Re: twin prime conjecture

In article <1160515285.625915.191680@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"larry.freeman@xxxxxxxxx" <larry.freeman@xxxxxxxxx> wrote:

Hi Everyone,

To make it easier for people to follow my argument, I have put together
an informal version of the proof that reduces the main argument to 1
page:

http://proposedproofs.blogspot.com/2006/10/twin-prime-conjecture-informal-proo
f.html

You can still find the complete proof here:

http://proposedproofs.blogspot.com/2006/10/proposed-proof-twin-prime-conjectur
e.html

-Larry


larry.freeman@xxxxxxxxx wrote:
Hi Math Experts,

My name is Larry Freeman and I am a math amateur. I have a draft of a
proposed proof of the twin primes conjecture which can be found here:
http://proposedproofs.blogspot.com/2006/10/proposed-proof-twin-prime-conject
ure.html

I would greatly appreciate it if someone who is an expert in number
theory could take a look at it and explain to me where I went wrong.
This solution came too easily to me for it to be correct.

I've spent close to 2 weeks time on the proof and the argument seems
very solid to me. It is based on very elementary number theory. The
proof is only 9 pages.

Before I spent a second looking at your write-up, you have to
convince me that you can actually do some number theory. Here
are 5 problems for you, problems that would not be out of place
in an intro number theory course. If you can't do them, there
isn't the slightest chance that you can do something as hard
as the twin prime conjecture.

Good luck. And please don't top-post.

1. Show that if integers x and y can be expressed as a sum of
two squares of integers, then so can xy.

2. Prove that the cube root of 36 is irrational. Prove that
the base-10 logarithm of 2 is irrational.

3. Find the smallest positive integer n such that 2 n is the
square of an integer, 3 n is the 3rd power of an integer, and
5 n is the 5th power of an integer.

4. The Fibonacci numbers are given by F_0 = 0, F_1 = 1, and
F_n = F_(n - 1) + F_(n - 2) for n = 2, 3, ... (so they go
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, ...). Let phi be the
number (1 + sqrt 5) / 2. Prove that
phi^(n - 1) < F_(n + 1) < phi^n if n > 1.
Prove that F_1 + F_2 + F_3 + ... + F_n = F_(n + 2)  - 1.

5. Find, with proof, an irreducible polynomial that has
sqrt 2 + sqrt 3 as a root.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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