The 10^9-th Bernoulli number

This is the first published computation of the 10^9-th Bernoulli number. We provide the number as an XZ-compressed ASCII text file: first line numerator, second line numerator, encoded as decimals. A second file gives more “human-readable” information about this number, e.g. approximations of the fraction and the numerator (following the usual rounding rules) and the first and last digits of the numerator. The number was computed using a distributed version of Eberl and Lammich's verified implementation of Harvey's algorithm. The result was sanity-checked by comparing with the approximation obtained through the Riemann zeta function from Mathematica and by reducing it modulo a number of large primes and comparing the result to that obtained from running Harvey's algorithm (for a single modulus, without CRT, both the verified version by Eberl/Lammich and Harvey's original implementation). Note: In the previous version, the “human-readable” file contained typos that were introduced while creating it by hand. The big file containing the value of B(10^9) was correct. We have since built a more robust tool to generate these human-readable files automatically and updated the file in the new version.