A New Error Analysis for Brun's Constant

Authors

Thomas R. Nicely

Document Type

Article

DOI

10.25778/84pa-ts78

Abstract

Enumeration of the twin primes, and the sum of their reciprocals, is extended to 3 x 10¹⁵, yielding the count π₂(3 x 10¹⁵) = 3310517800844. A more accurate estimate is obtained for Brun’s constant, B2 = 1.90216 05823 ± 0.00000 00008 . Error analysis is presented to support the contentioli that this estimate produces a 95 % confidence interval for B₂. In addition, published values of the count π(x) of primes, obtained previously by indirect means, are verified by direct coiiIit to x = 3 x 10¹⁵

Recommended Citation

Nicely, Thomas R. (2001) "A New Error Analysis for Brun's Constant," Virginia Journal of Science: Vol. 52: No. 1, Article 4.
DOI: 10.25778/84pa-ts78
Available at: https://digitalcommons.odu.edu/vjs/vol52/iss1/4