Integers

What percentage of the integers from 1 to 99999999 returns exactly zero hits in google?

I tried 20 random numbers in that range and got hits for exactly 10. Therefore, my guess would be approximately 50%, with a significant error margin (Ob: estimate this error). Somebody at Google could run a script that extracted all those numbers from the list of unique words in their database and calculated the exact percentage.

I would guess a percentage significantly smaller. Using 5 random numbers for each number of digits from 1 to 8 the following returned at least one hit. 1 100% 2 100% 3 100% 4 100% 5 100% 6 100% 7 100% 8 20%

I would assume that the 8 digit numbers are very rare since other random numbers have shown. However I would think 7 digit would be very common because that is a common length for phone numbers, and any smaller would be likely just because of its size. So I would guess about in the region of 10% to 20% of numbers from 1 to 99999999 would return no hits, and would obviously increase if you increase the upper limit. However decreasing the limit to 9999999 would probably decrease the percentage to very very small.

It is not necessary that the zero hit numbers be uniformly distributed, as long as one picks the test numbers at random. For instance, assume that 1, 2, ..., 100 are the numbers that have nonzero hits. Then the proportion of zero hits is (99999999 - 100)/ 99999999, which is exactly the expected proportion of zero hits in any random sample.

Daniel Stone:

Stephen Merriman:

But in most countries, phone numbers are punctuated into smaller units. 222-1234 is treated as a phrase by Google; a search on 2221234 won't find it.

On the other hand, it's not a hard and fast rule; unpunctuated phone numbers are often used too.

Is it the case that if you search for some number, say 5237, and do not find it, that you could also rule out any longer number which also contains that digit sequence? I'm not sure if Google does partial word matches on digit strings, but that would give you some further information.

Cheers,

This thread reminds me of the old proof that there exists no smallest uninteresting integer. Thus, each integer is interesting.

Proceed in order from one upward through the integers, assessing whether each has some interesting aspect. Eventually, you (may?) come to one for which you can find absolutely nothing interesting. Well, isn't that an interesting fact about that number?

Of course, the question then arises, whether you can use that ploy for even higher integers, again and again.

Peter H. Ten Eyck

*grin*

Usually that proof is constructed using the well-ordering of the natural numbers and contradiction.

Axiom: Any non-empty set of natural numbers has a minimum element.

Suppose some natural number is uninteresting.

Then, the set of uninteresting natural numbers is non-empty, and must have some minimum element, all it b.

But being the smallest uninteresting natural number is a very interesting property, which violates the definition of b. Therefore, there can be no uninteresting natural number.

But this is completely off track, so I'll shut up now.

Cheers,

For our purposes, we are looking at N slots, out of which M are occupied and N-M are empty. If you choose a slot at random (all slots equally likely), the probability that it will be occupied is M/N regardless of how the occupied slots are arranged. If the occupation rate was 50%, then finding a randomly chosen number would be equivalent to tossing a coin. For N tosses, you can take the binomial formula and calculate the probability of a result.

For the record, here are the numbers I tried:

67363119 19518765 93658912 23728675 28321156 97507877 10906361 16081816 62823940 91690888 78917053 43302914 27100827 53210302 55253631 2600785 5390230 45248011 99951567 33832350

I tried them again, I only get hits for 9 of 20. Maybe I made a mistake the first time, or maybe the database has changed (part of it could be down, a document could have been thrown out, etc).

Assume that my numbers are truly random. Here are the probabilities of getting exactly 9 out of 20 for different occupation rates:

20%: 0.007 30%: 0.065 40%: 0.159 50%: 0.16 60%: 0.07 70%: 0.01

It seems obvious that this sample size is to small to estimate N/M with a reasonable error. It would be much more accurate if we had, say, 900 out of 2000.

No, they do exact matching.

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But 90% of the numbers from 1 to 99999999 have 8 digits, and your results show that 80% of those did not return a hit.

Oops I kept changing between the number having some hits and the number have no hits. So I must've meant between 80% and 90% (as I predict that the percentage for 8 digit numbers is far lower than my trial).