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Graph issue

I think the graph in the article is wrong. There is a slow increasing line between 1950 -1960 indicating every year a bigger Mersenne prime was found with an increase in size equal to the previous each year, then between approx. 1960 -1962 for two years the rate increased. in my opionion there should be horizontal lines between discoveries of the finds and no steady increase. for the last few years it does not matter that much as the rate of finds are increased so much that the graph will be about the same (i think the point of the graph)195.240.149.123 (talk) 04:30, 13 August 2010 (UTC)[reply]

I think one of the words is wrong:
I think that the plot is a "logarithmic scale" and not a "double logarithmic scale". The term semi-log plot
The x-axis of time is linear for the year, but the y-axis for number of digits is the base 10 log. Peter10003 (talk) 18:41, 29 July 2016 (UTC)[reply]
You are correct. The scale on the y-axis is a logarithmic scale not a double logarithmic scale. If it were a double logarithmic scale the values corresponding to those actually shown would be 2, 3, 4, 5, 6 and 7. The type of graph is a semi-log graph - specifically a log-lin graph. I have changed the wording on the graph. AirdishStraus (talk) 12:22, 30 July 2016 (UTC)[reply]
No, if you actually read the caption you will see that it (1) does not say that the graph is double-log scale, and (2) is completely correct. --JBL (talk) 13:51, 30 July 2016 (UTC)[reply]
Apologies if I didn't make myself clearer in the previous edit. The y-axis is a logarithmic scale of the number of digits of the prime number but is a double logarithmic scale (rounded down to the nearest power of 10) of the value of the prime number. AirdishStraus (talk) 14:08, 30 July 2016 (UTC)[reply]
I don't know where you got the idea that there is rounding being done; as far as I can tell this is not true. --JBL (talk) 14:12, 30 July 2016 (UTC)[reply]

The last 3 digits of 2n-1

Mn = 2n-1


its well known that you can build Mn digits using only the digits of n


lets show a few examples:


if the last 2 digits of n are ....17 then Mn last 3 digits have to be ....071

if the last 2 digits of n are ....23 then Mn last 3 digits have to be ....607


i will only show the roles for an odd n because we wanna use it for primes


p Mp
... 03 ... 007
... 23 ... 607
... 43 ... 207
... 63 ... 807
... 83 ... 407
... 07 ... 127
... 27 ... 727
... 47 ... 327
... 67 ... 927
... 87 ... 527
... 11 ... 047
... 31 ... 647
... 51 ... 247
... 71 ... 847
... 91 ... 447
... 19 ... 287
... 39 ... 887
... 59 ... 487
... 79 ... 087
... 99 ... 687
or
p Mp
... 09 ... 511
... 29 ... 911
... 49 ... 311
... 69 ... 711
... 89 ... 111
... 01 ... 751
... 21 ... 151
... 41 ... 551
... 61 ... 951
... 81 ... 351
... 17 ... 071
... 37 ... 471
... 57 ... 871
... 77 ... 271
... 97 ... 671
... 13 ... 191
... 33 ... 591
... 53 ... 991
... 73 ... 391
... 93 ... 791


just so you know the same works for 3 digits of n lets show a few examples:


2... 639-1 = 2... 139-1 = ... 1887

2... 711-1 = 2... 211-1 = ... 8047


etc ...


the same works for any k digits of n


but for really big numbers you need a LOT of computer power :)


Isaac.mor (talk) 12:03, 24 October 2014 (UTC)[reply]

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New Largest (Mersenne) Prime Found

A new Mersenne prime was discovered on Jan. 07 2016. See http://www.mersenne.org/primes/. This calls for a substantial edit to this page as well as many other wikipedia pages, because "largest prime", "second largest prime", and "largest mersenne prime" are used extensively referring to now-incorrect numbers.

66.31.237.80 (talk) 05:34, 24 January 2016 (UTC)[reply]

The new record has already been added to more than a dozen articles including several mentions in this one. If you know of a specific article or place that still needs an update then please post it. PrimeHunter (talk) 06:06, 24 January 2016 (UTC)[reply]

The number 2?

I freely admit to not being a mathemetician, or indeed particularly number-savvy with regard to primes, but there is an inconsistency in the article with regard to the number 2. Within the confines of this article, is "2" considered a Mersenne prime? Part of the article suggests it is, and part not.

In the history section, 2 is listed as a prime (and the section states that "His list was accurate through 31",) and the image includes 2 as a Mersenne prime, yet the rest of the article - especially the lede: "The first four Mersenne primes (sequence A000668 in the OEIS) are 3, 7, 31, and 127." - doesn't include 2.

I see that there is reference to two different OEIS sequences - one of which includes 2, and one that doesn't, however this is confusing to those who don't have an in-depth understanding of the subject matter. In short - as it currently stands the article is inconsistent, and should:

  1. the number "2" be included in the lede as the first five Mersenne primes,
  2. the rest of the article be adjusted to remove the number 2?
  3. a small explainer be added in somewhere to clarify the inconsistency, and why it is and isn't included in different parts of the article? Chaheel Riens

(talk) 06:28, 1 January 2017 (UTC)[reply]

The sequence containing the "2" refers to the exponent (power) in Mp = 2p − 1. None of the sequences say that "2" is a 'Mersenne prime'. AirdishStraus (talk) 10:35, 1 January 2017 (UTC)[reply]
Thanks for replying, but you're kind of proving my point. I look at that and go "What?" If it's not a Mersenne prime, why is it listed in the History section, and why is it highlighted in the image? (The image, incidentally does say that it's Mersenne prime: "The first 64 prime exponents with those corresponding to Mersenne primes shaded in cyan and in bold".) I'm not picking a fight here, I'm just pointing out an unexplained discrepency in the article. Chaheel Riens (talk) 11:21, 1 January 2017 (UTC)[reply]
2 is a Mersenne prime exponent but not a Mersenne prime. The exponent is p in Mp = 2p − 1. The Mersenne prime with exponent 2 is M2 = 22 − 1 = 3. It's cumbersome and unnecessary to write a list of Mersenne primes (or alleged Mersenne primes) as 22 − 1, 23 − 1, 25 − 1, 27 − 1, 213 − 1, 217 − 1, 219 − 1, 231 − 1, 267 − 1, 2127 − 1, 2257 − 1. The exponents are usually listed instead: 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257. PrimeHunter (talk) 12:02, 1 January 2017 (UTC)[reply]
Ok, I get it - just, but the history section states that the number "2" is a "Mersenne Prime", not an "Mersenne Prime exponent". that needs addressing then. Chaheel Riens (talk) 12:25, 1 January 2017 (UTC)[reply]
Where does it claim that? I see only "The exponents listed by Mersenne were as follows: 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257." --JBL (talk) 16:24, 1 January 2017 (UTC)[reply]
In the table description: "The first 64 prime exponents with those corresponding to Mersenne primes shaded in cyan and in bold". Again, I hold my hand up and say I'm no expert of any stretch in this field, but given that the number 2 is both shaded, and in bold - the associated text - "corresponding to Mersenne primes" - suggests that 2 is a Mersenne prime. This may just be a poor description that needs tweaking. Chaheel Riens (talk) 16:46, 1 January 2017 (UTC)[reply]
What that says is that 2 is a prime exponent, and that it corresponds to (not "is") a Mersenne prime. But mathematical English is not always clear to those not fluent in it; do you have a suggestion for rewording? --JBL (talk) 17:02, 1 January 2017 (UTC)[reply]

Not yet, but now that it's been explained to me, I'll certainly think about. I solidly fall into the "not fluent" category, and it puzzled the hell out of me. Chaheel Riens (talk) 18:29, 1 January 2017 (UTC)[reply]

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Unsourced "pyramid charts" addition by Kulprit001

Does anyone understand what [1] means? It's not a minor edit, it's unsourced, it's been undone by four different editors, and User:PrimeHunter has been unable to find anything about the claim [2]. Meters (talk) 04:28, 3 December 2017 (UTC)[reply]

It is not a claim, it is a fact that is useful for generating pyramid charts. You wont find out by googling it, you will find out by doing it. — Preceding unsigned comment added by Kulprit001 (talk • contribs) 04:42, 3 December 2017 (UTC)[reply]

My addition of " Can also be useful for calculating the space in between points on a pyramid chart as well as the space surrounding it, where n represents the amount of levels of divulgation." to the /* /* Mersenne numbers in nature and elsewhere */ is continuously challenged. However it is a provable mathematical fact, simply open up any image editor and draw any series of pyramid charts as pixels to properly illustrate the point. If you do not believe me try it for yourself. draw any pyramid chart, and count the spacing between between points and inversely the space surrounding the points and you will see that for n levels of dilvulgation, the spacing can be calculated with the Mersenne formula. If anyone want to change this again, please tell me that you have tried this for yourself. If so and you still do not believe me, than i would suggest that you think about it for a bit longer, before immediately dismissing it again. — Preceding unsigned comment added by Kulprit001 (talk • contribs) 04:30, 3 December 2017 (UTC)[reply]
We're asking your for an independent reliable source to verify the claim. See WP:RS. Original research is not acceptable See WP:OR. Continuing to edit war over this is not a good idea. Meters (talk) 04:37, 3 December 2017 (UTC)[reply]

Your right, it is not a good idea for you, but it is a good idea for the page. As a great man once said, "if you cannot see what is right in front of you then you are indeed a fool." Please physically investigate this for yourself before any further complaints. this is a useful addition not a reckless destruction, so please do not treat it as such. — Preceding unsigned comment added by Kulprit001 (talk • contribs) 04:47, 3 December 2017 (UTC)[reply]

Please stop the vadalism, or i will have to email wikipedia about this. i am making a valid useful contribution anyone who checks it out for themselves will understand on be on my side. i cannot provide a source for nature and basic geometry so i am sorry, but your just going to have to use your eyes and brains. — Preceding unsigned comment added by Kulprit001 (talk • contribs) 04:58, 3 December 2017 (UTC)[reply]

Following Wikipedia's established guidelines is not vandalism. Why are you not willing to read the policies other editors have referred you to in their edit summaries, and follow them? Your edit needs a source -- Wikipedia is not meant for original ideas/discoveries, even if they are correct. You are not allowed to revert more than 3 edits within 24 hours, but you did this 7 times already. This behavior could result in a block. Gap9551 (talk) 05:01, 3 December 2017 (UTC)[reply]

If i get blocked than that just proves that wikipedia is a useless pile of rubbish and that indeed the vast majority of people are in fact not intelligent at all, but petty belligerent fools. — Preceding unsigned comment added by Kulprit001 (talk • contribs) 05:07, 3 December 2017 (UTC)[reply]

After the comments by several editors, has the possibility occurred to you that you may misunderstand the purpose of Wikipedia? It gives an overview of established facts using sources; it is not a place to publish facts that lack such sources. Sources are not only needed to verify the correctness of facts, but also to show that these facts are important enough for inclusion in Wikipedia. Gap9551 (talk) 05:12, 3 December 2017 (UTC)[reply]

wikipedia, a pun for world wide web encyclopedia. encyclopedia, a book giving information. My addition is information that is immediately verifiable and self evident, and is therefore viable information. how is Wikipedia ever to improve if it seeks to remove and destroy basic facts? then it would be called wikibook. so i am sorry but you are all wrong. please read my addition more carefully, try it for yourself and ponder it for at least a day before even thinking about removing it as the is no logical or reasonable basis for doing so. — Preceding unsigned comment added by Kulprit001 (talk • contribs) 05:23, 3 December 2017 (UTC)[reply]

Actually, your addition is not clearly stated. "pyramid chart" is not defined or linked to. The "points on a pyramid chart" are not identified. Any 2D chart contains an infinite number of points so you'd need to define which you mean. "the space surrounding it" is vague. "Can also be useful" is vague, it does not say how exactly it would be useful. The meaning of "levels of divulgation" is not defined or linked to. But even if all this would be clarified, you'd still need a source. Gap9551 (talk) 05:28, 3 December 2017 (UTC)[reply]

PLEASE STOP UNDOING! there is no need to. it does not change anything, it only adds an additional valid & verifiable point, which is in the spirit of wikipedia. It is a description of an image therefore it require no citation. please read and understand the rules before attempting to enforce them. — Preceding unsigned comment added by Kulprit001 (talk • contribs) 05:28, 3 December 2017 (UTC)[reply]

PLEASE STOP UNDOING! there is no need to. it does not change anything, it only adds an additional valid & verifiable point, which is in the spirit of wikipedia. It is a description of an image therefore it require no citation. please read and understand the rules before attempting to enforce them. Draw a pyramid chart, count the spacing, if you still do not understand than i don't think you have any authority to undo it, because you obviously don't understand it therefore have no right to comment.— Preceding unsigned comment added by Kulprit001 (talk • contribs) 05:30, 3 December 2017 (UTC)[reply]

It's not a description of an image or chart. As has been pointed out, there is no image to describe. And what you are doing is making a claim about how Mersenne primes numbers can be used to analyse a particular type of chart, not describing the chart. Since you say on your talk page [3] that you have written an app that uses Mersenne primes numbers to do this, it appears that this is WP:OR. Meters (talk) 09:08, 3 December 2017 (UTC)[reply]


@Kulprit001:, the belligerent and pig-headed way you approached this discussion was always doomed to failure: Wikipedia works on a collaborative model, and if you can't explain to others what you're doing politely then it will never work. That being said, @Everyone else: Kulprit is almost certainly trying to express that the number of nodes in a full (or complete) binary tree with n layers is the Mersenne number 2^n - 1. (Or something equivalent.) This is a totally true thing. And in fact Mersenne numbers are a common answer to lots of enumerative combinatorial questions, although they aren't usually called "Mersenne numbers" in that context. It is a reasonable question about whether these combinatorial facts should be listed somewhere, either in the section Kulprit was trying to add to, or in a separate subsection called "in enumeration" or something. --JBL (talk) 14:37, 3 December 2017 (UTC)[reply]

If that is what Kulprit001 is trying to say, then yes it correct. If we want to include it then we need to express it in some manner that is comprehensible though. My opinion is that mentioning Mersenne numbers for complete binary trees alone is not warranted. As Joel B. Lewis points out, this relationship shows up in many enumerations. There's nothing special about binary trees. The solution to the Wheat and chessboard problem is exactly the same progression. for example. If we want to include this trivial relationship just mention it as the result of summing a geometrically doubling series starting at 1. The number of nodes in a complete binary tree can be listed as one of the examples. Meters (talk) 19:54, 3 December 2017 (UTC)[reply]

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Mersennes in nature and pernicious

I removed the following text from the introduction:

equivalently that they be pernicious Mersenne numbers, namely those numbers whose binary representation contains a prime number of ones and no zeros

and this from "Mersenne numbers in nature":

In computer science, unsigned n-bit integers can be used to express numbers up to Mn. Signed (n + 1)-bit integers can express values between −(Mn + 1) and Mn, using the two's complement representation.

Both are based on the belief that a Mersenne number is 2n−1, which is a mistake. The correct "pernicious" part is that there be a prime number of 1's followed by a large number of 0's that seems too trivial to bother mentioning (especially in an introduction). Zaslav (talk) 04:13, 6 October 2018 (UTC)[reply]

Incomprehensible paragraphs

The section about "primitive part" is impossible to understand to the largest part of it. For example,

Besides, if we notice those prime factors, and delete "old prime factors", for example, 3 divides the 2nd, 6th, 18th, 54th, 162nd, ... terms of this sequence, we only allow the 2nd term divided by 3, if we do, they are ...

The phrase is grammatically incorrect and incomplete, and it is not clear what the author wanted to say. It's similar for the whole subsection and a later one, probably from the same "contributor". Is anyone please willing to improve this? Such "contributions" are annoying, the article would be better without it. I'd suggest to move the subsection here (i.e., delete it from the main page) until it is rewritten in correct English. As it stands, it barely qualifies for a comment on this talk page. But I don't know whether doing so is (WP-)"politically correct". — MFH:Talk 17:48, 5 December 2018 (UTC)[reply]

@MFH: I agree and have removed the section. Which other section(s) have the same problem, in your estimation? --JBL (talk) 18:26, 5 December 2018 (UTC)[reply]
Incidentally, the section is at least 3 years old (I got bored of looking back further). --JBL (talk) 18:33, 5 December 2018 (UTC)[reply]

Mersenne numbers in nature and elsewhere

Hi, currently reads that the wheat and chessboard issue is solved by M64, which is not the case. It's solved by T64, which is not the same thing. This needs to be correctly rectified. Beast01998 (talk) 12:29, 15 February 2020 (UTC)[reply]

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