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Approximately how big is the smallest positive integer that has never been spoken aloud by a human?

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I just said "the smallest integer that has never been spoken aloud by a human", thereby breaking the question
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I dunno, but I do know the smallest positive integer that has ever been spoken aloud by a human
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Here's a very loose upper bound: assume it takes two seconds on average to speak 3 digits and the appropriate -illion word, and that you can't keep speaking for over 72 hours without falling asleep and losing your place. Then, if you pick a number larger than about 10^(1000000), you can be absolutely certain it hasn't been spoken. I'm sure there are weirdos out there who could have spoken aloud all numbers between 716 and 717 million, for fun, for all I know, and maybe a group of such people distributed over human history has patched up any "holes" up to a large number, but if a single number is too large to speak of uninterrupted, that's sufficient.
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this is a horribly disappointing set of responses to an interesting question.  A statistical approach is going to be more realistic here. Financial transactions are almost always rounded off so I don't think that gives you much information. I also tend to agree it would be something random in the low millions. I would be fairly surprised if its greater than 10million, but that is just a hunch.
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I think you underestimate the laziness of humans.  Once a number is over 1-2 million, there’s no real need to discuss the exact number, so “never been spoken” could easily be between 2 and 10 million.
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A few considerations jump to my kind right away:

- Does it have to be the "official form" of the number eg: Seven Thousand and Eighty or is Seven Oh Eight Oh acceptable. If the later than we can rule out anything under 2 billion due to phone numbers.
- When someone is speaking a number, my intuition says that longer (syllable-wise) numbers are much less likely with each syllable, probably scaling with X^-n, where n is the number of syllables.
- This is reinforced by my notion that people would likely truncate or round numbers with excessive syllables.
- Given the context of spoken numbers, it's likely they follow Benford's law.
- There's probably exceptions in the above for numbers that are "special" in some way to humans eg: 999 999 999 or 789 789 789.
- Given this I would expect the number to probably be in the tens or hundreds of millions starring with lots of 7's in it something that probably looks like 72 776 937.
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I dunno. Maybe 73. I've never heard anyone say it.
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Reminds me of the Berry paradox e.g. "The smallest positive integer not definable in under sixty letters." is a phrase with 57 letters
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As soon as you find an answer its going to be wrong
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Whatever it is, you just spoke it, namely “the smallest positive integer that has never been spoken aloud by a human.”

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