. Integer Seq., 8:4 (2005) Article 05.4.1, 9 pp. (electronic). Available from http://www.cs.uwaterloo.ca/journals/JIS/. MR2165330
Abstract:
In 1947 Mills proved that there exists a constant A such that ⌊ A3n ⌋ is a prime for every positive integer n. Determining A requires determining an effective Hoheisel type result on the primes in short intervals---though most books ignore this difficulty. 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 to 6850 decimal places by determining the associated primes to over 6000 digits and probable primes (PRPs) to over 60000 digits. We also apply the Cramér-Granville Conjecture to Honaker's problem in a related context.
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