Wikipedia:Reference desk/Archives/Mathematics/2015 October 23

= October 23 =

5 millionth article
What is the predicted date and time? Anna Frodesiak (talk) 11:37, 23 October 2015 (UTC)


 * Have a look at Size_of_Wikipedia. Someone has fitted a model using Gompertz_function model of growth, but that fitting, done in 2010, has an asymptote at ~4.4 million articles. It is relatively straightforward to make a new fit to the data that would give an estimate for when we hit 5 million articles, or indeed to fit using some other type of growth function. Some other fun info at Statistics. Unless someone wants to do a bit of real work on fitting another curve, the best I can say using extrapolation is "probably sometime next year." SemanticMantis (talk) 17:07, 23 October 2015 (UTC)


 * "probably sometime next year." What graph are you extrapolating from?   shows 4,994,044 for the English Wikipedia, and with ~300K articles increase per year, I'd expect us to cross 5 million articles sometime next week.  Thursday at noon 1300 UTC would be my guess based on the 1055 articles per day year-to-date growth rate.  (Guesstimate based on values from WP:Size of Wikipedia.  6,000 articles-to-go / 1055 articles-per-day = 5.6872 days ≈ 5 days 16.5 hours.  A better guess could come from determining more recent (perhaps the last month's) growth rate, plus a look at whether there were any artificial spikes in growth rate near earlier "odometer turnover" times.) -- ToE 20:42, 23 October 2015 (UTC)
 * I was looking at the second graph in my first link, estimating the current more like 4.7 million, and forgetting that we still have a few good months left in this calendar year :) SemanticMantis (talk) 21:32, 23 October 2015 (UTC)
 * Thank you SemanticMantis and ToE. I'm going to go with what ToE says. :) But if you're ever my doctor saying how long I've got, I'll go with SemanticMantis. Anna Frodesiak (talk) 22:49, 23 October 2015 (UTC)
 * Ok, then I bet on anything between 00:00 Jan 1 2016 UTC and TOE's estimate. Let us know if you notice when it rolls over :) SemanticMantis (talk) 22:54, 23 October 2015 (UTC)
 * We will all notice. They will change the icon. :) Anna Frodesiak (talk) 23:43, 23 October 2015 (UTC)
 * Anna, will we get another piece added to the puzzle? -- ToE 22:09, 24 October 2015 (UTC)
 * The logo is discussed at WT:Requests for comment/5 millionth article logo. -- ToE 02:03, 29 October 2015 (UTC)
 * At 20:42 UTC today, we are at 4,994,668 articles, up 624 articles over the past 24 hours. At that rate, we should have the remaining 5,332 articles in just over 8 days 13 hours, or at a bit before 10:00 UTC on Monday, 2 November 2015.  I have not done any research on growth rates through 2015 beyond looking at WP:Size of Wikipedia and  yesterday and today (which at the time this page was last cached --  -- was  articles), but two ideas come to mind why the last 24 hours gave us only 624 additional articles instead of the 1055 articles per day were were running this year to date.  There may be day-of-week variations, and many Wikipedians were at the pub Friday night and slept in on Saturday instead of creating new articles.  More likely in my mind is that there was some editing trend which caused a spike of article creation earlier in the year, which has the YTD creation rate at 1055 articles per day despite a current growth rate in the 600 to 700 articles per day range.  The trend from the WP:Size of Wikipedia table has been a steady decrease of growth rate since 2006's 1822 articles per day, with the last three years running 814, 767, & 736.  This year's 1055 YTD number represents some sort of anomaly. -- ToE 22:09, 24 October 2015 (UTC)
 * Very, very interesting. Maybe it is in the news a bit so extra people have the idea of starting articles. I'm watching. :) Anna Frodesiak (talk) 23:25, 24 October 2015 (UTC)
 * 4,995,303 articles as of 20:42 UTC today, up 635 articles over the last 24 hours, giving a two day average growth rate of 629.5 articles per day, and a refined prediction of 7 days, 11 hours, and a few minutes from then, or about 08:45 07:45 UTC on Monday, 2 November 2015. -- ToE 22:04, 25 October 2015 (UTC)
 * -that would be the perfect birthday gift for me !!⇒-- Aryan fromहि है (talk) 07:46, 26 October 2015 (UTC)
 * 4,996,010 articles as of 20:42 UTC today, up 707 over the last 24 hours, giving a three day average growth rate of 655.3 articles per day, and a refined prediction of 6 days, 2 hours, and 7.5 minutes from then, or about 22:50 UTC on Sunday, 1 November 2015. -- ToE 23:48, 26 October 2015 (UTC)


 * For an earlier landmark, see WP:Millionth article FAQ.
 * Taking article deletions into account, it is possible to have multiple 5 millionth articles (an article created when there are 4,999,999 articles present), and all, some, or none may survive the the threat of subsequent deletion. -- ToE 14:41, 27 October 2015 (UTC)

Might be a dumb question, but what is the lag time between the number counter on the main page and the actual number of articles...? Cas Liber (talk · contribs) 01:29, 29 October 2015 (UTC)
 * I believe its only lag is due to the page's server cache. Purge discussed procedures for purging a page's cache, and for the Main Page, this URL will purge it's cache: https://en.wikipedia.org/wiki/Main_Page?action=purge
 * The result seems to be in sync with both Special:Statistics and the more terse https://en.wikipedia.org/w/api.php?action=query&meta=siteinfo&siprop=statistics&format=json
 * And those numbers do seem to be up to date, as if I track them I can see a new article appear on Special:NewPagesFeed at the same time the article count jumps. -- ToE 15:39, 29 October 2015 (UTC)
 * It seems to be accelerating. The table below looks several hours too slow....Cas Liber (talk · contribs) 01:16, 1 November 2015 (UTC)
 * (chuckle) a few of us tried to bum-rush it....so who nabbed the magic number? Cas Liber (talk · contribs) 12:36, 1 November 2015 (UTC)
 * You did! Congratulations.  I'm glad to see it go to such a prolific contributor, and there's something to be said about spotlighting our stubs, both for their own, intrinsic utility, and for their need to be fleshed out.
 * The bum-rush itself didn't surprise me, but the early acceleration did. I figured that there might even be a slowdown in the growth rate as the milestone approached and people held their preprepared articles in reserved to fire off all at the last moment.  I didn't even bother checking the stats today until shortly after the rollover had occurred. -- ToE 15:31, 1 November 2015 (UTC)

See: WP:Five million articles -- ToE 15:31, 1 November 2015 (UTC)

Daily growth rate table
Here is a table based on my 20:42 UTC readings (because that was when I took the first one), with the prediction disregarding any time-of-day variations (which are likely significant) in article creation (and deletion) activity. -- ToE 13:03, 27 October 2015 (UTC)

Currently:  articles as of.

The five millionth article, Persoonia terminalis (a botanical stub) was created by User:Casliber at 12:27, Sunday, 1 November (UTC).

There were at least 66 articles created between 12:27:00 (4,999,969 articles) and 12:28:00 (5,000,035 articles).

I only have a minute by minute log of the article count, so I don't know the specific deletion and creation rates, but can only see the net difference. I had planned on shifting my logging over to second by second, but the rollover caught me by surprise as I hadn't expected the creation rate to grow substantially until the count was closer to the milestone.

Casliber has long been a prolific creator of natural history stubs (primarily for biology and astronomy articles) and created 106 botany stubs today between 11:46 (article count = 4,999,749 @ 11:46:00) and 13:08 (article count = 5,000,170 @ 13:09:00), with Persoonia terminalis being the fifth of the six stubs they created at 12:27. -- ToE 14:41, 1 November 2015 (UTC)

Five virtual bucks on...

 * Saturday, 31 October 18:01 UTC Anna Frodesiak (talk) 00:03, 27 October 2015 (UTC)
 * Sunday, 1 November 20:42 UTC ToE 10:52, 28 October 2015 (UTC)

Growth rate tables
Hourly growth rate

Module:Chart does not display negative net growth rate bars (where there were more deletions than creations during the hour).

The Sunday 12h bar indicates that there was a net increase of 362 articles between 12:00:00 and 13:00:00.
 * 09h: +18, 10h: +35, 11h: +154, 12h: +362, 13h: +32, 14h: +72, 15h: +88

-- ToE 16:18, 1 November 2015 (UTC)

Per-minute growth rate

The 1227 bar represents the net increase of 66 articles between 12:27:00 and 12:28:00.
 * 1226: +10, 1227: +66, 1228: +52, 1229: +10

-- ToE 17:02, 1 November 2015 (UTC)

Perfect number generalization
Any formula anyone has for the following kind of number:

The sum of proper divisors of n is k*n, where k is a non-negative integer.

For k = 0, the only possible n is 1.

For k = 1, we have perfect numbers; starting with 6, 28, 496, 8128, 33550336, and 8589869056.

For k = 2, 120 is the smallest number that meets this criterion. That is, the sum of all proper divisors of 120 (1+2+3+4+5+6+8+10+12+15+20+24+30+40+60) is 240, or 2 times 120.

What's the smallest solution for k = 3?? How about k = 4?? Georgia guy (talk) 23:13, 23 October 2015 (UTC)


 * I don't know, but you might be interested in reading about a different generalization called Superperfect_numbers, or some of the generalizations described here . SemanticMantis (talk) 23:28, 23 October 2015 (UTC)


 * That article links to Multiply perfect number which answers the question I think. --RDBury (talk) 07:44, 24 October 2015 (UTC)
 * Yes, Multiply perfect number. When you know some terms of an integer sequence, try an OEIS search at http://oeis.org. A search on 1, 6, 120 leads to A007539. PrimeHunter (talk) 01:03, 28 October 2015 (UTC)