Registered: Nov 2003
Posts: 5

In the open problems and project paper there's a suggestion to:

"Characterize what numbers are common on the web."

I wrote a script to get going on this. It sends successive integers to Google and parses the reply to find out how many responses Google has by looking for the "of about" that's on the blue separator line.

I'm attaching a graph of the first ten thousand results. Notice the nested structure. n thousand has a lot of hits. n hundred somewhat less etc. Within each group there's a similar pattern with the 5 case doing better than it's peers.

There's one really large peak. Unsurprisingly it's at 2003.

I also noticed that these numbers aren't very stable. The graph I've included was generated in late August. I redid the run a couple of months later and everything was different in detail. I've even seen relatively large changes from one day to the next.

Two questions one could ask:
1) what is the biggest integer on the web
2) what is the smallest integer not on the web

(the first question comes from Stephen Wolfram. the second from Mitchel Resnick -- I'd guess that the first one is a recently discovered prime and that the second one has 8 digits)

Brian Silverman has attached this image:

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Registered: Dec 2003
Posts: 1

Brian:

I am here through a fluke of being distracted by the Wolfram site as part of looking for other stuff on Google.

This kind of problem seems to be reduced/cheapened once it has been posed: now all I gotta do is write something that continually places arbitrarily large/small integers on the web. :)

Not that that figure and your Googling effprt is not interesting. I can't make out the x axis, so I'm not sure what to make of the local peaks.

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Registered: Oct 2003
Posts: 2

I wonder if the integer first digit follows benford's law.

http://mathworld.wolfram.com/BenfordsLaw.html

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