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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 ]
 Nicely95
 T. Nicely, "Enumeration to 10^{14} of the twin primes and Brun's constant," Virginia Journal of Science, 46:3 (1995) 195204. MR 97e:11014
Abstract:
The count π_{2}(x) of the number of twin prime pairs ≤ x, as well as the count π(x) of the number of primes ≤ x, was tabulated by means of a computer search for values of x up to 10^{14} , at intervals of 10^{9} . The floating point sum of the reciprocals was also calculated, resulting in an improved estimate for Brun's constant of 1.9021605778, with a standard deviation of 2.1 × 10^{9} . An algorithm for estimating the standard deviation of such calculations is described. In the course of the computation a flaw was discovered in the hardware divider of the floating point unit of Intel Corporation's Pentium microprocessor.
[Available at http://www.trnicely.net/index.html]
