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Nicely95

T. Nicely, "Enumeration to 10¹⁴ of the twin primes and Brun's constant," Virginia Journal of Science, 46:3 (1995) 195--204.  MR 97e:11014

Abstract: The count π₂(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 10¹⁴ , at intervals of 10⁹ . 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.

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