## Q&A: Numerous Numbers

Steve D. wrote us to say:

I was listening to another podcast and they misread the copy and ended up

saying “What is the most numerous number?”. Well, what IS the most numerous number?

This is really a fascinating question! Have you ever wondered, for example, why there are **7** of so many things:

- 7 wonders of the ancient world
- 7 mortal sins
- 7 stars in the big dipper
- 7 days of the week
- 7 dwarves
- 7 brides for 7 brothers
- 7 items on this list

Really, it’s not that big of a mystery. The fact is, small numbers are very useful, and get called upon a lot. But there aren’t that many of them to go around.

Hence, the **First Strong Law of Small Numbers**: *There aren’t enough small numbers to meet the many demands placed upon them! *

The most numerous numbers, in a sense then, are the small ones. Google searches seem to confirm this:

- 1, 2, 3, 4, … (several billion hits each)
- 78, 122, 157, … (several hundreds of millions of hits each)
- 12122…(millions of hits)
- 1278232… (hundreds of hits)

Lotsa fun can be had in this way… With a little fishing, you can find some ridiculously large numbers with more hits than they deserve, but the principle is clear.

This same principle, incidentally, explains why, for example, the Golden Ratio appears in so many settings. There’s nothing really that mystical about it. The Golden Ratio is a root of the polynomial x^{2}-x-1=0. Roots of polynomials come up all over the place, in countless applications. And just as small numbers are in great demand, roots of *simple* polynomials will appear over and over again.

The Golden Ratio is just about the simplest non-integer root possible, and so, of course, shows up endlessly.

**Challenge Question** I’m kind of curious now: What is the smallest counting number that is NOT on the web?

210210876 was not on the web until just now, according to Google. Internet history has just been made!! But I’m sure you can find something smaller…

## kraDen said,

June 11, 2007 at 4:29 am

Hi,

I’ve found an 8 digit number that does not appear on the internet

So as not to disqualify it by listing it I will list its factorization

2x2x1153x9907

Cheers

Ken

## isenham said,

June 20, 2007 at 9:32 am

94897410

Googling the above number gave zero results. So a new low has been set (temporarily).

SCF

## isenham said,

June 20, 2007 at 9:35 am

93139519

Here is another entry. I have too much free time this morning.

SCF

## strauss said,

April 29, 2008 at 4:03 am

Things have really gotten crowded in just the last year. All of the numbers in the comments above now get at least a couple of hits and in some cases a great many.

It looks like the demand for numbers on the internet (for auctions, for indexing photos, etc) is running very high.

And some folks are

reallyhogging up numbers, listing all the primes and other wasteful practices.This will just get worse as time goes by!!

I’d love to see a systematic search done. For the moment, this is what I came up with. I’ll use something like Ken’s trick above to keep google at bay.

Two3001293Eight

Two0331125Six

## DWC said,

September 11, 2008 at 6:57 am

Not the smallest number by far but the smallest number using the fibonacci sequence’s consecutive terms strung together as a number.

one12358132134558914423337761098715972584418167651094six

Thought it was interesting how large it actually was.

## John Dalbec said,

September 18, 2008 at 8:07 pm

If you add enough leading zeroes, you can get 0 search results for almost any number. I guess that’s cheating, though.

## rmjarvis said,

September 20, 2008 at 3:48 pm

ONE 8523542 SEVEN

I suspect I used a slightly different strategy than most. Rather than googling 9 digit numbers, I googled:

“smallest number with no google hits”

and then clicked around to see what other people had already found. No sense duplicating effort, eh?

Credit where credit is due:

http://forums.topcoder.com/?module=Thread&threadID=623471&start=0&mc=37#1021543

Apparently, back in 2003, the lowest known was 13,965,321, which now has 70 hits (oops 71 as soon as Google scans this page again), so I wonder how long this result will last.