New Pattern Found in Prime Numbers

PhysOrg.com ^ | May 8th, 2009 | Lisa Zyga

[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.

[decimon]

Yeah, but sub-prime numbers qualify for TARP funds.

[TMSuchman]

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

[CodeToad]

lol!

[Batrachian]

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.

[PapaBear3625]

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.

[decimon]

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?

[PackerBoy]

This is hugh. I am series.

[Crawdad]

That’s the first thing I thought.

[decimon]

I am series.

Quite a claim in a math thread.

[Keith in Iowa]

Who is Hugh Series?

[humblegunner]

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?

[OneWingedShark]

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

Not unlike “I Am Legend”

[Squantos]

Closer than you think. Diffie knew.

[decimon]

Not unlike “I Am Legend”

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

[stripes1776]

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.

[Verginius Rufus]

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

[devere]

“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?

[Lancey Howard]

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

[decimon]

How much of my tax money was used to finance the discovery of this completely obvious result?

Que?

[GOPJ]

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!

[decimon]

I love this stuff.

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

[mikrofon]

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

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

[BlueStateBlues]

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

[SuziQ]

PING!

[Paved Paradise]

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

[Rapscallion]

Just before you squared the circle, right?

[SuziQ]

[kalee]

ping

[Hot Tabasco]

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.........

[decimon]

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.

[CodeMasterPhilzar]

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...

[headsonpikes]

This entire article is a series of mere tautologies!

What a gyp!

[decimon]

This entire article is a series of mere tautologies!

They ran out of slackologies.

[SunkenCiv]

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 ·

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[Lancey Howard]

Just before you squared the circle, right?

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

[caver]

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

[Revolting cat!]

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

[ResponseAbility]

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.

[Travis McGee]

Just as I always suspected.

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

[onedoug]

Fermat's Last Theorem

[Travis McGee]

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.

[Straight Vermonter]

ping

[Squantos]

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

[CodeToad]

“(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.

[Oatka]

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.

[grey_whiskers]

*PING*

[stripes1776]

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.

[Myrddin]

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.

[Myrddin]

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.

[Brellium]

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