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lacker

The larger numbers get, the more boring they are. 385734874675783289473 is really boring.

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Not true, that number is immortalized in this famous HN thread: https://news.ycombinator.com/item?id=35059068

Agreed. https://news.ycombinator.com/item?id=35059068.38573487467578... is also great for obvious reasons.

It's interesting that you can tell this is a number row smash. Here's a histogram of frequency.

          X   
      X   XX  
      XX  XX  
      XXX XX  
     XXXXXXXX 
    1234567890

Being able to tell that is interesting! It does not make the number interesting. There's so many equivalent smashes.

If we're going to use interesting in the sense in the article, that just means it has some attribute. We could formalize keyboard smash and this number would have that. If it's interesting in the common sense, then it's subjective. I found this number interesting enough to spend a few minutes on it, which is more than I give most numbers!

> some attribute

More than that. Every number is either even or odd! Super common attributes don't do enough.

> I found this number interesting enough to spend a few minutes on it, which is more than I give most numbers!

I would say you didn't find the number interesting, you found the context interesting. There are billions of similar numbers that could have gone in the same slot and you would have spent the same effort on them. But if you were set free to look for interesting numbers, without being fed this one, you never would have glanced at it. And more specifically, this is a context that would basically never produce the same number again; it's not a sequence with a generator.

The more we keep talking about it, the more interesting I find this number. It seems to have quite the ability to generate discussion. It may be the least boring number!

Let's imagine we have a ton of people try to come up with interesting numbers.

Half of them try this keysmash method, and half of them try to come up with numbers without such randomness.

Then we have them each vote for a number they find interesting.

In that case, numbers like the above will get one vote. Lots of other numbers in these sequences will have tens, hundreds, thousands of votes.

Are the votes wrong? Is your number really the most interesting? Is it even the most interesting number between n-10 and n+10?

Throwing out half the resumes you get won't help you pick a candidate with better luck. Happening to randomly generate a number once doesn't make it interesting.

Nothing in this discussion is specific to that number. All the interestingness of this discussion should be split trillions of ways across all the similar keysmash numbers.

Calling it the least boring number was a joke, really. I do maintain two points seriously. First, that the digit frequency in this number reveals how it was generated and that characteristic lifts it off the floor of "least interesting numbers". Yes, there are a lot of numbers in this keyboard smash group. There are also a lot of primes. Second, I am going to give some credit to this number, 385734874675783289473. You can come up with a hypothetical, describe what might have happened in other universes. But, that's not what actually happened. Not all of the interestingness should be split because only one of those numbers actually showed up in this discussion in this universe. There's something unromantic about forgetting that, like a man sending a small anniversary present to every woman he went to college with because maybe he'd have ended up marrying any of them.

Well, the people you meet only exist in this one lifetime. But the numbers themselves transcend that. I think it's okay to attach a tiny bit of significance to a number that happens to be randomly generated, but I don't think it's enough to move a number up to "interesting" unless it was right on the edge.

Brilliant! You are correct sir. Sometimes HN delivers ;-)

Its sum of divisors is 385735449676045680000, very close to the original number. In base ten that shares the first five digits with the number itself. It's also small since the expected value is the number itself times π²/6, whereas our sum of divisors is slightly less than the original number. This is probably due to its only having three prime factors, all multiplicity 1. That's unusual too but estimating what we would expect is awkward.

edit: I should add that all of this was well known to Ramanujan, with whom I share a birthday. He famously was able to refute the uninterestingness of 1729.

How did you figure out all of that? Surely, you don't mean that Ramanujan knew about 385734874675783289473 because the sibling comment shows that it was keyboard-smashed.

Whatever the number theory equivalent of keyboard mashing is. I just checked a few typical functions and that one seemed interesting. Ramanujan wrote his thesis (equivalent) on highly composite numbers and studied things like the "divisor functions" related to summing (powers of) a number's divisors. I'd almost be ready to say he wouldn't have had anything to say about Lacker's Number, but then he was responsible for quite a few results which he had no reasonable way of knowing, given the knowledge available.

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