4 ms·

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

by lacker 4y ago

kibwen 4y ago
Not true, that number is immortalized in this famous HN thread: https://news.ycombinator.com/item?id=35059068 https://news.ycombinator.com/item?id=35059068
- interestica 4y ago
  Agreed. https://news.ycombinator.com/item?id=35059068.385734874675783289473 https://news.ycombinator.com/item?id=35059068.38573487467578... is also great for obvious reasons.
Y_Y 4y ago
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.
- joshuaissac 4y ago
  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.
  - Y_Y 4y ago
    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.
travisjungroth 4y ago
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
- Dylan16807 4y ago
  Being able to tell that is interesting! It does not make the number interesting. There's so many equivalent smashes.
  - travisjungroth 4y ago
    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!
    - Dylan16807 4y ago
      > 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.
      - travisjungroth 4y ago
        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!

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

by lacker 4y ago

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

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

interestica 4y ago
Agreed. https://news.ycombinator.com/item?id=35059068.385734874675783289473 https://news.ycombinator.com/item?id=35059068.38573487467578... is also great for obvious reasons.

Y_Y 4y ago

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.

joshuaissac 4y ago
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.
- Y_Y 4y ago
  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.

travisjungroth 4y ago

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

Dylan16807 4y ago
Being able to tell that is interesting! It does not make the number interesting. There's so many equivalent smashes.
- travisjungroth 4y ago
  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!
  - Dylan16807 4y ago
    > 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.
    - travisjungroth 4y ago
      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!