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New Pattern Found in Prime Numbers
PhysOrg.com ^ | May 8th, 2009 | Lisa Zyga

Posted on 05/10/2009 5:17:09 PM PDT by decimon

In a recent study, Bartolo Luque and Lucas Lacasa of the Universidad Politécnica de Madrid in Spain have discovered a new pattern in primes that has surprisingly gone unnoticed until now. They found that the distribution of the leading digit in the prime number sequence can be described by a generalization of Benford’s law. In addition, this same pattern also appears in another number sequence, that of the leading digits of nontrivial Riemann zeta zeros, which is known to be related to the distribution of primes. Besides providing insight into the nature of primes, the finding could also have applications in areas such as fraud detection and stock market analysis.

(Excerpt) Read more at physorg.com ...


TOPICS: Science
KEYWORDS: math; mathematics; numbers; pattern; patterns; prime; primenumbers; stringtheory
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Yeah, but sub-prime numbers qualify for TARP funds.
1 posted on 05/10/2009 5:17:09 PM PDT by decimon
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To: decimon

Just goes to show that we can find GOD in the smallest of places.


2 posted on 05/10/2009 5:21:55 PM PDT by TMSuchman (I'll heat up & bring the tar, you bring the feathers & we'll meet in DC!)
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To: decimon

lol!


3 posted on 05/10/2009 5:22:00 PM PDT by CodeToad (If it weren't for physics and law enforcement I'd be unstoppable!)
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To: decimon

It would be wrong of me to describe something that I don’t understand as worthless, because what do I know? Well, at least this little study didn’t cost me anything. I hope.


4 posted on 05/10/2009 5:23:58 PM PDT by Batrachian
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To: decimon
Besides providing insight into the nature of primes, the finding could also have applications in areas such as fraud detection and stock market analysis.

And also in cryptography, relating to Public Key Encryption. It might be that it wasn't unnoticed, but the notice was just in classified papers.

5 posted on 05/10/2009 5:25:00 PM PDT by PapaBear3625 (The problem with socialism is that you eventually run out of other people's money -- Thatcher)
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To: Batrachian
It would be wrong of me to describe something that I don’t understand as worthless...

Are you joking? Don't you realize what advanced derivative securities can be...derived from this?

6 posted on 05/10/2009 5:26:34 PM PDT by decimon
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To: decimon

This is hugh. I am series.


7 posted on 05/10/2009 5:27:59 PM PDT by PackerBoy (Just my opinion ....)
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To: TMSuchman

That’s the first thing I thought.


8 posted on 05/10/2009 5:30:06 PM PDT by Crawdad (If you're in a fair fight, your tactics suck.)
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To: PackerBoy
I am series.

Quite a claim in a math thread.

9 posted on 05/10/2009 5:30:52 PM PDT by decimon
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To: PackerBoy
Who is Hugh Series?
10 posted on 05/10/2009 5:32:53 PM PDT by Keith in Iowa (ESPN MNF: 3 Putzes talking about football on TV while I'm trying to watch a game.)
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To: TMSuchman
Just goes to show that we can find GOD in the smallest of places.

Have you been there? How small is the university exactly?

Universidad Politécnica de Madrid in Spain

I doubt God hangs out in a Spanish university, but who knows?

11 posted on 05/10/2009 5:32:54 PM PDT by humblegunner (Where my PIE at, fool?)
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To: decimon

>>I am series.
>
>Quite a claim in a math thread.

Not unlike “I Am Legend”


12 posted on 05/10/2009 5:32:56 PM PDT by OneWingedShark (Q: Why am I here? A: To do Justly, to love mercy, and to walk humbly with my God.)
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To: PapaBear3625

Closer than you think. Diffie knew.


13 posted on 05/10/2009 5:34:07 PM PDT by Squantos (Be polite. Be professional. But have a plan to kill everyone you meet)
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To: OneWingedShark
Not unlike “I Am Legend”

Well, he didn't claim to be Infinite Series.

14 posted on 05/10/2009 5:38:39 PM PDT by decimon
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To: PapaBear3625
And also in cryptography, relating to Public Key Encryption. It might be that it wasn't unnoticed, but the notice was just in classified papers.

Well, it seems to me that this application to Public Key Encryption means that Public Key Encryption will be useless. If prime numbers can be predicted, then the encryption is broken.

As I recall, Public Key Encryption relies on the multiplication of two very large prime numbers. As things used to stand, it was impossible to predict where those primes fall in the sequence of integers. If now there is some algorithm that can predict where those primes exist, them it would be possible to use that algorithm to break the public key. Good-bye security.

15 posted on 05/10/2009 5:43:34 PM PDT by stripes1776 ("That if gold rust, what shall iron do?" --Chaucer)
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To: decimon

Actually, Al Gore made this discovery, but being the modest guy that he is, decided to let someone else get the credit.


16 posted on 05/10/2009 5:46:00 PM PDT by Verginius Rufus
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To: decimon

“Since the late ‘70s, researchers have known that prime numbers themselves, when taken in very large data sets, are not distributed according to Benford’s law. Instead, the first digit distribution of primes seems to be approximately uniform. However, as Luque and Lacasa point out, smaller data sets (intervals) of primes exhibit a clear bias in first digit distribution. The researchers noticed another pattern: the larger the data set of primes they analyzed, the more closely the first digit distribution approached uniformity. In light of this, the researchers wondered if there existed any pattern underlying the trend toward uniformity as the prime interval increases to infinity.”

You mean all the prime numbers between 900000 and 999999 all start with 9? I never would have guessed that! How much of my tax money was used to finance the discovery of this completely obvious result?


17 posted on 05/10/2009 5:52:33 PM PDT by devere
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To: decimon

I love this stuff.
Ever since I first trisected an angle with just a compass and a straightedge, I’ve loved this stuff.


18 posted on 05/10/2009 6:00:24 PM PDT by Lancey Howard
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To: devere
How much of my tax money was used to finance the discovery of this completely obvious result?

Que?

19 posted on 05/10/2009 6:02:57 PM PDT by decimon
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To: PapaBear3625
And also in cryptography, relating to Public Key Encryption. It might be that it wasn't unnoticed, but the notice was just in classified papers.

Ding, ding, ding - we have a winnah!

20 posted on 05/10/2009 6:04:03 PM PDT by GOPJ (If Nixon had been a Democrat, Woodward and Bernstein would have been Linda Tripp.)
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To: Lancey Howard
I love this stuff.

I posted this just for you, guy. ;-)

21 posted on 05/10/2009 6:05:14 PM PDT by decimon
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To: humblegunner
I doubt God hangs out in a Spanish university, but who knows?

Then again, no one expected the Spanish Inquisition...

22 posted on 05/10/2009 6:06:06 PM PDT by mikrofon (Pi-charting)
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To: PackerBoy

Please explain, in layman’s language, why it is huge. Thank you.


23 posted on 05/10/2009 6:09:15 PM PDT by BlueStateBlues (Blue State business, Red State heart. . . . . .Palin 2012----can't come soon enough!)
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To: SirKit

PING!


24 posted on 05/10/2009 6:10:22 PM PDT by SuziQ
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To: TMSuchman

Exactly. There is so much order in everything, how people can miss out on WHO put it there is beyond me.


25 posted on 05/10/2009 6:12:43 PM PDT by Paved Paradise
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To: Lancey Howard

Just before you squared the circle, right?


26 posted on 05/10/2009 6:14:36 PM PDT by Rapscallion (Is America's future written in Atlas Shrugged?)
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To: mikrofon

27 posted on 05/10/2009 6:19:17 PM PDT by SuziQ
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To: nnn0jeh

ping


28 posted on 05/10/2009 6:19:38 PM PDT by kalee (01/20/13 The end of an error.... Obama even worse than Carter.)
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To: decimon
They found that the distribution of the leading digit in the prime number sequence can be described by a generalization of Benford’s law.

I've been saying that for years but nobody listened to me.........

29 posted on 05/10/2009 6:21:46 PM PDT by Hot Tabasco (This country isn't going to hell in a handbasket, it's riding shotgun in an Indy car....)
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To: Hot Tabasco
I've been saying that for years but nobody listened to me.........

Geniuses are rarely recognized in their time.

Tell me, why did Riemann Zeta Zeros marry Michael Douglas.

30 posted on 05/10/2009 6:28:43 PM PDT by decimon
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To: Batrachian

Hmm... If I’m not mistaken, some public-key crypto systems are based on large primes... If you found a way of generating a lot of large primes in a reasonable amount of time, you might be able to “attack” some of these crypto systems... Warning, that is based on a vague memory about a PK system... May not be in use anymore, may not apply... Probably the engineer/computer geek in me, but I think this is kind of interesting...


31 posted on 05/10/2009 6:30:55 PM PDT by CodeMasterPhilzar (I'll keep my money, my guns, and my freedom. You can keep the "change.")
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To: decimon

This entire article is a series of mere tautologies!

What a gyp!


32 posted on 05/10/2009 6:35:14 PM PDT by headsonpikes (Genocide is the highest sacrament of socialism.)
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To: headsonpikes
This entire article is a series of mere tautologies!

They ran out of slackologies.

33 posted on 05/10/2009 6:37:51 PM PDT by decimon
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To: decimon; Perdogg; AdmSmith; bvw; callisto; ckilmer; dandelion; ganeshpuri89; gobucks; KevinDavis; ..
the distribution of the leading digit in the prime number sequence can be described by a generalization of Benford's law. In addition, this same pattern also appears in another number sequence, that of the leading digits of nontrivial Riemann zeta zeros, which is known to be related to the distribution of primes. Besides providing insight into the nature of primes, the finding could also have applications in areas such as fraud detection and stock market analysis.
"I learned this in college thirty years ago" in 3, 2, 1... ;')

Thanks decimon. Looks like I'd better dust my collection of nontrivial Riemann zeta zeros, in case all the freakin' mathmeticians show up. Perdogg, note that last sentence in the excerpt.

· Google ·

34 posted on 05/10/2009 6:44:43 PM PDT by SunkenCiv (https://secure.freerepublic.com/donate/____________________ Profile updated Monday, January 12, 2009)
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To: Rapscallion
Just before you squared the circle, right?

No. Can't be done. It's pi in the sky.

35 posted on 05/10/2009 7:07:21 PM PDT by Lancey Howard
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To: decimon

That clears that up. I had been wondering, aimlessly.


36 posted on 05/10/2009 7:08:00 PM PDT by caver (Obama's first goals: allow more killing of innocents and allow the killers of innocents to go free.)
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To: decimon

Numbers are no longer what they used to be in their prime!


37 posted on 05/10/2009 7:08:19 PM PDT by Revolting cat! (Let us prey!)
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To: TMSuchman; Crawdad

Have you heard of the movie Pi? A very strange movie about an agnostic Jew mathematical genius living in NY. As a boy he stared into the sun despite his mothers warning and suffered horrible headache for the rest of his life. He also saw patterns in the light from the sun. He was working on using prime numbers to see patterns in the stock market to predict the next days numbers.

He met an Orthodox Jew in a deli and they began talking about Torah numerology in the Hebrew language. Eventually he was told of the 216 numbers of G_d. His computer program spit out the numbers and the Jews were after him for the numbers(along with the bankers). He escaped the bankers by the help of the Jews, and a Rabbi demanded he give them the numbers.

He told them, you are not ready. I understand what the numbers mean and you are not ready. He then went home and drilled a hole in his head.


38 posted on 05/10/2009 7:21:21 PM PDT by ResponseAbility (Government tends to never fix the problems it creates in the first place)
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To: decimon; Myrddin; CodeToad; hiredhand

Just as I always suspected.

(Just kidding. I have no idea what they are talking about.)


39 posted on 05/10/2009 7:34:46 PM PDT by Travis McGee ("Foreign Enemies And Traitors" is being shipped from the printer.)
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To: Batrachian
Fermat's Last Theorem
40 posted on 05/10/2009 7:37:18 PM PDT by onedoug
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To: PapaBear3625; Squantos

The NSA’s old motto used to be “ten years ahead of the state of the art.”

They probably knew this and more ten years ago.

If they have been breaking PGP, they sure wouldn’t announce that fact.


41 posted on 05/10/2009 7:37:33 PM PDT by Travis McGee ("Foreign Enemies And Traitors" is being shipped from the printer.)
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To: buckrodgers

ping


42 posted on 05/10/2009 7:40:04 PM PDT by Straight Vermonter (Posting from deep behind the Maple Curtain)
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To: Travis McGee; hiredhand

Agree.......I would go as far as 20 years ahead in tech and such.


43 posted on 05/10/2009 7:55:13 PM PDT by Squantos (Be polite. Be professional. But have a plan to kill everyone you meet)
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To: Travis McGee

“(Just kidding. I have no idea what they are talking about.)

LOL! Sometimes my wife looks at me like a curious dog hearing a high pitched whistle.


44 posted on 05/10/2009 7:55:29 PM PDT by CodeToad (If it weren't for physics and law enforcement I'd be unstoppable!)
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To: stripes1776
If now there is some algorithm that can predict where those primes exist, them it would be possible to use that algorithm to break the public key. Good-bye security.

I am mathematically challenged but if it can be used to break a current key, could not the decoders go back to previous messages and break them also? If so, lots of new worriesd in the intelligence community.

45 posted on 05/10/2009 7:56:22 PM PDT by Oatka ("A society of sheep must in time beget a government of wolves." –Bertrand de Jouvenel)
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To: The_Reader_David

*PING*


46 posted on 05/10/2009 8:19:07 PM PDT by grey_whiskers (The opinions are solely those of the author and are subject to change without notice.)
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To: Oatka
I am mathematically challenged but if it can be used to break a current key, could not the decoders go back to previous messages and break them also? If so, lots of new worriesd in the intelligence community.

Yes, I think you are correct. If you could use an algorithm to break a key, it would not matter when that key was generated--now, in the past, in the future.

47 posted on 05/10/2009 8:29:50 PM PDT by stripes1776 ("That if gold rust, what shall iron do?" --Chaucer)
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To: decimon
The observed patterns may well impact the security of public key encryption e.g. RSA that depends on the product of two large prime numbers.
48 posted on 05/10/2009 8:32:02 PM PDT by Myrddin
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To: Oatka
I am mathematically challenged but if it can be used to break a current key, could not the decoders go back to previous messages and break them also? If so, lots of new worries in the intelligence community.

The common practice is to use of level of encryption that is unbreakable before the value of the information expires. If a message details troop movements tomorrow morning, but takes a week to crack, that is good enough. Just because you figured out the key for one message, you haven't accomplished much. The keys will be changed before the next message goes out.

49 posted on 05/10/2009 8:36:52 PM PDT by Myrddin
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To: Oatka
I am mathematically challenged but if it can be used to break a current key, could not the decoders go back to previous messages and break them also? If so, lots of new worriesd in the intelligence community.

We were doing that with the Soviets after the second world war.

http://en.wikipedia.org/wiki/VENONA

50 posted on 05/10/2009 8:42:24 PM PDT by Brellium ("Thou shalt not shilly shally!" Aron Nimzowitsch)
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