[HN Gopher] A formula for the nth digit of and ^n
___________________________________________________________________
A formula for the nth digit of and ^n
Author : georgehill
Score : 198 points
Date : 2023-01-15 13:12 UTC (9 hours ago)
(HTM) web link (arxiv.org)
(TXT) w3m dump (arxiv.org)
| tzs wrote:
| In "n'th digit of and ^n" are both n the same?
|
| In other words, for say ^50 does the formula only give me the
| 50th digit, or does it give me any arbitrary digit I want?
| gnramires wrote:
| Mathematicians (and other math subjects) use an interesting
| notation that is something like a "semantically local
| variable". A symbol like n can be reused multiple times, as
| long as the context is clear you're allowed to do that.
| coherentpony wrote:
| > In "n'th digit of and ^n" are both n the same?
|
| Yes.
|
| > In other words, for say ^50 does the formula only give me the
| 50th digit
|
| Yes.
|
| > or does it give me any arbitrary digit I want?
|
| It gives you the n-th digit of \pi^n. Here n is arbitrary.
| dmurray wrote:
| The article title says "powers of ", so presumably an arbitrary
| digit.
| mattkrause wrote:
| I'm not sure that's right.
|
| The abstract and text say the nth digit of \pi^n, and the
| worked example on page 2 uses the same n=1000 to find the
| thousandth digit of \pi^{1000}.
| dmurray wrote:
| Yes, it looks like you're right. But I don't understand the
| reasoning - is he actually saying you can use this formula
| to compute pi^n to n decimal places? So it doesn't produce
| arbitrary digits on their own, but excellent approximations
| to pi^n?
|
| And this was by taking 4 terms of the zeta function
| infinite product expansion. 2xn digits would presumably be
| given by taking more terms (but quite a few, one for every
| prime under 100, so in some sense this method has bad
| convergence when you want the mth digit of pi^n and m >>
| n).
| mattkrause wrote:
| Yeah, my sense is that the author knows this is more of a
| neat trick than a "practical" way of calculating pi.
|
| There's a bit on page 5 about how the Chudnovsky method
| totally blows this approach out of the water.
| dmurray wrote:
| Seems like the real breakthrough was computing large
| Bernoulli numbers without a very precise value for pi,
| and this is a relatively easy corollary for someone to
| spot and get a paper out of.
| mattkrause wrote:
| IOW, the arXiv title might have lost the "nth" because of
| some formatting thing. The title inside the PDF says "A
| formula for nth digit of \pi and \pi^n"
| [deleted]
| [deleted]
| [deleted]
| nyc111 wrote:
| Are there measurements of pi calculated by meausuring diameter
| and circumference? How many digits can that pi have?
| tucnak wrote:
| So does it mean that these pi-calculating competitions & record
| are now going to devolve to special olympiads in pointless
| storage capacity? What will the super computers going to do in
| view of this discovery? Fascinating times for humans as well as
| for the machines...
| imglorp wrote:
| pfs: Never worry about data again! -
| https://github.com/philipl/pifs
| mojomark wrote:
| Any file can be represented as a binary string, and a binary
| string is just an integer value - which is to say binary
| strings are simply indexes of files in binary space (i.e. the
| set of all possible permutations of bits).
|
| Looks to me like nfs is simply transforming a binary space
| index into a pi-space index. Some files may compress to a
| smaller value than they are in binary space (if you get
| lucky), but make no mistake, some files will be much much
| larger (i.e. the files you're trying to store don't show up
| in pi until an index value that is a virtually infinite
| number of digits long).
| cmehdy wrote:
| From the repo:
|
| Why is this thing so slow? It took me five minutes to store
| a 400 line text file!
|
| Well, this is just an initial prototype, and don't worry,
| there's always Moore's law!
|
| So I'm guessing they are quite aware of the joke, and props
| to them for the dedication to commit and write the code (or
| the other way around) :)
| pitaj wrote:
| Yeah, that's the joke.
| mojomark wrote:
| Ah, I'm slow. Thanks
| oh_sigh wrote:
| We just need a formula that finds a sequence of digits in pi
| instead of a single one.
| amelius wrote:
| Yes, we are too much focused on the reverse problem.
|
| We know exactly how much time we need to compute the nth
| digit of pi. But how much time do we need to find a
| specific string of digits? Seems like a more interesting
| question.
| adenozine wrote:
| This is one of my favorite software projects of all time. I
| remember seeing this several years ago and it has driven my
| imagination crazy since then.
| WithinReason wrote:
| But why?
| imglorp wrote:
| For me, it stimulates a mental shift that could be good
| exercise elsewhere: instead of storing the string, you
| find the string somewhere and store its index.
|
| It also stimulate the imagination: what other
| transcendental numbers might this work with? How long do
| you have to search in the digits to find your string?
| What can you say about the size of the index (how far you
| searched) vs your string length? Etc. It's patterns all
| the way down.
| eapriv wrote:
| It doesn't even work with pi.
| WithinReason wrote:
| I don't want to be a buzzkill, but to me this seems
| uninteresting, you need more information to store the
| index than the data, end of story.
| sterlind wrote:
| this is a great motivating example for the definition of
| Kolmogorov complexity.
| Jerrrry wrote:
| It is my favorite fake-counter example.
| zamadatix wrote:
| It's actually not known if pi contains every combination of
| digits (in any base 2 or greater) or not. It feels likely but
| really all we know is it's transcendental and seems pretty
| random from the parts we've generated.
|
| The library of babel could be a good "useless" backing though
| https://libraryofbabel.info/bookmark.cgi?hnexample
| Jerrrry wrote:
| You just now convinced me how that site wasn't a sham.
| Thank you.
|
| It takes the input, converts it into N, then calculates
| position using the N.
|
| Thank you. I argued for a long time simply by being
| ignorant.
|
| good bless ya sir.
| mkl wrote:
| Nothing will change there. There are already much more
| efficient methods of calculating p. What this lets you do is
| jump straight to the _n_ th digit without calculating all the
| ones before it.
| tyingq wrote:
| Couldn't you "cheat" a bit in a timed competition if you knew
| exactly how many digits you would reach, and kick this off in
| parallel to extract a few more to tack to the end? Or would
| the parallel job be too slow for that? Or the competitions
| constrain CPU or other resources to a ceiling?
| Someone wrote:
| Why would it? Calculating the first few trillion digits may be
| (and probably is) a lot faster than doing a trillion
| calculations of individual digits, but even if it isn't, people
| will simply raise the bar and compute even more digits.
|
| > What will the super computers going to do in view of this
| discovery?
|
| Whatever they do now. It's not like this is what supercomputers
| are built for. Computations like these more are used to get
| confidence that the hardware works.
| antiquark wrote:
| Good ole Plouffe!
| commandlinefan wrote:
| The paper seems absolutely brilliant, but the grammar is very
| strange (there's even what appears to be a typo in the paper
| where he says "rand n" instead of "rank n"). Odd that he wouldn't
| have worked with somebody with better written English before
| publishing.
| petschge wrote:
| You have no idea how atrocious the English is in papers that I
| see as a reviewer. And depending on journal I don't even get to
| reject it for that as long as the science is sound.
| MaxBarraclough wrote:
| Can you insist the writing be improved for publication?
| heywhatupboys wrote:
| > And depending on journal I don't even get to reject it for
| that as long as the science is sound.
|
| and you shouldn't. As long as it is somewhat legible, forcing
| people who are not native English speakers to conform to
| another language 100 % in order for their _science_ to be
| published is horrendous.
|
| There was a time 300 years ago, where great thinkers who did
| not speak French or German could not publish their thoughts
| and answers, and to us now it seems atrocius. Let us not go a
| head and redo that with English
| Y_Y wrote:
| The goal of publishing is that others can read your work.
| If it's badly written it will be hard to understand, and
| extra hard for non-natives.
| heywhatupboys wrote:
| actually, sometimes "native" English is much harder to
| read for non-natives than a non-native writing, due to 1.
| less vocabulary, and 2. more straight forward sentence
| structure.
| petschge wrote:
| The problem is that "somewhat legible" is not a given and
| you don't know if the version that comes out of language
| editing (if it is still done, a lot of journals skip it to
| save money) is still scientifically correct.
|
| Edit: A possible solution would be to have "good idea,
| please language edit and send back for further review" as
| an option along with "reject" / "needs major revisions" /
| "needs minor revisions" / "accept".
| anamexis wrote:
| It isn't published, it's a pre-print.
| xyzzyz wrote:
| If you can download it from arxiv, it is published.
| Researchers don't really care whether the paper went through
| formal peer review and publication process in some journal,
| because that process is of little value: they can figure out
| that the author meant rank instead of rand etc.
| petschge wrote:
| There is definitely a difference between "public(ly
| available on arxiv)" and "published (in a peer-reviewed
| journal)". Depending what I want to do I may prefer on or
| the other for my work as a researcher.
| xyzzyz wrote:
| Sure, but if the paper is never published in a journal,
| and just exist as a pdf on arxiv forever, you won't treat
| it any different than if it was published. You'll still
| ignore it if it looks crap, still read it if it looks
| promising, still tell your friends about it if it has
| interesting results, still cite it etc. In short, it
| doesn't matter much if the paper was formally published.
| eesmith wrote:
| The "doesn't matter much" is, I think, the crux of the
| matter.
|
| commandlinefan's earlier negative aside concerned
| language quality.
|
| IMO, I think people hold peer-review journal published
| papers to a (slightly?) higher language quality standard
| than what may be the first of several preprints. And I
| think anamexis was pointing out that difference.
|
| As Wikipedia says: "The immediate distribution of
| preprints allows authors to receive early feedback from
| their peers, which may be helpful in revising and
| preparing articles for submission."
| https://en.wikipedia.org/wiki/Preprint
|
| I expect that may include identifying and fixing typos.
| eesmith wrote:
| "Published" in this context is short for "published to a
| journal" or more completely for this thread "gone through
| the full edit cycle you would expect from a paper published
| to a journal".
|
| For example, https://arxiv.org/help/jref says:
|
| > When a article is published, the author may wish to
| indicate this in the abstract listing for the article. For
| this reason, the journal reference and DOI (Digital Object
| Identifier) fields are provided for articles.
|
| This can only make sense if "public abstract on arxiv" is
| not the same as "published" in the way you mean.
| kwhitefoot wrote:
| Don't abbreviate unless you have great confidence that
| everyone hearing or reading your words shares the same
| dictionary.
| eesmith wrote:
| And this is not the case here?
|
| I mean, there's always going to be today's 10,000 [1] who
| doesn't know what, say, "VB.NET"[2][3] means.
|
| [1] https://xkcd.com/1053/
|
| [2] https://news.ycombinator.com/user?id=kwhitefoot
|
| [3] https://en.wikipedia.org/wiki/Visual_Basic_(.NET)
|
| But explaining or footnoting everything defensively,
| rather than pointing out misconceptions as they arise,
| seems excessive.
|
| Further, someone may deliberately use a minority
| definition in order to stress a philosophical point. One
| valid viewpoint is that a publication is a publication is
| a publication. A preprint, a blog post, or a peer-
| reviewed journal publication should be given equal weight
| as being "published." I'll call this position #1.
|
| Another valid point is that some works are incomplete,
| and may go through multiple drafts before reaching the
| final, "published" form, which it's best known by, and is
| likely the most polished of the versions. I'll call this
| position #2.
|
| Often people want feedback, and one way to get feedback
| is by publishing a preprint. (There are others. I recall
| reading of a mathematician, about a century ago, who
| would first publish in his home country, and native
| language, to get friendly feedback from colleagues,
| before publishing in English. He's cited for his later
| publication.)
|
| Someone who holds position #1 might fully understand that
| I use the dictionary with position #2, and still
| deliberately use position #1 in order to popularize that
| #1 dictionary. The difference isn't one of confusion or
| lack of knowledge, but one of viewpoints.
|
| Let me be clear - I'm not saying that that's the case
| here. Instead, my example is meant to show it's not
| necessarily so simple as "shares the same dictionary" or
| not.
| xyzzyz wrote:
| I understand what it means, which you could have seen by
| reading my comment carefully. My point is that this
| publication process is of little value these days.
| anamexis wrote:
| I believe you when you say you understand, but your first
| sentence was "If you can download it from arxiv, it is
| published." Which is precisely what GP was responding to.
|
| Furthermore, this thread started with someone complaining
| about the lack of polish which the publication process
| can provide.
| _ache_ wrote:
| Plouffe ...
|
| He used to teach in my university. He is a fantastic man. This is
| serious, he is crazy about numbers. He is one of the guy behind
| OEIS (oeis.org).
|
| That is not the first formula he found about pi and some of the
| previous one had been used to break world record about the number
| of known decimals.
| _ache_ wrote:
| Ok, so the method is real but will not be used to break the
| next world record. Chudnovsky algorithm is better at that task.
| lifthrasiir wrote:
| Not this one, but algorithms that can calculate the specific
| digit positions but nothing else are indeed used for world
| records, mainly for the verification. If two radically
| different algorithms converge into the same digits at
| something like the trillionth position then you will have a
| high confidence for the rest of digits.
| exmadscientist wrote:
| Probably this is a good time for your irregular reminder that
| Plouffe has something of a feud with Bailey and Borwein:
| https://groups.google.com/g/sci.math.symbolic/c/a3kVKVYJhgc?...
|
| In my _very personal_ opinion, the overall publication history
| of the three provides some rather good evidence for Plouffe 's
| claims.
| sega_sai wrote:
| It is all curious, but it seems that procedure that calculates
| the n-th digit using some other functions that require O(n)
| calculations (i.e. Bernoulli numbers) is not that exciting, as
| it's just a speedup comparing to a naive calculation (maybe a big
| one but still).
|
| Although because pi is a transcendental number maybe it is
| impossible to have an algorithm to return the n-th digit in O(1)
| operations? Does anyone know ?
|
| Upd: thinking more about it, just to read all the digits of
| number n, one needs log(n) operations, so I guess anything that
| has performance of O(log(n)) can be considered easy (i.e. the
| digits of rational numbers can be computed in O(logn).
| paulpauper wrote:
| exactly. this paper is trivial, sorry to say.
| kdkdk wrote:
| Even rational numbers which have repeating digits at the end
| are not O(1) because in order to calculate the n-th digit you
| need to calculate n modulo k where k is the length until the
| number repeats its digits, which needs to read the entire input
| number n (thus runs in O(log(n)). The only exception are
| rational numbers with k being a power of two. Take
| 0.1010101010..., you can get the n-th digit by reading off the
| smallest digit of n and checking whether it is a 0 or a 1.
|
| There are transcendental numbers where the n-th digit can be
| computed in O(log n) like Champerowne constant though.
| ur-whale wrote:
| The interesting question is: are there real numbers whose N-th
| digit provably _cant_ be calculated in O(N)?
| yongjik wrote:
| Even better: there are (well defined) real numbers whose N-th
| digit provably _cannot be computed_ at all.
|
| https://en.wikipedia.org/wiki/Chaitin%27s_constant
| tooltower wrote:
| The normal method for computing digits of pi is not O(n), so
| this could still be interesting. I think it's probably better
| to compare this with the BBP formula [1]. The commonly used
| algorithm for pi I think still takes O(n log^3 n) time [2]
|
| [1]
| https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%9...
|
| [2] https://en.wikipedia.org/wiki/Chudnovsky_algorithm
| scythe wrote:
| The interesting question, I think, is whether this formula can
| help address the question of the normality of pi:
|
| http://en.wikipedia.org/wiki/Normal_number
|
| This is particularly exciting because the prevailing opinion had
| been that we lack the mathematical tools to attack that problem.
| moloch-hai wrote:
| Doubting this will help show whether e^pi or pi^e is
| transcendental.
| lyschoening wrote:
| > Note that the calculation of Bernoulli numbers can be done in
| several ways, one of which requires knowing p with good precision
|
| This seems to be the catch.
| phyphy wrote:
| It's written "one of which," not "all of which."
| 867-5309 wrote:
| it's like "can find meaning of life" but "must already know
| 6*7"
| childintime wrote:
| Chatgpt, please write a function in python for the nth digit of
| pi. Sure, here is a function in Python that
| calculates the nth digit of Pi using the Chudnovsky algorithm:
| from decimal import * def nth_digit_of_pi(n):
| getcontext().prec = n + 1 C = 426880 *
| math.sqrt(10005) M = 1 L = 13591409
| X = 1 K = 6 S = L for i in
| range(1, n): M = (K ** 3 - 16 * K) * M // i ** 3
| L += 545140134 X *= -262537412640768000
| S += Decimal(M * L) / X K += 12
| return +str(S / C)[n]
|
| Seems off, but I learned something:
| https://www.wikiwand.com/en/Chudnovsky_algorithm
| _visgean wrote:
| Here is an article with an actual implementation
| https://www.craig-wood.com/nick/articles/pi-chudnovsky/
| robinhouston wrote:
| Interesting! If you correct the obvious errors, then it appears
| to calculate 1/pi: >>> from decimal import
| Decimal >>> import math >>> >>> def
| nth_digit_of_pi(n): ... getcontext().prec = n + 1
| ... C = Decimal(426880 * math.sqrt(10005)) ...
| M = 1 ... L = 13591409 ... X = 1
| ... K = 6 ... S = L ... for i in
| range(1, n): ... M = (K ** 3 - 16 * K) * M // i
| ** 3 ... L += 545140134 ... X
| *= -262537412640768000 ... S += Decimal(M * L)
| / X ... K += 12 ... return str(S /
| C)[n] ... >>> "".join([ nth_digit_of_pi(i) for
| i in range(50) ])
| '0.318309886183790698041462054251035408427213165074'
| leoff wrote:
| since this is Python, `nth_digit_of_pi(-1)` should give us the
| last number of Pi.
| manojlds wrote:
| But it's not a list
| 4gotunameagain wrote:
| Traceback (most recent call last): File "<stdin>",
| line 1, in <module> AttributeError: 'manojlds' object
| has no attribute 'humour'. Did you mean: 'joke'?
| manojlds wrote:
| [flagged]
| [deleted]
| mjd wrote:
| Genius.
| detrites wrote:
| Has anyone converted the formula to code?
| z3t4 wrote:
| here you go: n => Math.PI.toString()[n+2]
| Maursault wrote:
| But... pi is _in_ the formula. If you already know it, then why
| bother?
| [deleted]
| [deleted]
| davesque wrote:
| Not sure where you're seeing that. Did you misread a formula?
| Maursault wrote:
| The very first denominator seen is (2p)^2n, the last
| denominator on that line is the same, the first denominator
| of the second line is p^2n+1 and the second denominator in
| the second line is the same. Are you not seeing that?
| rdlw wrote:
| Are you talking about the inequality on the first page?
| That is at the end of a sentence that starts "The
| calculation is made from the two inequalities ...". The
| next sentence is "By isolating p in both cases, we can
| derive an approximation of the latter."
|
| That is not the formula.
| krick wrote:
| It isn't.
| Maursault wrote:
| Look at the first denominator seen in both lines of the
| equation, the last denominator in the first part of the
| equation, and the second denominator in the second part of
| the equation.
| colanderman wrote:
| See also Plouffe's earlier (1995) formula to extract hexadecimal
| digits of pi:
| https://en.m.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80...
| userbinator wrote:
| ...which Fabrice Bellard improved upon:
| https://en.m.wikipedia.org/wiki/Bellard%27s_formula
| karmakaze wrote:
| We should also have decimal/binary/hex digits of Tau to
| complete the set.
| cleak wrote:
| Decimal is the only tricky one. Given that tau=2pi, simple
| use f(n-1) in the original binary formula for pi, and I'm
| sure something just as trivial for hex.
| craigharley wrote:
| Here is another
|
| const nDigitOfPi = (n) => (22/7).toString()[n+1]
| NeutralForest wrote:
| Finally, we can find the last digit of pi
| sulam wrote:
| This also means I can finally crack Jeff Dean's password.
| spicybright wrote:
| Now we just have to figure out what the last integer is
| sidcool wrote:
| The last digit of pi is e.
| vittore wrote:
| I thought it was keleven...
| layer8 wrote:
| According to most examples I've seen, the last digit of pi is
| "...".
| detrites wrote:
| Spoiler: it's zero, recurring.
| bhk wrote:
| That would make it a rational number, so we can rule that out
| detrites wrote:
| Exactly, the only possible "last digit" it _could_ have (in
| keeping with the silly premise that it has one), is zero.
| tremon wrote:
| The only possible "last digit" it could _not_ have is
| zero: if the last digit were to be a zero, that digit
| would be superfluous and could be discarded, making the
| digit before that the real "last digit".
|
| Proof: the first digit of pi is 3, not zero.
| detrites wrote:
| _sigh_ It was said in jest, in response to another
| comment also said in jest.
|
| That aside, the apparent "empty space" on the either side
| of a number is in reality consisting of infinite zeroes.
|
| Just because we typically choose to "display" most
| numbers without those zeroes, it doesn't mean they aren't
| there in a very real, practical and important sense.
|
| They are there, because if they aren't there, then
| something else _might be_ , and then all our numbers
| would have to be assumed to be wrong or incomplete... so
| instead, we assume the zeroes.
|
| The terrible reality is the zeroes extend off infinitely
| in either direction, and we use empty space as shorthand
| for this so we don't have to spend longer than the age of
| the universe to write a single number with full accuracy.
| delaaxe wrote:
| Why is zero different than any other number?
| qorrect wrote:
| It acts as a terminator or terminal, see
| https://news.ycombinator.com/item?id=34391483.
| layer8 wrote:
| If 0 would act as a terminator, then 1.203 would be equal
| to 1.2.
|
| The thing that is actually special about the digit 0 is
| that it is implied for all positions for which no digit
| is given. That is, when we write
| 1.2
|
| we really mean ...00000001.20000000...
| Flockster wrote:
| I don't think that would be true seeing 1/3 = 0.3333.. ,
| or am I reading this wrong?
| detrites wrote:
| 3 recurring represents a particular quantity continuing
| forever.
|
| 0 recurring represents the end of a quantity, and the
| absence of any further quantity, forever.
|
| Eg: 0.012500000000000...
|
| The significant portion is 0.0125 - the recurring zeroes
| serve a mathematical role akin to that of a full-stop in
| a sentence. Hence zero being (jokingly, but in a sense
| truthfully) _always_ the "last digit".
| knome wrote:
| This is just an artifact of representing it in base-10.
| In base-3 0.0125 has the same value but would have a non-
| terminating representation of 0.00010001...
|
| I will grant that in base-p, p is 10, however.
| tedunangst wrote:
| Can you prove it's not nine, recurring?
| detrites wrote:
| Yes... proving that would require an infinite-capacity
| rounding mechanism, which cannot exist, because when trying
| to build it, you always run out of universe. Thusly,
| "impossible" is equivalent to "false", by default.
| aqme28 wrote:
| Yup, just plug in -1.
| ashvardanian wrote:
| Looks interesting! Does anyone know a practical application where
| something like this would help?
| xoa wrote:
| > _Does anyone know a practical application where something
| like this would help?_
|
| It's another way to help verify super long calculations of pi
| are correct, and in turn I guess one basic "practical
| application" of calculating pi to many digits is as part of the
| suite for verifying new hardware. How do you know that fancy
| fresh new silicon is actually crunching the numbers correctly,
| not producing garbage in some subtle way at enough significant
| digits? While there are lots and lots of checks used to avoid a
| repeat of hardware bugs of days past (like the forever infamous
| Pentium FDIV), one simple sanity check/stress test is
| calculating out numbers like pi a bunch of different ways to
| huge numbers of digits and making sure the result is always
| correct. If it's not there's clearly a problem somewhere.
| chrisshroba wrote:
| I believe it can be used to verify calculations of new digits
| of pi. For example, if you tell me you just computed five
| trillion digits of pi, I can ask you for specific digits near
| the end and check that they match what this formula produces
| CSMastermind wrote:
| Wanted to compliment this paper for being well written. I'm not a
| practicing mathematician but I was able to easily follow along
| here and that was a cool feeling.
|
| Could someone who is a practicing mathematician speak to the
| practical application of this? From what I understand from
| reading this seems like an interesting curiosity but the
| Chudnovsky formula it refers to seems to be better at doing the
| same thing for any practical purpose.
| nico wrote:
| Is there a physical limit to how many digits of pi can ever be
| computed/represented in the universe?
|
| For example, let's say we need one atom for each digit of pi that
| we want to store, the max limit of digits of pi would be
| something like the total number of atoms in the universe, minus
| the atoms required to compute and store the digits.
|
| Has that been studied/calculated?
| telotortium wrote:
| in the title is a character I haven't seen before, [Mathematical
| Italic Small Pi](https://unicode-table.com/en/1D70B/).
| Sharlin wrote:
| Yes, and there's also bold (pi), bold italic (), sans-serif
| bold (), and sans-serif bold italic (), all distinct from the
| run-of-the-mill Greek Small Letter Pi (p) which is often
| rendered quite differently from the "standard mathematical pi"
| in addition to, of course, being semantically different.
| There's a lot of fun stuff in the Mathematical Alphanumeric
| Symbols block (https://unicode-
| table.com/en/blocks/mathematical-alphanumeri...)
| ars wrote:
| This is a type of https://en.wikipedia.org/wiki/Spigot_function
| if you want to lookup more info.
| saddist0 wrote:
| Something like this can be used for "proof of work" in the
| blockchain world.
| swazzles0 wrote:
| That's an interesting point. You could use this to hash 8-bytes
| values (assuming int64) with infinitely scaling difficulty by
| providing an offset to n where n = difficulty + n
| paulpauper wrote:
| There is nothing of note here. This paper should be in 'general
| math', not number theory. You need to know the Bernoulli numbers
| in order for this to work, which is more computationally
| difficult than computing pi. So what. Yeah, Plouffe is a famous
| person in computer science and math, but this does not measure up
| to the hype. It reminds me of the stuff i tinkered with in high
| school when i first learned infinite series ..but not
| publishable-level, sorry.
| dvt wrote:
| > but not publishable-level, sorry
|
| No one's saying it is, this is arXiv, after all (not a
| journal). Still a fun little interesting paper, though.
| Someone wrote:
| I would think the "explicit expression" part is new and enough
| to make it publishable, and fail to see why not being useful in
| practice ever should be a factor in determining whether
| something is number theory.
|
| Now, for the hype, I don't see any from the authors.
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