Google Games
This morning I happened upon the Google Weblog. Apparently they've put up the following billboard on a busy northern California freeway:
Apparently those gnomes know exactly how my mind works. That's a carrot on the end of a stick which I cannot turn from. Fortunately, I had done a lot of musing with e while I was in Netmath. I'd even computed it to 50,000 digits.
Figuring out if a number is prime is easy; Fermat's Little Theorem does all the legwork for you1. I wrote a small program to do this while moving sequentially through blocks of 10 digits in e. But the gnomes at Google wouldn't let you off that easy; 10 digit numbers are too big for the data types most programming languages use. Languages like Java have a BigInteger built into the language but I found an open implementation for C# within a few seconds on Google. I will post my solution tommorow (I forgot it at work!).
There's also a cheat if you don't want to hassle yourself with primality, Fermat, or big numbers. You can move through 10 digit blocks and use a networking class to try and resolve the address. I put a version of that in my solution but it's what my brother and I would call "cheap styles."
Once you've solved that, the website is itself a problem involving e.
I will post a solution for this as well tomorrow, but it isn't horrible once you can determine what these numbers (each a pattern found in e) have in common with each other (hint: the square of 7).
It took my lunch hour from me but the solution took me to the congratulatory page from Google Labs. All this while I was thinking I had adult ADD because it was so hard to focus at work and yet I was able to lose myself completely in this problem. Good news, I guess.
1This works on smaller numbers - with big numbers estimation is involved. I put a javascript implementation of the theorem up so you can "view source" and see how simple it is for yourself.
9:50:43 PM 
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