One of my respected colleagues at Hewlett-Packard is a guy named Patrick Demichel. He’s one of the “titans“, having held various world records on the number of digits of π and things like that.

But a couple of weeks ago, he talked to me about something really intriguing. During a conference on high-performance computing, he told me about a number he had computed, and that even if he was not sure that the value was right, he considered it highly unlikely that anybody could prove him wrong, because there weren’t enough atoms in the universe to do so. How does that sound?

Well, it turns out that he was talking about the Skewes numbers. More specifically, he has computed the first Skewes number to be most probably equal to 1.397162914×10^{316}. See another reference in Wolfram’s MathWorld.

You can find the complete presentation of that research here. The general idea is that we have something that is extremely difficult to compute, so we compute it at reduced precision, skipping through large ranges of numbers. In doing so, we do a probabilistic estimate of the risk that we miss the right values. It’s really low, to the point that finding a counter example would take more computations than what can have been done in the entire universe since the Big Bang. However, we clearly have not tested all possible values (which would take even more power).

OK, in reality, this depends on the behavior of the Zeta function, more specifically on the Riemann hypothesis. So there is still an infinitesimal chance that all this huge computing power went to waste, and that 1.397162914×10^{316} is actually not the first Skewes number. Time will tell…

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## Published by Christophe de Dinechin

To the dismay of my beloved wife and kids, I still try to change the world. It's been hopelessly a work in progress for a few decades now…
I'm passionate about programming techniques and programming languages, interactive 3D, real-time computing, OS design, free software, physics research, religion, the meaning of life, and so much more (see http://c3d.github.io for a few links)…
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