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# Andrica’s conjecture

Conjecture (Dorin Andrica). Given the $n$th prime $p_{n}$, it is always the case that $1>\sqrt{p_{{n+1}}}-\sqrt{p_{n}}$.

This conjecture remains unproven as of 2007. The conjecture has been checked up to $n=10^{5}$ by computers.

The largest known difference of square roots of consecutive primes happens for the small $n=4$, being approximately 0.67087347929081. The difference of the square roots of the primes $10^{{314}}-1929$ and $10^{{314}}+2318$ (which cap a prime gap of 4247 consecutive composite numbers discovered in 1992 by Baugh & O’Hara) is a very small number which is obviously much smaller than 1.

# References

- 1 D. Baugh & F. O’Hara, “Large Prime Gaps” J. Recr. Math. 24 (1992): 186 - 187.

Synonym:

Andrica conjecture

Type of Math Object:

Conjecture

Major Section:

Reference

## Mathematics Subject Classification

11A41*no label found*

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## Comments

## Update of entry?!

Dear Prime Fan, I have updated the article in Wikipedia here

http://en.wikipedia.org/wiki/Andrica%27s_conjecture

please tell me whether you can update it here also, for example is there any way that images are incorporated in PlanetMath posts. I am newcommer here, your help is appreciated.

D. Georgiev

## Re: Update of entry?!

Dear Danko Georgiev, I can update it here also but not today. You'll have to give me a few days to absorb the update. I don't know of any way to incorporate images into PlanetMath posts. It's been hard enough for me to figure out how to get them into PlanetMath articles.

John

## Incorporation of graphics

Dear prime fan,

if you want I can send you .eps files of the Andrica function, some of them I have uploaded in Wikipedia. Then you can attach them to the entry, and then incorporate the images into the PlanetMath article with the command \includegraphics{name} .. of course first you have to start the \usepackage{graphicx} in the preamble of the PlanetMath entry by deletion of the "%" sign !!! This is what I have discovered today :-)

Please check the entry generalized Andrica conjecture opened by me --

http://planetmath.org/?op=getobj&from=objects&id=9636

and you can improve the entry on Andrica conjecture.

p.s. I think the "'s" is not needed in the title.

Danko

## Parentheses holdover

I removed parentheses per one of Mathprof's corrections but they're still showing in HTML w/images even after a rerender. I think it's just a stubborn cache on my side.

## Re: Parentheses holdover

One of my objects was doing the same thing last night...it made me loony. It's working properly now though...just give it some time I suppose :)

## Re: Parentheses holdover

The holdover's done. Now I'm convinced that, as azdbacks4234 said, it's just a matter of giving the client-side cache time.

## Re: Incorporation of graphics

Thanks for the offer, but I can make graphics like these myself quite easily. Adding graphics to this is on my to do list but it's not as urgent as some other things I have to take care of, especially thanks to the graphics you have included in your entry. As for the title, the "'s" should, if nowhere else, at least be included in the synonyms field because we can be sure at least a few people will search for it that way.