## Sunday, June 7, 2015

### 429 is an Astonishing Number

6/07/2015

I have three ideas about numbers.

First, I think every number has a purpose - otherwise why would a number exist?

Second, I think every number is interesting - even if we haven't yet found out what it's most interesting properties are.

And Third, I think some of the most interesting things about numbers start to occur when they start getting big.

Take 429 for example.  I looks kind of plain, and not very interesting.  But 429 is really an astonishing number.  If you add all of the integers from 4 to 29 you get a total of 429.

But it's not prime, it's not a square, or a cube.  It's not even he largest or the smallest astonishing number.

15 is the smallest astonishing number.   If you add all of the integers from 1 to 5 you get a total of 15 - kind of neat, isn't it.  Next is 27.  If you add all of the integers from 2 to 7 you get 27.

Some astonishing numbers work backwards - like 204.  If you add all of the integers from 20 (counting backwards) to 4 you get a total of 204.  And if you add all of the integers from 21 (counting backwards) to 6 you get a total of 216.

I don't think there is a "largest astonishing number", but the largest one I know about is 891,406,343,154,063.

I won't spoil the surprise by telling you more - you can figure it out.

Source: http://www.numbersaplenty.com/set/astonishing_number/

David