RE: [PrimeNumbers] Re: Andrica
- 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
#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
#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
#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))
#(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.
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
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@...> wrote:
> With such a dodgy start, most Mathematicians would be rolling aboutJon,
> 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",
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 (
(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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