Talk:Oppermann's conjecture

Correction in the page name

A correction in the page name is needed after researching the reference. I found that many use the misspelling of L. Oppermann's name.

Reddwarf2956 (talk) 01:11, 6 December 2010 (UTC)

I have moved it from Opperman's conjecture to Oppermann's conjecture. PrimeHunter (talk) 02:21, 6 December 2010 (UTC)

Thanks Reddwarf2956 (talk) 02:36, 6 December 2010 (UTC)

Multiple Issues

How do you remove the "This article has multiple issues" block since now it does have a cited source? I see other conjectures have been linked to it also. However, these link make need to be corrected for the name change stated above. Reddwarf2956 (talk) 03:21, 6 December 2010 (UTC)

You can just remove {{Multiple issues}} from the article source when the issues have been resolved. PrimeHunter (talk) 03:27, 6 December 2010 (UTC)

proven?

vixra.org/pdf/1303.0047v1.pdf

they claimed that they have proven this conjecture, should we re-write the content?--EPN-001GF IZEN བཀྲ་ཤིས་བདེ་ལེགས། 19:51, 6 February 2014 (UTC)

Vixra preprints (like arXiv preprints) are self-published sources and therefore unreliable. Vixra has the additional problem that it is largely seen as a fringe site for people who don't want to conform to even the very minimal submission standards set at arXiv. (For mathematics, the arXiv rules amount to: they won't take a preprint that claims a breakthrough on a known open problem but appears to be completely devoid of new ideas that might be able to solve the problem. For computer science, the rules are even weaker: it has to be formatted as a paper.) So the answer is: no. Unless this result is published in a reliable mathematics journal, or well-known experts come out to say that it is valid, it is not usable as a source here and we should hold off on doing anything. See also WP:DEADLINE. —David Eppstein (talk) 02:34, 7 February 2014 (UTC)

viXra is an unreliable source for the same reason that arXiv or any other e-print repository is an unreliable source: it does not have peer-review. The statement above by Eppstein is false on numerous levels. arXiv's requirements for submission say nothing about breakthrough claims or new ideas. They require that the author has an endorser and meets some technical formatting requirements. Such endorsers are hard to come by for many independent scientists regardless of the quality of their research. This is why they use viXra instead. Weburbia (talk) 08:31, 8 December 2014 (UTC)

Source #2, after translation from Danish to English does not contain the information claimed in the article

I relied on Wikipedia to find out what the source of Oppermann's conjecture was, but when I paid for a translation from Danish to English, it does not say that there is a prime number from x^2 to x^2 + x, or that there is a prime number between x^2-x and x^2.

The article I was reading was titled: Om vor Kundskab om Primtallenes Mængde mellem givne Grændser.

Af

Lndv. Oppermann.

(Meddelt i Mødet den 10de Februar 1882.) — Preceding unsigned comment added by 2001:1970:4FA0:A900:1532:DBCD:CBCF:B4C6 (talk) 21:45, 17 September 2019 (UTC)

I found https://archive.org/stream/oversigtoverdetk1881kong/oversigtoverdetk1881kong_djvu.txt which includes the 1882 article. It's a text file which must be based on flawed OCR, for example calling him "Ludr. Oppermaiin", but it's good enough to guess that the article does mention the conjecture. It says:

ved samme Lejlig- hed meddelte jeg den endnu ikke beviste Erfaringssætning, at der, naar n er et helt Tal >• 1 , ligger mindst eet Primtal mellem ?i(w — 1) og iv- og ligeledes mellem n- og n(n -\- 1).

I'm Danish and don't need a translation but can make one. The Danish is good so the used OCR probably had a Danish dictionary to help guess words, but it's poor at guessing formulas where it lacks context. Assuming it's sensible mathematics and not random characters, "?i(w — 1) og iv" must be OCR guess of "n(n − 1) og n²", while "n- og n(n -\- 1)" must be "n² og n(n + 1)". My direct translation then becomes: "at the same occasion I announced the not yet proven experience statement that there, when n is an integer > 1, lies at least one prime number between n(n − 1) and n², and also between n² and n(n + 1)." PrimeHunter (talk) 00:06, 18 September 2019 (UTC)

Okay. I see the statement now. Sorry for the mistake. One thing I do want to note, however is that he doesn't say explicitly that he himself was the person who formed the conjecture in March 1877, just that he "informed" it. As a non-Danish speaker, I can believe that the word "informed" in my translation could very well be better translated as "announced". Still, this article does provide a mention of the conjecture. I have copied the text from my translation and pasted it below.

Legendre was, as far as is known, the first to specify such (although only approximately valid) law, namely that the quantity of prime number below the boundary x should be

approximately A and B being Constants determined by experience; he demonstrated that A = 1, B = 1 08366 gives very good results up to x = 10 6 . J. W. L. Glaisher has (in the 3rd volume of Proceedings of the Cambr. Philos. S o c.) shown that when A = I, then one cannot stand by assuming B constant. Already-9. In March 1877, I pointed out in our company (in an unpublished lecture) that A and B are determined by the quantity of the prime numbers calculated by Meissel for Boundaries 10 7 and 10 8 , giving A = 1 0030514 1/6, B = 1 1201812 4 / 7, then far better results are obtained than when A = 1, B == 1 08366, but needing to end with A l.x - B adding new parts or considering A or B (or both) as constants, but as functions of x; at the same occasion I informed the unproven experience statement that when n is an integer > 1, at least one prime number lies between n (n - 1) and n 2 and also between n 2 and n (n + 1).

"meddelte" could also be translated as informed and other words but I think it indicates something coming from him or somebody he speaks on behalf of, not something he just read or heard somewhere. "meddelte" is a word made from "delte med" which translates directly as "shared with". If he was speaking on behalf of somebody then I would expect him to name the person, especially when he names many others and it's part of a carefully written text. But it's 137 years old and I'm not an expert on old Danish. PrimeHunter (talk) 23:45, 18 September 2019 (UTC)

About the prime gap

here; it is given as gn<√pn; but I am not able to find the source. If there is a source, shouldn't there be a link to the consequence attached to it? ISHANBULLS (talk) 12:12, 28 April 2020 (UTC)

It is a direct consequence and it is explained in the following paragraph. Jeanlucaslima (talk) 14:07, 2 June 2023 (UTC)