
The number 3608528850368400786036725 - wglb
http://www.blog.republicofmath.com/the-number-3608528850368400786036725/
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jkrems
I'm a little confused - why is this attributed to a recent blog post/tweet?
The number was part of the original wikipedia page on "Polydivisible number",
published in 2003[1]. Am I missing something?

P.S.: Just to clarify - it's an interesting problem. But the wording ("the
Vitale property" / "Ben announced") seems to suggest there is something
special about this not covered by polydivisible numbers.

[1]
[https://en.wikipedia.org/w/index.php?title=Polydivisible_num...](https://en.wikipedia.org/w/index.php?title=Polydivisible_number&oldid=1851396)

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ars
It's just a mistake. The author thought he found something new, not realizing
it had been found before.

There is an addendum at the bottom of the article mentioning that.

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chx
Ben posted this on February 20, 2015 (and this link is up unlike the one in
the original):
[https://benvitalenum3ers.wordpress.com/2015/02/20/num3er-360...](https://benvitalenum3ers.wordpress.com/2015/02/20/num3er-3608528850368400786036725/)
Also, it's the longest such number and the only 25 digit one. This
[https://www.reddit.com/r/math/comments/2wl55r/fun_with_numbe...](https://www.reddit.com/r/math/comments/2wl55r/fun_with_numbers_3608528850368400786036725/corx62s)
reddit thread gives you code to check.

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hirak99
Here's IPython equivalent.

[http://nbviewer.ipython.org/gist/hirak99/e7902bd49454cbc23bc...](http://nbviewer.ipython.org/gist/hirak99/e7902bd49454cbc23bca)

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gberger
Thanks. Mathematica is indecipherable to me.

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mojotoad
Interestingly, in hexadecimal there end up being three largest numbers of
length 39:

    
    
      0x34e4a468166cd8604ec0f8106ab4326098286cf
      0xaa44ce207c78fc30003c3cc0d8382e2078d07ef
      0xfae06678c2e884607eb8b4e0b0a0f0603420342

~~~
madcaptenor
You'd expect longer numbers in larger bases. The estimate at Wikipedia
([https://en.wikipedia.org/wiki/Polydivisible_number#How_many_...](https://en.wikipedia.org/wiki/Polydivisible_number#How_many_polydivisible_numbers_are_there.3F))
can be generalized: let F_k(n) be the number of n-digit polydivisible numbers
in base k. Then F_k(n) ~ (k-1) * k^(n-1) / n!. This gets bigger as n increases
up to n = k, then it gets smaller. If I'm doing the asymptotics right you have
F_k(ek) approximately equal to 1 - so in base k the largest polydivisible
number should have about ek digits.

The length of the longest polydivisible number in base k is in the OEIS
([http://oeis.org/A109783](http://oeis.org/A109783)) along with this
conjecture.

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rokhayakebe
For those sharing mathematical or other scientific facts it would be helpful
to give the layman a short explanation of why the topic is important.

~~~
chx
It isn't. But this is what makes mathematics so full of wonders, literally.
You start out with the really simple Peano axioms so that you can do
elementary counting and somehow it follows that the largest such number
happens to be 25 digits long and this particular number. It's the kind of
thing where you revert to a three year old and ask: Why? Why? Why?

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Vintila
This would make a good Project Euler problem.

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Hanua
this number looks pure beautiful XD I wonder about the value of polydivisble
numbers written in digits different than 10 XD . and if there was any further
algorithm to be found within it

