An image of a man pointing to mathematic formulas.

9th Dedekind Number Unveiled

The 8th Dedekind number was found in 1991.


Lennart Van Hirtum’s master’s thesis project at KU Leuven morphed into a triumphant breakthrough. The one-time computer science student, now a research associate at Paderborn University, embarked on a quest to decode the 9th Dedekind number. This math enigma, a pursuit for scholars since 1991, has now been cracked.

The achievement puts Van Hirtum and his colleagues in an exclusive league. The series’ early numbers were discovered by notable figures such as Richard Dedekind, Randolph Church, and Morgan Ward. Van Hirtum reflects, “Solving D(9) was a daunting challenge, its feasibility uncertain for 32 years.”

From the 8th to the 9th Dedekind Number: A Journey in Computation

The 8th Dedekind number was found in 1991, utilizing the era’s most potent supercomputer, the Cray 2. Inspired by this, Van Hirtum believed that computing the 9th number should be feasible with today’s robust supercomputers.

Dedekind numbers relate to monotone Boolean functions. Van Hirtum likens this to a game with an n-dimensional cube. The objective: count the unique red-white intersections. “This task quickly creates enormous numbers; D(8) already has 23 digits,” he says.


Unraveling D(9): A Game of Massive Numbers

To comprehend the complexity of Dedekind numbers, consider the chess game legend. A game board filled following the inventor’s grain-doubling request results in a 20-digit number, still less than D(8).

To uncover D(9), Van Hirtum and his team used a method devised by Patrick De Causmaecker, the P-coefficient formula. Despite its power, it quickly escalates in computational time. “What takes eight minutes for D(8) would need hundreds of thousands of years for D(9),” Van Hirtum explains.

Overcoming Computational Barriers

The key hurdle is the formula’s rapid term growth. Using symmetries in the formula, the team reduced the terms to ‘only’ 5.5×10^18, a number achievable by modern supercomputers.


Noctua 2, based at the Paderborn Center for Parallel Computing, possessed the essential FPGA system. “We wanted to support this moonshot project,” says Prof. Dr. Christian Plessl, head of PC2. After five months of computation, the team made the breakthrough on March 8. They revealed the 42-digit 9th Dedekind number: 286386577668298411128469151667598498812366.

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Written by Ivan Petricevic

I've been writing passionately about ancient civilizations, history, alien life, and various other subjects for more than eight years. You may have seen me appear on Discovery Channel's What On Earth series, History Channel's Ancient Aliens, and Gaia's Ancient Civilizations among others.

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