THE VIRGINIA ACADEMY OF SCIENCE
Virginia Journal of Science


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