Talk:Skewes's number

Confusion
The results from google are confusing, can't guarantee the accuracy of this article. &#1603;&#1587;&#1610;&#1662; Cyp 13:32 20 Jun 2003 (UTC)

I believe the treatment in mathworld, which this article follows, is wrong. I edited the article to reflect my current understanding. AxelBoldt 14:06, 30 Sep 2003 (UTC)

So, what's the best known lower bound for Skewes' number? this seems a rather interesting mathematical constant.

How is it that $$e^{e^{e^{79}}} \approx 10^{10^{10^{34}}}$$ if
 * $$e^{e^{e^{79}}} \approx$$
 * $$e^{e^{2.038 \times 10^{34}}} =$$
 * $$e^{\left(e^{2.038} \right)^{10^{34}}} \approx$$
 * $$e^{7.677^{10^{34}}} << $$
 * $$10^{10^{10^{34}}}$$

MIT Trekkie 07:35, Dec 17, 2004 (UTC)
 * With really large numbers, the concept of approximately equal is much broader, since such numbers are difficult to even write down with precision. For example, $$e^{e^{e^{79}}} \approx 10^{10^{10^{33.9470483816574311735621520930}}}$$. A small uprounding in the last exponent causes an enormous increase in the power tower, but they are so large numbers that nobody can notice. However, I'll change the text to a slightly more accurate value.--Army1987 15:46, 7 August 2005 (UTC)

Is Skewes' first name Samuel or Stanley? The :de wiki says Stanley, but I always thought it was Samuel. Both have references on Google.

Demichel result
It seems to me that the Demichel result should not be included here, as it appears not to have been properly reviewed and published (i.e., it violates WP:OR). Can anyone explain why it should stay? I notice that MathWorld includes it, but I don't think that's a good reason for it to be here. Doctormatt 00:52, 17 August 2007 (UTC)
 * Good point. (I'm going to be away from the Wiki for a bit, so I don't have time to look at it in detail.)  It doesn't seem to have been published, and it states it's probable that it's the correct answer, without giving an estimate of the probabilities in question.  &mdash; Arthur Rubin |  (talk) 01:00, 17 August 2007 (UTC)
 * MathSciNet makes no mention of anything published by Demichel. Doctormatt 01:14, 17 August 2007 (UTC)
 * If WAREL had removed Demichel, as well as adding his 2006 result, he wouldn't have been blocked. I don't know why he doesn't support his edits when he has support, but.... &mdash; Arthur Rubin |  (talk) 01:16, 17 August 2007 (UTC)
 * OOPS, it looks as if WAREL's result is from arXiv, which is not much better. &mdash; Arthur Rubin |  (talk) 01:21, 17 August 2007 (UTC)
 * Do you mean the Chao/Plymen result? Yes, that is unpublished and I think we should remove it, too.  Doctormatt 01:56, 17 August 2007 (UTC)
 * I'm at WP:3RR for a few more hours. Someone else will have to revert.  &mdash; Arthur Rubin |  (talk) 07:10, 17 August 2007 (UTC)

Possible Category Misplacement
I believe that the placement of this article into Category:Integers is perhaps mathematically incorrect. The article gives reference to the "historical" Skewes' number (i.e. the 1933 upper bound proven assuming the RH), which cannot be an integer (or rational number, for that matter) which is implied by the fact that e is irrational. The article also speaks of a Skewes' number (in some sense) in which I believe there is very little reason to believe that the "true" Skewes' number given by the least upper bound for a violation of the defining inequality is an integer. It seems to me that it would be very odd and unnatural and perhaps even disconcerting if the least upper bound (Skewes' number) was given by an integer exactly. For, while the prime counting function takes on only integer values in its range, the logarithmic integral function is continuous (even if defined around its point of discontinuity by the Cauchy principal value of the defining integral), and so moves through a range of values continuously except at prime arguments. This would seem to indicate that the chances of Skewes' number being an integer are pretty much nil. If this seems to be too picky, feel free to ignore me, but it seems to me that placing the article in the integers category would likely be mathematically incorrect. 75.204.164.105 10:01, 3 October 2007 (UTC)


 * You are right. I removed the Integers categorization. Owen&times; &#9742;  12:07, 3 October 2007 (UTC)

Genitive spelling
I tried to fix the spelling of the article name but I was persuaded to revert because this is a common error in publications. --Yecril (talk) 21:14, 5 October 2008 (UTC)


 * English is my second language and I'm not good at English grammar but spelling like in Skewes' number seems common to me and OK with Wikipedia talk:WikiProject Grammar which mentions the similar Selous' Mongoose. There is Requested moves if you want more input. PrimeHunter (talk) 22:01, 5 October 2008 (UTC)

If s/he is called Skewe it should be Skewe's number. If s/he is called Skewes, it is fine. However, I have found evidence that his/her name is Skewe at http://thinkzone.wlonk.com/MathFun/BigNum.htm


 * His name is Stanley Skewes and the article should remain at Skewes' number. CRGreathouse (t | c) 23:21, 4 December 2009 (UTC)

Asimov's article
In 1975 Dr Isaac Asimov wrote a book "Of matters great and small", which contained an 1974 article about the Skewes' number entitled "Skewered!". In this article he elaborates on the magnitude of the Skewes' number and developes a "T number" notation method for trying to judge the relative size of competitive number values.WFPM (talk) 12:04, 9 August 2009 (UTC) PS It's too bad he didn't live long enough to write about Graham's number.


 * Thanks, that sounds like a good reference for us to work into the article somehow. &mdash; Carl (CBM · talk) 12:24, 9 August 2009 (UTC)

First Skewes' number
I am interested in the first Skewes number, but could not know how it came up. Could some explain? Particularly, I want to know why the number 79 takes place. Thanks. Motomuku (talk) 00:34, 21 November 2009 (UTC)

Point of View
The article includes In the unlikely event that the Riemann hypothesis is false ... Isn't this POV and against Wiki rules? Jamesdowallen (talk) 16:44, 28 January 2010 (UTC)
 * It is tricky to talk about the "likelihood" of a mathematical hypothesis being true or false. But in this context, considering almost all mathematicians would be greatly surprised if RH is shown to be false, and taking into account the vast literature supporting this view (much of it referenced in the RH article), I'd say the statement is supported by the current prevailing view among mathematicians, not that of the editor. The editor correctly reflected that consensus in his comment. Owen&times; &#9742;  17:22, 28 January 2010 (UTC)

To CRGreathouse
There's nothing to discuss. It's all written in the second and third pages of Chao-Plymen's. Cheers.Orera (talk) 20:17, 10 December 2010 (UTC)
 * Yes, and I have a more recent source that improves on Chao & Plyman. CRGreathouse (t | c) 23:37, 10 December 2010 (UTC)
 * I've added a reference, as requested. CRGreathouse (t | c) 07:33, 12 December 2010 (UTC)

Leading digits
First digits of "number of digits" of first Skewes' number are: 330029255166326825898754163191261961592660037254068... (there are exactly 8852142197546379817324538072456058 (~8.852 decillion) digits).

First digits of "number of digits" of second Skewes' number are: 19250175074550025517358274500420096629624959931105... (there are ~ 10963 digits).

All computed by logarithms and very precise calculators like this: --http://markknowsnothing.com/cgi-bin/calculator.php

Is it possible to determine leading digits in decimal expansion of Skewes' numbers? 31.42.235.14 (talk) 10:20, 31 October 2012 (UTC)

A question, probably idiotic and probably also out of place, but nevertheless ...
From the article:


 * John Edensor Littlewood, Skewes' teacher, proved (in (Littlewood 1914)) that there is such a number (and so, a first such number); ...

Why does it follow that there is a first number. Littlewood proved, according to the wording here, that there is an upper bound. I can't for the life of me see that a first number has to be a consequence of that. What am I missing? All the best 85.220.22.139 (talk) 01:46, 9 March 2013 (UTC)


 * Please disregard the text above. The prime counting function is discrete. Mea culpa, but I just came home from a party, so ... Well, write drunk, edit sober. All the best 85.220.22.139 (talk) 01:51, 9 March 2013 (UTC)

What's ment by e^{727.9 ..}?
What is really ment by " e^{727.95133} " ? I presume e to be the base of the natural logarithms, around 2,71. But the exponent - is it 72795133 or 727,95133 ? If the first is corret (which seems likely, then why the dot. I mean 72.795.133 wouldn't be difficult to understand but the "3 dot 5" figures makes me uncertain. Boeing720 (talk) 17:58, 3 May 2014 (UTC)


 * It's a correctly used decimal point and shouldn't be changed. You are from a country where a comma is used instead (so am I), but this is the English Wikipedia and a period is dominant in English speaking countries. See our Manual of Style at WP:DECIMAL. PrimeHunter (talk) 18:20, 3 May 2014 (UTC)

This article needs an explanation of what it is about.
This may all be very interesting to mathematicians, but there is no attempt at explaining to the lay reader what Skewes' number is about / for. Could someone please add a paragraph to summarise what the significance of this subject is? Richard75 (talk) 15:33, 27 August 2017 (UTC)

I agree with Richard! Us dummies want to know the significance of this finding.- tim