Twin Primes

[CRGreathouse]

Originally Posted by Hugh

On reflection I think axn was right about the last prime. The existence of gaps means we need ever higher primes to fill the gaps, but not necessarily ever higher twin primes. Doh.

Recognizing that your argument was mistaken puts you above almost everyone else I've conversed with who has come up with this same proof; maybe there's still hope.

If you really look over it you'd see that what it actually proves (when appropriately cleaned up) is this: that for any N, there exist infinitely many pairs (n, n+2) where no prime smaller than N divides either member.

[Hugh]

Originally Posted by R.D. Silverman

What I have never been able to understand is how people without a
math degree can EVER delude themselves into thinking that they
can magically contribute something to a famous unsolved problem.

It's a good question, and no, I'm not usually the sort of person who thinks he can find the cure for cancer. So it's interesting to observe myself sliding into cranksville on this particular occasion.

Here's an honest answer. The problem with maths is perhaps that untrained people can just about get a grip of what some incredibly difficult problems involve. Any idiot like me can get their head around stuff like what twin primes are and what the Goldbach Conjecture means.

And then, one of the nice things about maths is when you do occasionally have sudden moments of revelation, which can be immensely gratifying. (By which I only mean basic stuff like seeing why a well known proof like that for the infinitude of primes works, or whatever.)

On this occasion I started out getting fascinated by patterns in numbers with no idea I could find anything new out. (I was a decent mathematician at school, was accepted for a maths degree, but changed course, and now haven't done any for years, so have forgotten a huge chunk of what I once knew.)

I recently rediscovered the fun of it, at a fairly basic level, mostly from having to explain stuff to my daughter. I was just getting my head around some of the absolute basics like why all primes over 3 are 6n + or - 1 and what happens when you multiply two of them together, why that is always the difference between two squares, and how that relates to the basic geometry of squares, rectangles, and series of consecutive odd numbers etc. I've always liked that pattern of successive odd number differences you get from 5x5, 4x6, 3x7 etc and was interested to realise that was also related to the Goldbach problem.

I was happy enough pottering about, but then had a deranged moment when I saw the way that the repeating primorial patterns in twin primes and chains of Goldbach pairs are related by the 2/p thing, and at about the same time realised how that fraction Euler equated to the harmonic series works. Then I just got thoroughly carried away with myself. I feel foolish now, deservedly so.

Anyhow, my point is that maths is a subject in which you can suddenly understand just enough to make wild claims, but not enough to see why they are so wild. But I swear I won't make a habit of it.

[Hugh]

Originally Posted by CRGreathouse

Recognizing that your argument was mistaken puts you above almost everyone else I've conversed with who has come up with this same proof; maybe there's still hope.

If you really look over it you'd see that what it actually proves (when appropriately cleaned up) is this: that for any N, there exist infinitely many pairs (n, n+2) where no prime smaller than N divides either member.

Yes, that seems correct. Thanks.

[cmd]

perhaps 1 play dice ?

columns x p

[davar55]

Originally Posted by R.D. Silverman

Maybe if you actually bothered to LEARN some mathematics instead
of spouting drivel (in this case about "averaging" and "sieving") you
would look less like a crank.

Go learn some number theory. Start with Hardy & Wright.
If you want to have even a basic understand of sieve methods, you
need to read Halberstam and Richert's book.

You are a classic crank. --> ignorant yet believing that you can somehow
prove a result that has eluded the world's finest mathematics for centuries.

STOP

Isn't the author of this diatribe cranky?

[cmd]

where are the quadruplet

see

[cmd]

Some sources also call {5, 7, 11, 13, 17, 19} a prime sextuplet. Our definition, all cases of primes {p-4, p, p+2, p+6, p+8, p+12}, follows from defining a prime sextuplet as the closest admissible constellation of six primes.
A prime sextuplet contains two close pairs of twin primes, a prime quadruplet, four overlapping prime triplets, and two overlapping prime quintuplets.

SEX_TUPLE_T :

column which contain "prime sextuplet" ?

b y d i c o p x

It is not known if there are infinitely many prime sextuplets. Once again, proving the twin prime conjecture might not necessarily prove that there are also infinitely many prime sextuplets. Also, proving that there are infinitely many prime quintuplets might not necessarily prove that there are infinitely many prime sextuplets.

p,s, ;-)) ah ... forget that we have to be eccentric people .. (rank

[cmd]

7°°|\/|

^^^^^^

u say "z()()m


column "i" in light colors

try reverse colors (link "| \ / |") to see what
happen


Note the circled

[davar55]

Originally Posted by R.D. Silverman

Maybe if you actually bothered to LEARN some mathematics instead
of spouting drivel (in this case about "averaging" and "sieving") you
would look less like a crank.

Go learn some number theory. Start with Hardy & Wright.
If you want to have even a basic understand of sieve methods, you
need to read Halberstam and Richert's book.

You are a classic crank. --> ignorant yet believing that you can somehow
prove a result that has eluded the world's finest mathematics for centuries.

STOP

The author of this diatribe is extremely cranky today.
I wonder wonder why.

[cmd]

(_|\/|_)

|\/|

cWd

[davar55]

I have a foundational question:

Does anyone (in the world) know for certain
that no one in the world has ever successfully,
completely, accurately, mathematically proved
the twin prime conjecture, i.e. that there are
an infinite number of pairs of consecutive
(differing by two) positive prime integers?

IOW is it possible (in your view) that such a proof
was kept secret?