- I am wondering if this is positive or saying that it is not strong enough. I

also think I may be unclear so I restated it again below.

----- Original Message -----

From: "djbroadhurst" <d.broadhurst@...>

To: <primenumbers@yahoogroups.com>

Sent: Saturday, August 03, 2002 4:05 AM

Subject: [PrimeNumbers] Re: Andrica

> Let p and q be successive primes.

> Andrica conjectures that

> q - p < sqrt(q) + sqrt(p)

> whereas Tschebysheff proved merely that

> q - p < p

> which is far weaker.

rewriten as q < 2p

include p itself p < q < 2p

take sqrt, sqrt (p) < sqrt (q) < sqrt(2)*sqrt(p) --- length of side with

square q

take out the factor sqrt (p), 1< sqrt (q) / sqrt(p) < sqrt(2)

subtract the area p from q by

take the sqrt, sqrt (p)

take out the factor sqrt (p), 1 --- length of side with square p

so

1-1 = 0 < (sqrt (q) / sqrt(p) - 1) < sqrt(2) - 1

1 < (sqrt (q) / sqrt(p) - 1) < sqrt(2) - 1 < 1

using the difference of two squares

q - p = (sqrt(q) + sqrt(p)) (sqrt(q) - sqrt(p))

(q - p) / (sqrt(q) + sqrt(p)) = (sqrt(q) - sqrt(p))

and

(sqrt (q) - sqrt(p)) < (sqrt(2) sqrt(p)) - (sqrt(p))

(sqrt (q) - sqrt(p))/sqrt(p) < (sqrt(2) - 1)(sqrt(p))/sqrt(p)

S = sqrt (q) / sqrt(p) -1 < sqrt(2) - 1 < 1

so the first number with p = 2 is < 1 and the limit S as p -> oo = 0.

QED

I'm just a college student in physics so it would help if I could get some

feedback.

Thanks David.

John - What David is saying is that you have merely re-worked Tschebysheff's proof.

Without having put in anything extra into the system, all you have done is

find new expressions for existing formula.

As a Mathematician, your proof is lacking in several areas:

#rewriten as q < 2p

#include p itself p < q < 2p

This could be written as: there exists a prime q, p<q<2p

#take sqrt, sqrt (p) < sqrt (q) < sqrt(2)*sqrt(p) --- length of side with

#square q

#take out the factor sqrt (p), 1< sqrt (q) / sqrt(p) < sqrt(2)

OK.

#subtract the area p from q by

#take the sqrt, sqrt (p)

#take out the factor sqrt (p), 1 --- length of side with square p

#so

#1-1 = 0 < (sqrt (q) / sqrt(p) - 1) < sqrt(2) - 1

#1 < (sqrt (q) / sqrt(p) - 1) < sqrt(2) - 1 < 1

Line 2 makes no sense, nor does line 3

Line 5 is OK, but Line6 contains obvious errors.

At this point what we have is sqrt(q)/sqrt(p) - 1 < 1, which you managed to

get to in your first proof, but seem to have failed to in this one.

From here, we can get sqrt(q)-sqrt(p)<sqrt(p), but this is far from

Andrica's conjecture.

#using the difference of two squares

#q - p = (sqrt(q) + sqrt(p)) (sqrt(q) - sqrt(p))

#(q - p) / (sqrt(q) + sqrt(p)) = (sqrt(q) - sqrt(p))

#and

#(sqrt (q) - sqrt(p)) < (sqrt(2) sqrt(p)) - (sqrt(p))

#(sqrt (q) - sqrt(p))/sqrt(p) < (sqrt(2) - 1)(sqrt(p))/sqrt(p)

#S = sqrt (q) / sqrt(p) -1 < sqrt(2) - 1 < 1

#so the first number with p = 2 is < 1 and the limit S as p -> oo = 0.

#QED

With such a dodgy start, most Mathematicians would be rolling about on the

floor by now in tears, but persistence is to be encouraged.

Line 1 is good, but you can begin to see why this conjecture is considered

hard.

Line 2 is good.

After here, you need to explain where your subtitutions are coming from.

Also needed is a statement declaring how the algebra will lead to a proof of

the conjecture. This assists any reader in following your work, and takes

the pressure off the reader in trying to follow the work.

Jon Perry

perry@...

http://www.users.globalnet.co.uk/~perry/maths

BrainBench MVP for HTML and JavaScript

http://www.brainbench.com - --- Jon Perry <perry@...> wrote:
> With such a dodgy start, most Mathematicians would be rolling about

Jon,

> on the

> floor by now in tears, but persistence is to be encouraged.

I don't know if you're trying to be "Me Too" to David's "Big Dog",

http://www.winternet.com/~mikelr/flame3.html ?

However, you're not really in a position to make snide comments about

proofs, particularly in such a patronising way, and especially

considering some analyses of your own proof style (

http://groups.yahoo.com/group/primenumbers/message/7546 )

Phil

(No bonus points for spotting the irony herein!)

=====

--

The good Christian should beware of mathematicians, and all those who make

empty prophecies. The danger already exists that the mathematicians have

made a covenant with the devil to darken the spirit and to confine man in

the bonds of Hell. -- Common mistranslation of St. Augustine (354-430)

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