# How Many Zeros in a Row are Possible in Pi? **URL:** \ **Category:** Factual Questions\ **Tags:** science-math\ **Created:** [September 21, 2024, 5:12pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562 "2024-09-21T17:12:42Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [September 23, 2024, 3:01pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/61 "2024-09-23T15:01:58Z")
Perhaps such numbers might be referred to as “Liouville Sluggers”? ---
**Author:** ![GailForce](https://avatars.discourse-cdn.com/v4/letter/g/dfb087/32.png) [@GailForce](https://boards.straightdope.com/u/GailForce)\ **Post date:** [September 23, 2024, 6:04pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/62 "2024-09-23T18:04:04Z")
If pi extends into infinity (does it? I think so) then isn’t the answer that zeros will at some point appear an infinite number of times consecutively? ---
**Author:** ![N9IWP](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/n9iwp/32/3154_2.png) [@N9IWP](https://boards.straightdope.com/u/N9IWP)\ **Post date:** [September 23, 2024, 6:10pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/63 "2024-09-23T18:10:27Z")
In base pi, pi is 1 followed by an infinite number of zeros after the “decimal” point 😉 Brian ---
**Author:** ![bleach](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bleach/32/3106_2.png) [@bleach](https://boards.straightdope.com/u/bleach)\ **Post date:** [September 23, 2024, 7:16pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/64 "2024-09-23T19:16:54Z")
> [@GailForce](#): > > If pi extends into infinity (does it? I think so) then isn’t the answer that zeros will at some point appear an infinite number of times consecutively? No because then pi would become a rational number. ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [September 23, 2024, 7:44pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/65 "2024-09-23T19:44:34Z")
> [@ftg](#): > > I consider 2^83 as “infinity for all practical purposes” when counting something. E.g., digits of Pi. That’s about 10^24 For context there are [10^82 atoms in the observable universe](https://www.livescience.com/how-many-atoms-in-universe.html). There are perhaps something under [10^186 Planck lengths](https://davidpratten.com/2008/02/11/addressing-the-observable-universe/) in the volume of the observable universe. Oh pish posh. Let’s consider the dinner party problem. For N guests, how many ways are there to seat them? That would be N!. 2! = 2 10! = 3,628,800 61! = 5.076e83, more than the number of atoms in the visible universe 120! = 6.69e198 , far more than a billion times the number of Planck units in the volume of the observable universe. 500! = 1.22e1134 , TILT, though this falls way short of Graham’s number, never mind TREE(3). ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [September 23, 2024, 9:44pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/66 "2024-09-23T21:44:15Z")
Yeah, factorial growth is practically a flat line compared to some functions out there. ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [September 23, 2024, 10:04pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/67 "2024-09-23T22:04:06Z")
Does infinity actually exist? It’s a very useful intangible abstraction and we should not discard it but I’m not sure it actually exists. Any answer to this question is dependent on what one means by the words “actually” and “exist.” ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 23, 2024, 10:38pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/68 "2024-09-23T22:38:44Z")
> [@Ynnad](#): > > I concede to the distinction between “simply normal” and "normal” However, if I had said, ” Suppose there is a limit on the number of zeros in a row in pi when expressed in base 10. So long as the same limit applies to all of the other digit values, pi would still be **simply** normal.” then that might be correct? It would be possible for a number to meet your criterion, while still not being simply normal. For instance, you could have a number with a hundred zeroes after the decimal point, and all other digits limited to a hundred in a row, but then no more zeroes ever after the 101st decimal place. > [@Ynnad](#): > > Does infinity actually exist? It’s a very useful intangible abstraction and we should not discard it but I’m not sure it actually exists. Any answer to this question is dependent on what one means by the words “actually” and “exist.” Most mathematics doesn’t actually concern itself directly with the concept of “infinity”, but simply dances around the edges of it. You can discuss all of the concepts in this thread without ever caring about the “actual existence” of infinity. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 23, 2024, 10:57pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/69 "2024-09-23T22:57:25Z")
> [@Lumpy](#): > > Yeah, factorial growth is practically a flat line compared to some functions out there If you took a number N, and had a rule that says “add a number of factorial symbols equal to the number itself”, and then applied that rule N times, it would _still_ be a flat line compared to TREE(N), etc. And any “normal” number, whether 500 or a googolplex with that rule applied would be infinitesimal compared to TREE(3). ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 23, 2024, 11:09pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/70 "2024-09-23T23:09:33Z")
But remember, TREE(3) is a very small number. Almost all positive integers are much, much larger than it. ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [September 23, 2024, 11:17pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/71 "2024-09-23T23:17:33Z")
Is the TREE(n) function monotonic in n? Has that been proven? This seems like a highly relevant question for applications where n\>3. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [September 23, 2024, 11:23pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/72 "2024-09-23T23:23:59Z")
> [@Ynnad](#): > > Does infinity actually exist? It’s a very useful intangible abstraction and we should not discard it but I’m not sure it actually exists. Any answer to this question is dependent on what one means by the words “actually” and “exist.” No number actually exists–they’re all very useful intangible abstractions. ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [September 23, 2024, 11:28pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/73 "2024-09-23T23:28:37Z")
That’s reassuring, somehow. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [September 23, 2024, 11:28pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/74 "2024-09-23T23:28:53Z")
Well of course in-finite literally means without end; properly one (usually) cannot talk about having “arrived at” infinity. ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [September 23, 2024, 11:31pm UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/75 "2024-09-23T23:31:06Z")
Though some infinities are bigger than others: > **[A Deep Math Dive into Why Some Infinities Are Bigger Than Others](https://www.scientificamerican.com/article/a-deep-math-dive-into-why-some-infinities-are-bigger-than-others/)** > > The size of certain infinite sets has been a mystery. Now, it turns out, each one is different than the next, and they can all be ordered by size ---
**Author:** ![Topologist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/topologist/32/3208_2.png) [@Topologist](https://boards.straightdope.com/u/Topologist)\ **Post date:** [September 24, 2024, 12:00am UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/76 "2024-09-24T00:00:44Z")
> [@Lumpy](#): > > Well of course in-finite literally means without end; properly one (usually) cannot talk about having “arrived at” infinity. That’s a controversial statement and false in practice. Most mathematicians are perfectly happy working with completed infinities, particularly sets with infinitely many elements, like \mathbb Z, the set of all integers. Even collections that are too large to be called sets, like the class of all sets. ([Russell’s Paradox](https://en.wikipedia.org/wiki/Russell%27s_paradox) tells us that we aren’t allowed to call that a set.) Cantor showed us the way. ---
**Author:** ![Ynnad](https://avatars.discourse-cdn.com/v4/letter/y/4491bb/32.png) [@Ynnad](https://boards.straightdope.com/u/Ynnad)\ **Post date:** [September 24, 2024, 12:08am UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/77 "2024-09-24T00:08:10Z")
> [@Topologist](#): > > … completed infinities … What does “completed infinities” mean? Is that a term of art in mathematics? ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 24, 2024, 12:12am UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/78 "2024-09-24T00:12:23Z")
The subheading of that article… “…has been a mystery”, “Now, it turns out,…”, makes it seem like it’s talking about some very recent discovery (say, since the previous issue of Scientific American), not something that’d been settled for nearly 60 years at the latest. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [September 24, 2024, 12:15am UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/79 "2024-09-24T00:15:13Z")
Quite true. Though almost all those numbers are inaccessible. There is a function, called the Busy Beaver function or BB(N), which tells you the most number of steps an N-state Turing machine can run for (among Turing machines that halt eventually). There is a 745-state Turing machine that halts if and only if ZFC is inconsistent. So if we knew BB(745), we could run the experiment of running that Turing machine BB(745) steps. If it halted in that time, then ZFC must be inconsistent and our entire basis for computing BB(745) was wrong. But if it didn’t halt, then we’ve proved the consistency of ZFC using only its own axioms, which we know from Godel is impossible. Of course we knew already that BB was incomputable, since otherwise we could solve the halting problem. But we might think that in any _particular_ case, you could maybe just enumerate the possibilities and figure it out. And we can do so up to BB(5). Just not BB(745)! And probably not for much lower numbers as well. That entire space of integers is just inaccessible to mathematics, even in principle. ---
**Author:** ![Topologist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/topologist/32/3208_2.png) [@Topologist](https://boards.straightdope.com/u/Topologist)\ **Post date:** [September 24, 2024, 12:21am UTC](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562/80 "2024-09-24T00:21:26Z")
> [@Ynnad](#): > > > [@Topologist](#): > > > > … completed infinities … > > What does “completed infinities” mean? Is that a term of art in mathematics? As opposed to the potential infinities @Lumpy was referencing. Consider the integers: Someone who believes only in potential infinities would say that you can’t take the whole set of integers; to say that there are infinitely many integers is only to say that, if you have finitely many in hand, there is always another you don’t have. Someone who allows completed infinities (like most working mathematicians) is perfectly happy talking about the set of all integers as a complete thing in itself. [I may not have done this justice; I’m a working mathematician, not a philosopher.] [Previous page](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562.md?page=3) [Next page](https://boards.straightdope.com/t/how-many-zeros-in-a-row-are-possible-in-pi/1007562.md?page=5)