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
Twin primes are two prime numbers that differ by a value of two - for instance, 17 and 19, or 29 and 31.
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.
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!
For example, in mathematics, it is a well-known fact that it is an easy problem to multiply two numbers. It is a very hard problem to take a number and factor it into the numbers that were multiplied to get the number, especially if it is a very large number.
If we multiply two very large prime numbers, the result is a very large number that is very difficult to factor; when it is factored, the result will be that it factors only into the original two very large prime numbers.
Prime numbers also have application in the idea of 'remote coin flipping.' ie. Using prime number theory, it is in theory possible for me to do the equivalent of flipping a coin and you having to guess if it's heads or tails.
If you still don't understand, consider this. Which is easier to do:
Multiply 13*17*19*29*57*91*43
--or--
Factor 27159925611 into it's prime factors.
If you can find an easy way to do the second problem, you just might find yourself considered a threat to national security.
Wh47 d1d j00 541, 31337 15n't t3h r0xor5 ne m0r3???
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".
No sweat: 4294967279 * 4294967291
Everybody knows, that the best tool for factoring numbers is google:
http://www.google.ca/search?q=18446743979220271189