Slashdot Mirror
Twin Prime Proof Erroneous
mindriot writes "The fairly recent perceived breakthrough in prime number theory regarding twin primes, as mentioned on slashdot, is apparently not quite perfect: 'On April 23rd, Andrew Granville of the Universite de Montreal and K. Soundararajan of the University of Michigan found a technical difficulty buried in one of the arguments in the preprint of Goldston and Yildrim. The main issue is that some quantities which were believed to be small error terms are actually the same order of magnitude as the main term. For now this difficulty remains unresolved.' A more detailed technical description is also available."
The last paragraph of the "more detailed technical description" is interesting (shown here in LaTeX notation):
The consensus is that the definition of $\gamma_R$ needs to be changed so that terms like this one do not appear. However, it is not obvious how to do this change. Work is continuing by Goldston and Yildirim and others to rectify the problem. It does seem reasonable to believe that an improvement on the current world record for small gaps between primes will be achieved by these methods; however, the more dramatic result $p_{n+1} - p_n < (\log n)^\alpha$ for some $\alpha < 1$ seems less likely.
Unless I'm misunderstanding something, it would be more clear if they said that the inequality above holds for infinitely many $n$, because it certainly couldn't hold for all $n$.
Essentially they're claiming that it's less likely now that the twin prime conjecture will ever be proved using this method, but there's still a pretty reasonable chance that the proof will result in something along the lines that there are infinitely many pairs of consecutive primes that differ only by x, where x is not quite as small as 2 (which is what the twin primes conjecture says) but x is smaller than any value of x that was previously proven. Which would be cool, but nothing to open champagne over.
heard this in an engineering class the other day... What's the contour integral around Western Europe? A: Zero, because all the Poles are in Eastern Europe!
Scott
I have no idea how this proof works because the server melted already.
Wh47 d1d j00 541, 31337 15n't t3h r0xor5 ne m0r3???
Their webserver it seems, " is apparently not quite perfect:" It has already been /.ed
Obviously evidence of a conspiracy to cover up the mistakes in the theorem. Sssshhh!
Twin primes are two prime numbers that differ by a value of two - for instance, 17 and 19, or 29 and 31.
but the space that I'm allowed to type in here is too short.. :-)
There's a gorilla from Manilla whose a fella that stinks of vanilla and has salmonella.
To think you solved something like that, and to be ready to publish, after all that hard work.... then...... oops. guess that doesns't work
man. i feel sorry for those guys
/bin/fortune | slashdotsig.sh
aimath.org/primegaps/
aimath.org/primegaps/residueerror/
I'm still working on mirroring all 47 images, but the text is there, and the img tags have great alt text descriptions.
Yeah, right, like I can imagine CmdrTaco rejecting a story because he read the math and found the error.
I see a lot about these sorts of massive mathematical problems. I can understand calculating pi to the nth point as it is used in calculations, but what sort of benefit does mankind get from working out twin primes? In fact, do primes do anything for us anyway?
I'm well aware of what primes are, I just have never found a use for them!
This story doesn't have anything to do with SCO! Come on, where's today's SCO story? This isn't funny, man, I need my fix!
Q: What did the constipated mathematician do?
A: He worked it out with a pencil!
Q: What's purple and commutes?
A: An Abelian grape.
Q: Why do you never hear the number 288 on television?
A: It's two gross.
Q: What do you get when you cross a mosquito with a rock climber?
A: Nothing. You can't cross a vector and a scalar.
Q. How many mathematicians does it take to change a lightbulb?
A. 1, he gives the lightbulb to 3 engineers, thus reducing the problem to a previously solved joke.
Q: What's big, grey, and proves the uncountability of the reals?
A: Cantor's diagonal elephant.
Q: What's yellow and equivalent to the Axiom of Choice?
A: Zorn's Lemon.
Q: What's yellow, normed, and complete?
A: A Bananach space.
Q: What is very old, used by farmers, and obeys the fundamental theorem of arithmetic?
A: An antique tractorisation domain.
Q: What is hallucinogenic and exists for every group with order divisible by p^k?
A: A psilocybin p-subgroup.
Q: What is often used by Canadians to help solve certain differential equations?
A: the Lacrosse transform.
Q: What is clear and used by trendy sophisticated engineers to solve other differential equations?
A: The Perrier transform.
Q: Who knows everything there is to be known about vector analysis?
A: The Oracle of del phi!
=======
Halfway through a recent airplane flight from Warsaw to New York, there was nearly a major disaster when the flight crew got sick from eating the fish. After they had passed out, one of the flight attendants asked over the intercom if there were any pilots in the cabin.
An elderly gentleman, who had flown a bit in the war, raised his hand and was rushed into the cockpit of the 747. When he got there, took the seat, and saw all the displays and controls, he realized he was in over his head. He told the flight attendant that he didn't think he could fly this plane. When asked why not, he replied,
"I am just a simple Pole in a complex plane"
So, they just had to rely on the method of steepest descents.
=======
You know that during the Great Flood, Noah brought along two of every species for reproductive purposes. Well, after a few weeks on the ark, all the couples were getting along fine, except for these two snakes. Day and night, Noah worried that this was going to mean the end of this species.
Finally when the flood ended and the ark hit ground, the two snakes darted out of the ship and headed to the nearest picnic table where they started to "go at it". It was then that Noah realized that...
Adders can't multiply without their log tables.
Note to M1-ers: a curt but otherwise insightful message is not "Flamebait" or "Troll".
Yeah, right, like I can imagine CmdrTaco rejecting a story because he read the math and found the error.
Actually, the most probable result is that CmdrTaco read the story and didn't find the error, but the error's order of magnitude was too large and so it resulted in a dupe.
"The large print giveth, and the small print taketh away" -Tom Waits
Even the most precise calculations don't need that many digits of pi. It's amazing how fast orders of magnitude build up.
Take this extreme example. Suppose you know the radius of the galaxy (define the radius going out to the galactice halo, for instance) to arbitrary precision and your calculation of the circumference is limited only by the precision of pi. If you want to know the circumference town to 10^-15 meters (ie, about the size of an atomic nucleus). How many digits of pi are sufficient?
The radius of the Milky Way galaxy out to the galactic halo is about 65,000 light years, or about 6e20 meters. Only 36 digits of pi would be necessary!!! And this extreme example is of many orders of magnitude larger than precisions of anything that can be calculated in laboratories today. In actuality, one wouldn't really need more then 12-15 digits of pi, if even that much.
make world, not war
2+2 does equal 5, for sufficiently large values of 2.
:)
I love being a mth dork
Matt Fahrenbacher
James Tiberius Kirk: "Spock, the women on your planet are logical. No other planet in the galaxy can make that claim."
it's not pointless, that"s why you were modded down. Now don't ask ME what the point is, i really suck in mathematics (but stil love it though) but if you see somewhere the word 'prime', think computer en/decryption, et. c. i even guess it could be used for cancer research....
What would be really important is to prove the Reimann Hypothesis. That would tell us a lot about the distribution of primes.
If I remember correctly:
;)
true + true = true
true + false = true
false + true = true
false + false = false
and
true x true = true
true x false = false
false x true = false
false x false = false
Which means that addition is like or'ing booleans together and multiplication is like and'ing booleans together. Therefofore, multiplication would seem to be the correct operation, as women are both time and money, not one or the other.
QED
Matt Fahrenbacher
James Tiberius Kirk: "Spock, the women on your planet are logical. No other planet in the galaxy can make that claim."
Yeah, and it's not even close. "order of magnitude" is more popular by a... heck of a lot. (heh.)
Remember that an error was found when the British mathematician first announced that he had a proof of Fermat's Theorem a few years ago. He was able to fix it, however, and AFAIK his proof is currently considered sound (albeit LONG).
This post is dedicated to all of those
It was in here.
Unfortunately, I devoured it. Damn you Bill Cosby!
No sweat: 4294967279 * 4294967291
Everybody knows, that the best tool for factoring numbers is google:
http://www.google.ca/search?q=18446743979220271189
I still wouldn't mind these guys helping me understand my calculus homework...
Fuck! <> Back to my job at the gas station, I guess....