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Smarandache constant (Conjecture)

The Smarandache constant is the minimal solution $x_{\min}$ of the generalized Andrica equation: $p_{n+1}^{x}-p_{n}^{x}=1$ where $p_n$ is the n$^{{th}}$ prime number, and $x \in \mathbb{R}$ . The exact value of the Smarandache constant and whether it exists is currently unknown, however according to the generalized Andrica conjecture proposed by Florentin Smarandache the value of the Smarandache constant is $x_{\min}\approx0.5671481302\ldots$

The Smarandache constant should not be confused with a list of sixteen Smarandache constants $s_{1}-s_{16}$ defined as limits of different convergent series involving the Smarandache function.




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"Smarandache constant" is owned by dankomed.
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See Also: Florentin Smarandache

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Cross-references: Smarandache function, convergent series, limits, Florentin Smarandache, generalized Andrica conjecture, prime number, equation, solution, minimal
There are 2 references to this entry.

This is version 14 of Smarandache constant, born on 2007-06-22, modified 2007-07-18.
Object id is 9642, canonical name is SmarandacheConstant.
Accessed 1253 times total.

Classification:
AMS MSC11A41 (Number theory :: Elementary number theory :: Primes)

Pending Errata and Addenda
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Open access for editting by dankomed on 2007-07-25 09:53:30
Well, I am leaving open for editting the created by me entries.

The idea for this encyclopedia is suitable for anonymous edits, unfortunately I have been met with requests to post and reveal my I.P. and to confirm my identity, now this information is used in highly un-ethical way. I have no time to lose in ridiculous debates and since I shall not contribute, please edit the entries in the most appropriate way, according to your own taste.

Regards :-)

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dankomed's incorrect use of minimum by vonneumann on 2007-07-18 03:16:08
dankomed has now reverted his article on Smarandache's constant to his initial account. This defines the constant as the minimum of a countable set of positive numbers. Such a minimum need not exist, although the infimum always will. This is incorrect mathematics.

dankomed has failed to include the fact that the constant is the value of x for the prime pair (113,127). So the article is technically and factually inaccurate.
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Smarandache constant by asteroid on 2007-07-16 17:05:54
I'm new in PM. I decided to give my contribute here because, among other reasons, I like this feeling of doing something that (I believe) has some social and even scientific importance..

But then I started seeing all this Smarandache stuff, the entries and the discussions in the forums, etc.. and suddenly I lost all the will I had two weeks ago..
I'm not really sure if want to keep doing this anymore. Am I the only one who feels that?

Concerning this entry on the Smarandache constant I would just like to say this:
 - Why all that discussion of whether the generalized Andrica conjecture is provable, disprovable or undecidable and the bifurcation stuff??
 I mean, it can be done for every single conjecture in mathematics..
 That absolutely DOES NOT give ANY importance to that Smarandache constant at all!!

I don't demand an answer from the owner of this entry for two reasons:
1- It is a rhetorical question.
2- I don't wish to start or participate in any discussion about this Smarandache stuff.

I just wanted to post this here so that people can be aware of the controversy around Smarandache and the possible fraud that is still taking place.

Thank you,
Rui
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Smarandache constant by vonneumann on 2007-07-14 19:06:23
Dankomed should stop writing mathematical drivel. This contribution is
a disgrace.
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