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Zbl 1215.11016
Harvey, David
A multimodular algorithm for computing Bernoulli numbers. (English)
[J] Math. Comput. 79, No. 272, 2361-2370 (2010). ISSN 0025-5718; ISSN 1088-6842/e

Summary: We describe an algorithm for computing Bernoulli numbers. Using a parallel implementation, we have computed $ B_k$ for $ k = 10^8$, a new record. Our method is to compute $ B_k$ modulo $ p$ for many small primes $ p$ and then reconstruct $ B_k$ via the Chinese Remainder Theorem. The asymptotic time complexity is $ O(k^2 \log^{2+\varepsilon} k)$, matching that of existing algorithms that exploit the relationship between $ B_k$ and the Riemann zeta function. Our implementation is significantly faster than several existing implementations of the zeta-function method.

MSC 2000:: *11B68 Bernoulli numbers, etc.
11Y60 Evaluation of constants

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