| Virginia
Journal of Science.
2001. Vol 52 (1) : 45-55 |
|
A New Error Analysis for Brun’s Constant Thomas R. Nicely, 1113 Dandridge Drive, Lynchburg, Virginia 24501-2231 USA 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 |