A multimodular algorithm for computing Bernoulli numbers

Paper

Preprint is here.

Data

The 10,000,000-th Bernoulli number

• The denominator of B_10,000,000 is 9601480183016524970884020224910.
• Download the rational number B_10,000,000 as a Sage object (24MB).
• Download the numerator of B_10,000,000 in decimal as plain text (24MB).
• The value may be verified against Pavlyk's computation (see also this blog post).

The 31,622,776-th Bernoulli number

• The denominator of B_31,622,776 is 369037807590.
• Download the rational number B_31,622,776 as a Sage object (83MB).
• Download the numerator of B_31,622,776 in decimal as plain text (81MB).

The 100,000,000-th Bernoulli number

• The denominator of B_100,000,000 is 394815332706046542049668428841497001870.
• Download the rational number B_100,000,000 as a Sage object (284MB).
• Download the numerator of B_100,000,000 in decimal as plain text (278MB).

Code

I implemented the algorithm described in the paper in a C++ package called bernmm. It depends on GMP and NTL.

The code has been submitted for review for inclusion in Sage.

It will also be released soon as a separate package. Watch this space.