Talk:Andrica's conjecture

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Comment to User:Mathsci, all graphs are COMPUTED and programmed by ME - Danko D. Georgiev, in Wolfram's mathematica 5.2. I have released my figures under GFDL. The text is definition, and re-worded from definition which is available at MathWorld but also appears at numerous other sites -- Perez Danko Georgiev MD 10:40, 10 June 2007 (UTC)

On User:Mathsci misunderstanding of Andrica's conjecture
User:Mathsci, repeatedly stated he is PROFESSIONAL MATHEMATICIAN!!! THIS IS UTTER NONSENSE -- it is impossible for professional mathematician to misunderstand such a simple definition of math conjecture. Hence I conclude User:Mathsci is anonymous self-proclaimed vandal, several times he reverted my edits of Florentin Smarandache, and also accused me several times for violations of copyrights, in cases where I have released MY OWN intellectual property - graphs or text. User:Mathsci: Thus if $$x$$ is the Smarandache constant defined as the solution of $$127^x - 113^x=1$$, the conjecture states that $$p_{n+1}^y - p_{n}^y <1$$ if $$y<x$$. Ha-ha. I GUESS this is text produced of professional mathematician??? Hi-hi. This is the most funny thing I have read. The Smarandache constant is defined as the smalles possible x amongst all solutions $$x_1, x_2, ...,$$ of all countable but infinite list of equations, generated when you substitute n=1,2,3 ... in
 * $$ p _ {n+1} ^ x - p_ n ^ x = 1 $$

So, you have the infinite list
 * $$ p_{2} ^ x - p_1 ^ x = 1 $$ -- solution $$x_1$$
 * $$ p_3 ^ x - p_2 ^ x = 1 $$ -- solution $$x_2$$
 * $$ p_4 ^ x - p_3 ^ x = 1 $$ -- solution $$x_3$$

...

So in this notation of all $$x_i$$ the solution $$ x_{30}$$ is the smallest, and it appears for the 30th prime $$p_{30} = 113$$. I hope after you have revealed enough your math incompetence you will stop bother me. I now fully recognize that you ARE NOT PRO MATHEMATICIAN, but self-proclaimed layman. Danko Georgiev MD 13:20, 10 June 2007 (UTC)

Inequality vs. equation
Obviously User:Mathsci had big problems with the proper understanding of the Generalized Andrica's conjecture written as equation. So I have added explicitly stated inequality, which is redundant. IF one knows the generalized Andrica equation and its minimum solution, one can write down infinite number of inequalituies any way he likes. Danko Georgiev MD 01:58, 11 June 2007 (UTC)

Inserted edit by unknown user
The following passage " Andrica's conjecture can be rewritten to simply state that

$$g(p_n) < 2\sqrt{p_n} + 1, where g(p_n)= p_{n+1} - p_n$$." has been inserted by unknown user. I don't see "why" this expression is "simply" or "simpler" than the provided in the text, so I have removed it. Please discuss. Danko Georgiev MD 03:05, 22 June 2007 (UTC)

If you look at the first sentence of the page, it mentions prime gaps. But, it does not mention the "how" connection between prime gaps and the square root of two consecutive primes. The point of the added sentence is to make that connection for the reader. I know that I may have not wrote in a clear way - that is my issues with a LD, but I know the reader does need a connection between these concepts.

If you like another page which would show that connection can be made, but why when you can do it yourself?
 * Hello, thanks for the provided clarification. Why don't you open an account, and contribute to Wikipedia? If you need some help and question, please ask me after you have opened an acount. Anonymous edits are not necessarily bad, however the communication with the editor is lost. For example the edit can be occasional, and a reader might not have the chance to ask for clarification. Regards, Danko Georgiev MD 02:58, 27 June 2007 (UTC)

Empirical evidence
Several comments on http://primepuzzles.net/conjectures/conj_008.htm might be useful.

Reddwarf2956 (talk) 12:53, 25 May 2009 (UTC)

Possible source
It seems likely that the following would be a useful reference:  The Zentralblatt review describes it as "a summary of the current results concerning the author's conjecture". Spectral sequence (talk) 17:09, 5 August 2013 (UTC)

External links modified
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Andrica's Conjecture is true for any tandem of positive real numbers differing by 2.
Andrica's Conjecture is true if the smaller number is greater than 0.25 (such that the larger number is larger than 2.25). That the two numbers are a pair of twin primes is just a special case. 2605:E000:6246:ED00:4F8:3C2B:8ECC:9A33 (talk) 16:37, 19 November 2019 (UTC)