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

Included in

Mathematics Commons