## Twin Prime Proof Erroneous 199

Posted
by
michael

from the 2+2=5 dept.

from the 2+2=5 dept.

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."*
## Idea may lead to new record, not twin prime proof (Score:5, Informative)

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.

## Re:Idea may lead to new record, not twin prime pro (Score:2)

I am definitely not flaming Dominic the poster, but if all the moderators that read this post understood it then I'd be real freakin' suprised. "Oh look! symbols! [+1 Informative]

## Re:Idea may lead to new record, not twin prime pro (Score:1)

I am definitely not flaming Dominic the poster, but if all the moderators that read this post understood it then I'd be real freakin' suprised. "Oh look! symbols! [+1 Informative]No offense taken!

## Re:Idea may lead to new record, not twin prime pro (Score:2)

...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,...Uh, yeah. So are my GPG keys safe or what?

## What the hell is wrong with you? (Score:2)

## reminds me of a bad math joke (Score:5, Funny)

## Re:reminds me of a bad math joke (Score:3, Informative)

Because he left his residue at every pole

Ducks

## Maths jokes = Instant karma! (Score:5, Funny)

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.

## Re:Maths jokes = Instant karma! (Score:2)

## Re:Maths jokes = Instant karma! (Score:2, Funny)

A man had to take a plane but he was very nervous thinking there might be somebody with a bomb on board. He went to the pilot and asked how likely it was that there was somebody with a bomb on board.

The pilot answered "Well, I wouldn't worry about it at all. It's very unlikely. Probably something like 1 chance in a million". The man feeling somewhat better then asked: "And what is the chance of that there are two bombs on board?".

## Re:Maths jokes = Instant karma! (Score:1)

## Re:Maths jokes = Instant karma! (Score:5, Informative)

Q: What did the constipated mathematician do?A: He worked it out with a pencil!

OK, not going to try to explain this one.

Q: What's purple and commutes?A: An Abelian grape.

A group is a set of things (think "numbers", but they could be sides of a cube, or colors, or anything you want) along with an operation defined on them (like addition or multiplication, but it doesn't have to work like those). When the operation on the group happens to be commutative (like 2+4 = 4+2), the group is called Abelian [wolfram.com]

Q: Why do you never hear the number 288 on television?A: It's two gross.

A "gross" is a dozen dozen, or 144. Not a very mathematical joke.

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.

The joke is referring to a Cross Product [wolfram.com], an operation defined on two vectors. You can't take the cross-product of 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.

When a mathematician needs to prove that A implies B, they may instead prove that A implies C where "C implies B" was already proved by someone else, or in a previous theorem.

Q: What's big, grey, and proves the uncountability of the reals?A: Cantor's diagonal elephant.

The joke is referring to the Cantor Diagonal Argument [wolfram.com], a proof technique that Cantor originally used to prove that even if you tried to associate one real number with every integer, there'd still be real numbers left over. (Amazingly, you can "count" the rational numbers - i.e. all of the possible fractional numbers. As a math major to show you sometime, it's a neat trick.)

Q: What's yellow and equivalent to the Axiom of Choice?A: Zorn's Lemon.

Zorn's Lemma [wolfram.com] is a mathematical statement which turns out to be true if the Axiom of Choice is assumed to be true, or false if the Axiom of Choice is assumed to be false.

Q: What's yellow, normed, and complete?A: A Bananach space.

A is space (a set of numbers with a lot of useful operations defined on them) that has a normalization operator defined, and is "complete", which means that the limits of all sequences you can define using numbers in the space are also in the 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.

A Sylow p-Subgroup [wolfram.com] is a certain type of subgroup (see the definition of a group above).

Q: What is often used by Canadians to help solve certain differential equations?A: the Lacrosse transform.

The is a technique that makes certain differential equations a lot easier to solve - essentially you take a complicated D.E., substitute certain things in place of any derivatives you see by looking them up in a table, then solve the resulting equation using normal algebra, and finally transform it back also by looking up things in a table.

Q: What is clear and used by trendy sophisticated engineers to solve other differential equations?A: The Perrier transform.

The Fourier Transform is also used in signal processing, including sound analysis and sound compression algorithms like MP3 and Ogg Vorbis.

Q:## Re:Maths jokes = Instant karma! (Score:4, Informative)

The joke is referring to the Laplace transform. There is no Lacrosse transform.

The del operator is fundamental in vector calculus. You can define the gradient, curl, divergence and the Laplacian with it. It's also known as nabla.

No. You're talking about the gradient descent method. The method of steepest descent is a way to find the asymptotic series of a function. I know Weisstein's Mathworld [wolfram.com] agrees with you, but check their references on that page. Arfken and Morse, Feshbach agree with me! I know because I've been studying those two books on this very subject the whole evening before I checked Slashdot. I was mightily surprised to see the method's name mentioned here, believe me.

## Re:Maths jokes = Instant karma! (Score:1)

Q: What is very old, used by farmers, and obeys the fundamental theorem of arithmetic?A: An antique tractorisation domain.

You missed this one. The joke is referring to unique factorisation domains. For example, the integers is a unique factorisation domain. 12=2*2*3, 15=3*5... You know what it means. Of course, changing the order of the factors doesn't count as a different factorisation.

## Re:Maths jokes = Instant karma! (Score:1)

Sorry to reply again, but this one still needs clearing. Pole is always a singularity. In fact an analytic function may have two different kinds of singularities: poles and essential singularities. Poles are those singularities that can be removed by multiplying the function with a polynomial of a high enough degree. For example, 1/

## Re:Maths jokes = Instant karma! (Score:1)

## Re:Maths jokes = Instant karma! (Score:2)

Just to be extra pedantic. . .

The cross product is in fact only defined for pairs of (real, i think) 3-vectors.## Re:Maths jokes = Instant karma! (Score:5, Funny)

## Re:Maths jokes = Instant karma! (Score:1)

shouldn't all the Poles be in the lhp?

Pardonne

## Re:Maths jokes = Instant karma! (Score:2)

s/pilot/copilot/

s/left/right/

## Missed one (Score:2)

Well, the special day finally arrives when all three women go into labor. The shaman directs them to go to the specially prepared tent and each lie down on one of the animal skins.

The woman on the deer skin gives bir

## Re:Maths jokes = Instant karma! (Score:2)

Q: What's purple and commutes? A: An Abelian grape.Q: What's purple, commutes, and has $N$ worshippers?

A: A finitely-venerated abelian grape.

Moooooooooooahahahahah

## Re:Maths jokes = Instant karma! (Score:2)

## Re:reminds me of a bad math joke (Score:2)

They see a prize buck.

One statistician fires... Bang... 10 meters to the left.

The second statistician fires... Bang... 10 meters to the right.

The third statistician jumps up and down, yelling "We Got It!".

## Error? (Score:1, Funny)

## from a mathematics student (Score:4, Funny)

## The Slashdot effect (Score:3, Funny)

## Re:The Slashdot effect (Score:1)

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!

Maybe they should set the maximum connections on the server to a prime number.

## Re:The Slashdot effect (Score:1)

## I have an alternate proof (Score:5, Funny)

## Re:I have an alternate proof (Score:2)

## Re:I have an alternate proof (Score:2)

## Re:I have an alternate proof (Score:1)

100 pages of plain text, assuming a maximum of 200 characters per line and no more than 70 lines, runs to just 14,000 characters100 x 200 * 70 > 14,000.

## Re:I have an alternate proof (Score:1)

## Re:I have an alternate proof (Score:2)

read what he typed again

100 x 200 * 70 > 14,000he wrote an inequality

## wow, that's gotta suck (Score:5, Insightful)

man. i feel sorry for those guys

## Re:wow, that's gotta suck (Score:1)

## mirror (Score:5, Informative)

aimath.org/primegaps/residueerror/ [roysdon.net]

I'm still working on mirroring all 47 images, but the text is there, and the img tags have great alt text descriptions.

## A serious question - i'm not trolling, honest! (Score:2, Interesting)

I'm well aware of what primes are, I just have never found a use for them!

## Re:A serious question - i'm not trolling, honest! (Score:2, Insightful)

## Re:A serious question - i'm not trolling, honest! (Score:5, Informative)

The longer answer to your question is: who the hell knows? One of the fascinating things about math is how results that seem utterly abstract when they're [invented | discovered] (not going to get into that argument right now) turn out to have profound applications years or decades or even centuries down the road. Linear algebra was an interesting but rather small and not terribly important field of study before computers came along

The twin prime problem may remain a curiosity of number theory forever, or it may turn out to be fundamental to some new application that's just down the road; there's no way to know. But given the history of math's progress from pure theory to the basis of technology we use every day, I'm betting on the latter.

## Re:A serious question - i'm not trolling, honest! (Score:1)

Whether knowing anything about the occurrence of twin primes has any bearing on crypto, I have no idea.I have very little knowledge of primes and cryptography, but I do know that the holy grail is the search for larger primes.

Could the importance of twin primes be that if a corrolary is found that will allow one to predict higher prime numbers because of the

nthat separates them, it would then become easier to "discover" larger and larger prime numbers?## Re:A serious question - i'm not trolling, honest! (Score:3, Informative)

I do know that the holy grail is the search for larger primes.Actually, finding large primes is pretty easy [wolfram.com]. Taking a large number and finding its prime factors is not. This conjecture/proof doesn't seem to have any immediate bearing on cryptography.

TTFN

## Re:A serious question - i'm not trolling, honest! (Score:3, Informative)

## Re:A serious question - i'm not trolling, honest! (Score:2)

## Re:A serious question - i'm not trolling, honest! (Score:5, Informative)

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.

## Re:A serious question - i'm not trolling, honest! (Score:4, Funny)

$ factor 2715992561127159925611: 3 7 13 13 17 19 19 29 43

$ echo '13*17*19*29*57*91*43' | bc

27159925611

Thus, on the command line, the factorization is easier!

## Re:A serious question - i'm not trolling, honest! (Score:4, Informative)

Now factoring a number 200 digits long with only two (and equally-sized) factors would be a world record.

## Re:The sibling comments are being wiseass. (Score:2)

sure

18446743979220271189! =

184467439220271189 *

184467439220271188 *

184467439220271187 *

...

5 * 4 * 3 * 2

That was easy!

## Re:The sibling comments are being wiseass. (Score:1)

## Re:The sibling comments are being wiseass. (Score:5, Informative)

If you're so damn good at factoring products of primes, factorise 18446743979220271189!No sweat: 4294967279 * 4294967291

Everybody knows, that the best tool for factoring numbers is google:

http://www.google.ca/search?q=18446743979220271189 [google.ca]

## Re:How to be a threat to national security (Score:1, Insightful)

see: here [utm.edu] for proving primality and

here [utm.edu] for some other interesting facts about primes.

Why do I point you to pages about primes, when you're talking about factoring? Well

## Re:A serious question - i'm not trolling, honest! (Score:4, Interesting)

How, exactly, is calculating billions of digits of pi useful, again?

On the other hand, primes are used for all kinds of good stuff, such as protecting your credit card numbers from evil people. Your conceptions seem backwards.

## Re:A serious question - i'm not trolling, honest! (Score:1)

2. Test out new computer hardware/software

3. The thrill of the chase. Some people climb mountains, other people calculate billions of digits of Pi.

## Re:A serious question - i'm not trolling, honest! (Score:1)

1. To look for patterns (See Carl Sagan/Contact)Right.... You'd be more productive feeding the Bible into a random number generator.

2. Test out new computer hardware/softwareThis is not useful. There are better ways to test hardware/software.

3. The thrill of the chase. Some people climb mountains, other people calculate billions of digits of Pi.This is not useful.

If you're going to reply to posts, you should try to be more relevant to what they say. I never said calculating billions of digits was bo

## Re : Necessity of calculating pi? (Score:5, Informative)

I can understand calculating pi to the nth point as it is used in calculationsEven 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.

## Re:A serious question - i'm not trolling, honest! (Score:1)

Nevertheless, prime numbers are important for cryptography. This has to do with factoring a number into prime powers. Any positive integer can be written uniquely as a product of prime powers. If I give you two primes such as 6421 and 7873, it's easy to just multiply them and get 50552543. However, given 50552543 it's not at all obvious that the only way to write this as a product

## Re:A serious question - i'm not trolling, honest! (Score:2)

With all due respect, who cares? What sort of benefit does the mankind get from the Mona Lisa? From NASCAR? From owning pets? Need I go on . . . . ?

Why does everything have to be for some benefit? Most math

doesn'thave an application, not now and not ever. We're doing more math everyday than we'll ever find uses for. Mostly it is an aesthetic pursuit. People## Re:A serious question - i'm not trolling, honest! (Score:5, Interesting)

No; we calculate the umpty-bazillionth digit of pi for the same reason Mallory wanted to climb Everest:

because it's there-- and there's cool shit to see along the way.## Art, not engineering (Score:2)

You do it because the problem is beautiful and the solution is likely to be beautiful. If you are lucky the solution will turn out to be not only beautiful but also make a statement about life (or some aspect of life).

## For crying out loud! (Score:5, Funny)

## What is really important (Score:3, Insightful)

## Re:What is really important (Score:1)

What would be really important is to prove the Reimann Hypothesis. That would tell us a lot about the distribution of primes.Actually that's the R

iemann hypothesis, but your mistake seems to be a common misspelling, so don't feel too bad.It would be nice to know that the Riemann Hypothesis is true. You see the prime counting function pi(x) (= number of primes less than or equal to x) can be approximated with the integral Li(x) = integral from 0 to x of 1/log(t) dt. The Riemann hypothesis is equivalent to

## cough (Score:1)

## Re:cough (Score:3, Funny)

i've concluded that the most popular phrase on slashdot is 'order of magnitude'Yeah, and it's not even close. "order of magnitude" is more popular by a... heck of a lot. (heh.)

## Re:cough (Score:2)

n : ???

(n+1) : Profit!

## They could still pull it out (Score:3, Interesting)

## Re:They could still pull it out (Score:2)

## Re:They could still pull it out (Score:1)

## I found the proof... (Score:5, Funny)

Unfortunately, I devoured it. Damn you Bill Cosby!

## Re:I found the proof... (Score:1)

In the query string

'jlo_family_pudding'## I still wouldn't mind... (Score:2, Funny)

## Re:I still wouldn't mind... (Score:2, Funny)

## 2+2=3 (Score:1)

from the 2+2=5 deptStep 1: -1/1 = 1/-1

Step 2: Taking the square root of both sides:

Step 3: Simplifying:

Step 4: In other words, i/1 = 1/i.

Step 5: Therefore, i / 2 = 1 / (2i),

Step 6: i/2 + 3/(2i) = 1/(2i) + 3/(2i),

Step 7: i (i/2 + 3/(2i) ) = i ( 1/(2i) + 3/(2i) ),

Step 8:

Step 9: (-1)/2 + 3/2 = 1/2 + 3/2,

Step 10: and this shows that 1=2.

therefore 2+2=1+1=3; QED

Thanks for the proof [toronto.edu]

## Re:2+2=3 (Score:2)

1/9 = .11111111 repeating

* 9 *9

---- ----------

9/9 = .99999999999 repeating

1 = .99999 repeating

Granted, the parent post isn't true while mine is but this is cool to show to people who aren't that math knowledgable. Had some guy looking at it for 2 hours trying to find the problem in it.

## Re:2+2=3 (Score:2)

## Damn it! (Score:4, Funny)

## Re:anyone got some asprin? (Score:2)

Realgeeks.It would also appear that their server was a bit fragile, it isn't responding fast and I think it'll be succumbing to the

## Re:anyone got some asprin? (Score:5, Informative)

## Re:anyone got some asprin? (Score:1)

## Re:anyone got some asprin? (Score:4, Funny)

## Re:anyone got some asprin? (Score:1)

## Not a bad question (Score:2)

Matt Fahrenbacher

## Re:i dunno man (Score:1)

Hmm... I wonder why I was modded down when it was neither a flamebait nor was it offtopic?

## If the cures need a more powerful computer... (Score:1)

Knowledge never is a waste of time.

## IANAMathGeek, but (Score:3, Insightful)

## Re:If the cures need a more powerful computer... (Score:1)

## Re:i dunno man (Score:1, Offtopic)

How much more do we need to know about the causes for cancer or AIDS?Shouldn't we be looking for the cures instead?I am firmly convinced that people with this attitude should be killed and eradicated from the face of the earth as soon as possible. Perhaps I should not "feed the troll", but rest assured this shall be the vilest meal this troll will eat, and I've karma to burn.

Trust too, alas, that I'm far too much of a coward to seek out this troll and perform the deed myself. But, this is Slashdot, an

## Re:i dunno man (Score:1)

## Re:imagine that! (Score:3, Funny)

## Re:imagine that! (Score:3, Funny)

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.

## Re:The answer... (Score:1)

## Even more (Score:2)

We know that 42 is the answer, but we don't know what the question is. Clearly we haven't found the question yet.

Matt Fahrenbacher

## Re:Even more (Score:2)

i interpereted this as a kind of "indirect proof", whereby if you can actually prove that 6x9=42, you can prove literally anything.

## Re:Even more (Score:2)

i interpereted this as a kind of "indirect proof", if you can actually prove that 6x9=42I interpreted this as implying that the universe was created in Base-13 [google.com].

## Re:predicted posts to this article (Score:2)

## Formulajamboree v2.0 (NEW with correct formatting) (Score:1, Troll)

WOMEN = TIME x MONEY (Logical statement that women require time AND money - statement only TRUE when both "time" and "money" are TRUE)

TIME = MONEY ("Time is Money")

WOMEN = (MONEY)^2

MONEY = sqrt(EVIL) ("Money is the Root of all evil)

WOMEN = (sqrt(EVIL))^2

WOMEN = EVIL

## Boolean addition versus multiplication (Score:3, Interesting)

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

## Re:Boolean addition versus multiplication (Score:2)

Correct. Which is exactly why I stated that both TIME and MONEY had to be "true" for the whole stateme

## It's true! (Score:4, Funny)

I love being a mth dork

Matt Fahrenbacher