# Largest Twin Prime Yet Discovered

#### kdawson posted more than 7 years ago | from the Hardy-Littlewood-conjecture dept.

160
Chris Chiasson writes *"The Twin Internet Prime Search and PrimeGrid have recently discovered the largest known twin prime. A twin prime is a pair of prime numbers separated by the integer two. The pair discovered on January 15th was 2003663613 * 2 ^{195,000} ± 1. The two primes are 58,711 digits long. The discoverer was Eric Vautier, from France."*

## Are you kidding? (5, Funny)

## greg_barton (5551) | more than 7 years ago | (#17641272)

Are you kidding? Those are easy to find! Try getting two primes separated by the integer three...

## Re:Are you kidding? (5, Funny)

## EmagGeek (574360) | more than 7 years ago | (#17641306)

137

The primes are 1 and 7, separated by the integer 3...

## Re:Are you kidding? (4, Informative)

## Peter Cooper (660482) | more than 7 years ago | (#17641372)

## Re:Are you kidding? (1)

## Manatra (948767) | more than 7 years ago | (#17642240)

(for the record I don't treat 1 as a prime number)

## Re:Are you kidding? (1)

## Chacham (981) | more than 7 years ago | (#17642336)

1 isn't a primeYes, it is [example.com] .

## More like who are you kidding? (1)

## Xenographic (557057) | more than 7 years ago | (#17642950)

It so happens that I have a degree in mathematics, but anyone can just claim that, so I doubt you'll listen to that any more than a Wikipedia link, even if the revision I saw gave the definition of prime numbers correctly.

## Re:Are you kidding? (1)

## eldepeche (854916) | more than 7 years ago | (#17644284)

## Re:Are you kidding? (1)

## Propaganda13 (312548) | more than 7 years ago | (#17642396)

I've read several definitions over the years. Some read as if 1 could be prime (divisible only by 1 and itself), some specifically exclude 1 as a case, and some definitions like Wikipedia (if I don't go edit it

## Re:Are you kidding? (1, Insightful)

## Anonymous Coward | more than 7 years ago | (#17642580)

## Re:Are you kidding? (1)

## Garridan (597129) | more than 7 years ago | (#17643320)

Math & written language must coexist, but at the same time, the line between them must not be blurred.

## Re:Are you kidding? (5, Informative)

## Secret Rabbit (914973) | more than 7 years ago | (#17642672)

Actually, if one considers 1 a prime problems end up happening e.g. inconsistencies with algebraic number theory (prime ideals) and elementary number theory. Basically, if you pop in 1, elementary number theory is fine (at least up to where I've studied it doesn't really matter aside from making some proofs more difficult than necessary). But, then some further developments like algebraic number theory start having problems, like the before mentioned inconsistency in the definition of a prime.

Leaving 1 out as a prime makes the elementary number theoretic definition consistent with the algebraic number theoretic definition. Just thought I'd point that out as math is all about detail and consistency. And not having a consistent definition of a prime is a rather large f**k up as we all know how important primes are.

So, although 1 has been considered a prime in the past, it does seem (keep in mind, I've looked through several libraries) that 1 has been dropped as a prime. Modern mathematics seems to have taken care of this discussion.

## Re:Are you kidding? (0)

## Anonymous Coward | more than 7 years ago | (#17644348)

## Re:Are you kidding? (0, Redundant)

## SeanMon (929653) | more than 7 years ago | (#17641382)

## Re:Are you kidding? (3, Insightful)

## fredmosby (545378) | more than 7 years ago | (#17641358)

## Re:Are you kidding? (4, Funny)

## proverbialcow (177020) | more than 7 years ago | (#17641624)

And when you're done with that, find two perfect cubes whose difference is also a perfect cube. I did this once, but there wasn't enough room in the margin to write the answer.

## Re:Are you kidding? (0)

## Anonymous Coward | more than 7 years ago | (#17641876)

A^n + B^n = C^n

A^n + B^n - C^n = 0

A^n - C^n = - B^n

C^n - A^n = B^n

Since 3 isn't 2, then I assume that what you said isn't possible.

## Re:Are you kidding? (0)

## Anonymous Coward | more than 7 years ago | (#17642874)

## Re:Are you kidding? (4, Informative)

## cperciva (102828) | more than 7 years ago | (#17641958)

Now try finding two primes whose difference is 7.How about 5 and (-2)?

## MOD PARENT +37 KICKASS (1, Funny)

## Anonymous Coward | more than 7 years ago | (#17642182)

## Re:Are you kidding? (1)

## DahGhostfacedFiddlah (470393) | more than 7 years ago | (#17642296)

## Re:Are you kidding? (2, Informative)

## cperciva (102828) | more than 7 years ago | (#17642702)

Nice [mathforum.org] try [google.ca] .Somehow I'm not surprised to find that materials written for consumption by grade school students (and teachers) get this wrong. A prime element of an integral domain is a non-zero non-unit

psuch that ifpdividesab,pdivides eitheraorb(or both). The integers are an integral domain, and (-5) is a prime.## Re:Are you kidding? (1)

## Garridan (597129) | more than 7 years ago | (#17643438)

Similarly, many don't even agree what log(

x) means!For high school math, log(

x) is log base 10.In undergraduate math, and statistics, log(

x) is the natural log.Later on in math, log(

x) is of the most convenient base for the application, unless this is ambiguous or non-obvious. In computer science, log(x) is frequently base 2, but nobody really cares 'cause change of base is just multiplication by a constant.## Re:Are you kidding? (2, Informative)

## stupid_is (716292) | more than 7 years ago | (#17644256)

log(x)was base 10, andln(x)was the natural log. Other ways of writing it would be to include the base as a subscript to thelog(), which made it more obvious when doing those tedious exercises to convert the base.## Re:Are you kidding? (1)

## saforrest (184929) | more than 7 years ago | (#17642872)

Nice try.Yeah, it was a nice try. A nice, successful try. Until I read the post, I was going to suggest 2 and -5, which would've worked too.

Generally speaking in algebra, any unit multiple of a prime is considered a prime. Because -1 is the only unit other than 1, the negative numbers aren't usually counted, but there's no good reason not to apply the more general definition here.

## Re:Are you kidding? (1)

## Gobiner (698872) | more than 7 years ago | (#17642260)

And when you're done with that, find two perfect cubes whose difference is also a perfect cube. I did this once, but there wasn't enough room in the margin to write the answer.My answer is 3 and 7.

Who are you to tell me what numbers are perfect and what aren't? I shall decide for myself, in the way of my fathers.

## Re:Are you kidding? (1)

## Criffer (842645) | more than 7 years ago | (#17643602)

## Re:Are you kidding? (1)

## greg_barton (5551) | more than 7 years ago | (#17642228)

OK, here's the joke. Yeah, 2 and 5 are primes separated by 3. There aren't any others because all primes other than 2 are odd, and adding 3 to an odd number results in a composite number, which can't be prime.

So you'll be searching for such primes forever. Get it?

Jeez. Apparently the joke is ya'll searching forever for your sense of humor...

## Re:Are you kidding? (1)

## rbarreira (836272) | more than 7 years ago | (#17643454)

## Re:Are you kidding? (0)

## Anonymous Coward | more than 7 years ago | (#17641990)

## Re:Are you kidding? (0, Redundant)

## xouumalperxe (815707) | more than 7 years ago | (#17643412)

Do I get a cookie?

## Good example of a /. story. (4, Insightful)

## Ninjaesque One (902204) | more than 7 years ago | (#17641290)

## Don't seem too excited (1)

## presidentbeef (779674) | more than 7 years ago | (#17641294)

Odd?

## Re:Don't seem too excited (5, Funny)

## odasnac (570543) | more than 7 years ago | (#17641324)

i'm so sorry.

## Re:Don't seem too excited (2, Funny)

## cperciva (102828) | more than 7 years ago | (#17641504)

most prime numbers are odd.Only on slashdot would the parent get moderated as "informative"...

## Re:Don't seem too excited (5, Funny)

## Danny Rathjens (8471) | more than 7 years ago | (#17642250)

It's the only even prime number.

## Re:Don't seem too excited (1)

## Grey Ninja (739021) | more than 7 years ago | (#17644140)

## Re:Don't seem too excited (0)

## Anonymous Coward | more than 7 years ago | (#17642528)

There, fixed it for you.

## Re:Don't seem too excited (1)

## presidentbeef (779674) | more than 7 years ago | (#17643494)

Thanks.

## But... aren't all odd numbers prime ? (5, Funny)

## dargaud (518470) | more than 7 years ago | (#17644100)

How to prove that all odd numbers are prime?Well, this problem has different solutions whether you are a:

usage: prime [-nV] [--quiet] [--silent] [--version] [-e script] --catenate --concatenate | c --create | d --diff --compare | r --append | t --list | u --update | x -extract --get [ --atime-preserve ] [ -b, --block-size N ] [ -B, --read-full-blocks ] [ -C, --directory DIR ] [--checkpoint ] [ -f, --file [HOSTNAME:]F ] [ --force-local ] [ -F, --info-script F --new-volume-script F ] [-G, --incremental ] [ -g, --listed-incremental F ] [ -h, --dereference ] [ -i, --ignore-zeros ] [ --ignore-failed-read ] [ -k, --keep-old-files ] [ -K, --starting-file F ] [ -l, --one-file-system ] [ -L, --tape-length N ] [ -m, --modification-time ] [ -M, --multi-volume ] [ -N, --after-date DATE, --newer DATE ] [ -o, --old-archive, --portability ] [ -O, --to-stdout ] [ -p, --same-permissions, --preserve-permissions ] [ -P, --absolute-paths ] [ --preserve ] [ -R, --record-number ] [ [-f script-file] [--expression=script] [--file=script-file] [file...]

prime: you must specify exactly one of the r, c, t, x, or d options

For more information, type "prime --help''

Segmentation fault, Core dumped.

Oops, let's try that again:3 is prime, 5 is prime, 7 is prime, 9 is

Um, right. Okay, how about this:3 is not prime, 5 is not prime, 7 is not prime, 9 is not prime...

So much for the beta releases. Ship this:3 is prime, 5 is prime, 7 is prime, 9 is a feature, 11 is prime...

and put on the cover "More prime numbers than anyone else in the industry!"Proof:

isis.## Re:Don't seem too excited (3, Insightful)

## cgibbard (657142) | more than 7 years ago | (#17641628)

Also, if you're asking about real-world practical considerations, the primes used in practical work by comparison are tiny. Using such large primes for things like cryptography would be stupid for a number of reasons, not the least of which being that there are only so many known such primes out there, the size of your key would give it away. Personally, I don't know of any practical use for twin-primes or Mersenne primes, or any of the other classes of large primes being searched for.

It's really more just for fun, like computing digits of pi. However, devising new ways to access large twin primes, for instance, results in improvements of our knowledge of them. It's those new theorems and algorithms which people might get excited about. Running a computer for hours or days or months to actually find the things is less interesting.

## How is this meaningful? (3, Interesting)

## JimMcc (31079) | more than 7 years ago | (#17641300)

## Re:How is this meaningful? (2, Funny)

## hamburger lady (218108) | more than 7 years ago | (#17641352)

## Re:How is this meaningful? (1)

## JimMcc (31079) | more than 7 years ago | (#17641360)

## Re:How is this meaningful? (3, Funny)

## QuantumG (50515) | more than 7 years ago | (#17642350)

completelydifferent domains. That's the beauty of math.## Re:How is this meaningful? (1)

## jallen02 (124384) | more than 7 years ago | (#17642606)

## Re:How is this meaningful? (3, Funny)

## heinousjay (683506) | more than 7 years ago | (#17642616)

## Re:How is this meaningful? (3, Informative)

## 0rionx (915503) | more than 7 years ago | (#17641412)

## Thanks (1)

## JimMcc (31079) | more than 7 years ago | (#17641494)

## Re:How is this meaningful? (1)

## Sku-Lad (990269) | more than 7 years ago | (#17642738)

## Re:How is this meaningful? (1)

## 0rionx (915503) | more than 7 years ago | (#17643296)

## I am a math major... (1, Informative)

## eklitzke (873155) | more than 7 years ago | (#17641440)

I am a math major (although I don't study prime numbers). This is totally, utterly useless, in a practical sense. Well, it might be useful in the field of CS, although I don't know enough about these project to know if any novel algorithms were used. It is sort of interesting though, because the twin prime conjecture (i.e. the statement that there are an infinite number of such pairs) is still unproven, so it's kind of cool to be able to say "Look, we found another pair!"

(On a side note, I don't know of any mathematicians who doubt the validity of the twin prime conjecture. If you proved that the conjecture was

false, then you'd be really famous.)## Re:I am a math major... (5, Funny)

## Anonymous Coward | more than 7 years ago | (#17641502)

One down, infinity more to go. Proof by enumeration, here we come...

## Re:I am a math major... (2, Funny)

## AKAImBatman (238306) | more than 7 years ago | (#17641516)

Are you kidding me?!? I'm going to use that as my new encryption key! It will be like UBER-secure and take ten hundred billion, billion YEARS to guess!

[...]

Um... I wasn't supposed to tell you that, was I?

## Re:I am a math major... (0)

## Anonymous Coward | more than 7 years ago | (#17642434)

You misspelled

type, but you're right. Since password entry doesn't let you use exponential notation, you're stuck entering a lot of characters every time you want to log in... I'd tell you how many, but my computer isn't powerful enough to calculate log_10(2003663613 * 2^195,000 ± 1)## Re:I am a math major... (1)

## MajroMax (112652) | more than 7 years ago | (#17642670)

Because of the properties of log (log(a*b) = log(a) + log(b)), the answer's quite easy: it's approximately 58710.1509793 (continued for a while) ± 1/(2003663613 * 2^195,000)/log_e(10). The ± 1 bit is relatively easy to account for -- a Taylor series expansion of log_e(x + 1) ~= log(x) + 1/x for very large x.

## Re:I am a math major... (1)

## TrickiDicki (559754) | more than 7 years ago | (#17642840)

## Re:How is this meaningful? (-1, Flamebait)

## Duncan3 (10537) | more than 7 years ago | (#17641498)

Go download Folding@home, it's real research into things that effect us here in in the real world.

## Re:How is this meaningful? (5, Informative)

## TravisW (594642) | more than 7 years ago | (#17641572)

It depends on what you mean by "of value."

At any rate, any particular pair of twin primes is unlikely* to be especially "significant." However, an important open problem in math is, "Do there exist infinitely many twin primes?" Experts think it's likely enough that the answer is yes that they've named that supposition "Twin Prime Conjecture," which indicates that those experts consider it definitely less than a theorem but much more than a wild guess.

That the problem is so simply stated but remains unsolved is a testament to its difficulty (cf. Fermat's Last Theorem a.k.a. Wiles' Theorem). Hardy and Wright wrote to this effect: "The evidence, when examined in detail, appears to justify this conjecture, but the proof or disproof of conjectures of this type is at present beyond the resources of mathematics."

*If the conjecture is false, that is, if there are only finitely many twin primes, certainly the largest pair is important.

Incidentally, the "Pentium bug" was discovered when someone computed the reciprocals of two large (twin) primes and noticed an error after about 10 decimal paces.

Twin Prime (Wikipedia) [wikipedia.org]

## Re:How is this meaningful? (1)

## Kjella (173770) | more than 7 years ago | (#17644044)

If the conjecture is false, that is, if there are only finitely many twin primes, certainly the largest pair is important.Except finding one more pair (or ten, or hundred) doesn't do anything for the theoretical question, because it's possible that there's no twin prime numbers beyond X, where X is far greater than computers can muster. And even if it was the last, you'd have no way of knowing it actually is the last.

Regarding the conjencture, we know there's an infinite number of primes, and we know their statistical distribution. Let's call that probability (for a given value, it's a function) p. Chanches are pretty good twin pairs exist with a probability of about p^2. All you lack is the actual proof.

To show why you need a proof, let's take triple prime numbers. With a probability of about p^3, we should find three primes in a row, right? Wrong, there is exactly one triple prime set (3,5,7). Why? Because x, x+2, x+4 = 0,1,2 mod 3 = one is always divisible by 3.

## Re:How is this meaningful? (1)

## rifftide (679288) | more than 7 years ago | (#17641820)

Specifically: "My dad's useless numbers are bigger than your dad's useless numbers."

## Re:How is this meaningful? (0)

## Anonymous Coward | more than 7 years ago | (#17642078)

## Re:How is this meaningful? (1)

## vga_init (589198) | more than 7 years ago | (#17642544)

## Re:How is this meaningful? (1)

## pyite (140350) | more than 7 years ago | (#17642640)

Well, it is generally believed that prime numbers are infinite...Not sure if you meant twin primes there. It is

provablethat there are infinitely many primes. Assume that there exists a finite number of primes... p_1, p_2,## Re:How is this meaningful? (1)

## Petrushka (815171) | more than 7 years ago | (#17643936)

## Fun stuff (2, Interesting)

## A beautiful mind (821714) | more than 7 years ago | (#17641308)

I find it interesting that the guy who works with insanely cool things like primes gave mind-numblingly boring lectures. He basically read his book out aloud. Some people are just very good at research and very bad at teaching.

## Re:Fun stuff (1)

## Mini-Geek (915324) | more than 7 years ago | (#17641408)

Hedidn't have to be good at anything except loading the program that searches for the twin primes on his computer...## Re:Fun stuff (1)

## A beautiful mind (821714) | more than 7 years ago | (#17641468)

## Re:Fun stuff (2, Funny)

## DirePickle (796986) | more than 7 years ago | (#17641890)

## Re:Fun stuff (0)

## Anonymous Coward | more than 7 years ago | (#17642352)

## In other news... (0)

## Anonymous Coward | more than 7 years ago | (#17641316)

## Huh? What? (0)

## Bright Apollo (988736) | more than 7 years ago | (#17641362)

Oh, wait, my wife tells me the whole number is a prime. Well, that's why she has the Master's in math and I make the money.

-BA

## Re:Huh? What? (3, Interesting)

## tepples (727027) | more than 7 years ago | (#17641396)

Actually, a twin prime is a pair of numbers

n+ 1 andn- 1 such that both are prime. For example, 41 and 43 are twin primes. Incidentally, ifnis greater than 4, thennis always a multiple of 6; this is fairly easy to prove to yourself.## Re:Huh? What? (4, Informative)

## XaXXon (202882) | more than 7 years ago | (#17642288)

That gives us 5 other things to try:

No odd numbers can be the base of a twin prime because adding or subtracting one leaves an even number which cannot be prime (except 2), so that knocks out

6n+1, 6n+3, 6n+5.

6n+2 and 6n+4.. why are those no good?

6n+2 doesn't work because 6n is always a multiple of 3, adding 2 and then 1 (for the higher of the potential of the 2 twin primes) is also divisible by three, so it can never be a prime.

6n+4 has the same problem, just on its lower possible twin prime.

That took me longer to figure out that I'm happy with, but I think I got it

## Learn some English (1)

## l2718 (514756) | more than 7 years ago | (#17642368)

## Re:Learn some English (0)

## Anonymous Coward | more than 7 years ago | (#17642398)

either ofa pair of numbers..."## Re:Huh? What? (0)

## Anonymous Coward | more than 7 years ago | (#17643228)

1) For each multiple of 6, test num-1 and num+1 for prime

2) ???

3) Profit! Er, Get Prime Twins!

## Is it useful? (-1, Flamebait)

## Short Circuit (52384) | more than 7 years ago | (#17641444)

Mathematics for mathematics sake aren't usually Slashdot's usual fare. And prime numbers? We could have a "Largest prime yet found" article every day, if was really that interesting. And then suddenly it wouldn't be.

## Obligatory South Park Reference (1)

## Imexius (967514) | more than 7 years ago | (#17641604)

## Re:Obligatory South Park Reference (1)

## Gemini_25_RB (997440) | more than 7 years ago | (#17641684)

## Is this relevant in any way shape or form? (-1, Troll)

## The Undeniable Truth (1052256) | more than 7 years ago | (#17641690)

## Re:Is this relevant in any way shape or form? (0)

## Anonymous Coward | more than 7 years ago | (#17642042)

## No Biggest Prime: Proof (2, Informative)

## seawall (549985) | more than 7 years ago | (#17642602)

Most people here probably know this but:

There is no biggest prime number and the proof is 2 sentences long.... here it is:

Assume there is a largest prime P(n) and thus there is a finite list of all prime numbers: P(1), P(2), P(3),.....P(n). "*" here means multiply.

Well then (P(1)*P(2)*...*P(n))+1 must be prime: whenever you divide that number by prime(s) you always have a 1 left over....but (P(1)*.....*P(n))+1 is obviously bigger than P(n) so our initial assumption of a largest prime number must be wrong. QED.

One of the interesting things for mathematicians (or at least this ex-mathematician) is that you tweak the question just a little bit: "Is there a largest "twin prime"?" and heavy duty brains pound on the question for centuries with no answer. I have had NIGHTMARES over that one....which is one reason I am an ex-mathematician.

Another funny thing about higher math is it has been defended as useless (Hardy: A Mathematicians Apology) but then three guys go and invent RSA and all of a sudden my privacy depends on the properties of prime numbers.

## NO NO NO (2, Insightful)

## Kjella (173770) | more than 7 years ago | (#17644122)

Well then (P(1)*P(2)*...*P(n))+1 must be prime:No, no and even more no. Let's say my list of known primes is (3,5). 3*5+1 = 16 is not prime, all you've proven is that your list of primes is incomplete. It is only an existance theorem, and can

notbe used to find new primes.## Re:NO NO NO (2, Insightful)

## Kjella (173770) | more than 7 years ago | (#17644194)

2*3*5*7*11*13=30030

30030+1=59*509

## Minor correction (5, Interesting)

## Zadaz (950521) | more than 7 years ago | (#17641836)

I never felt like I should be allowed to take credit for what my screen saver does. Espcially since the whole point is that it does it when I'm not doing anything.

'Course this will all be sorted out when computers can vote.

## Re:Minor correction (1)

## RealGrouchy (943109) | more than 7 years ago | (#17641942)

You mean vote

for themselves(as opposed to deciding what your vote will be).- RG>

## Re:Minor correction (1)

## Kuvter (882697) | more than 7 years ago | (#17642312)

Course this will all be sorted out when computers can vote.I can tell you now, mine votes against DRM.

## Re:Minor correction (1)

## malsdavis (542216) | more than 7 years ago | (#17642372)

## Good for security. (4, Funny)

## r00t (33219) | more than 7 years ago | (#17641860)

## Re:Good for security. (1)

## tloh (451585) | more than 7 years ago | (#17642328)

I think that was unintentionally funny.

## ugh (1)

## ILuvRamen (1026668) | more than 7 years ago | (#17642088)

## Re:ugh (1)

## dreadclown (842647) | more than 7 years ago | (#17642720)

It is truly sad that no-one cares about the plight of those poor souls infected by aliens.

## Re:ugh (0)

## Anonymous Coward | more than 7 years ago | (#17643328)

## GMP (2, Informative)

## bellyjean (1018896) | more than 7 years ago | (#17642196)

## Super Double Hashing Table (1)

## Arakageeta (671142) | more than 7 years ago | (#17642880)

## Why call them twin primes... (5, Funny)

## sehlat (180760) | more than 7 years ago | (#17642892)

## To quote Fark (2, Funny)

## symbolset (646467) | more than 7 years ago | (#17643308)

## power consumtions (2, Interesting)

## AndyST (910890) | more than 7 years ago | (#17643376)

It occurs to me that the power consumed for this kind of calculations is quite high. Back when I was doing seti@home [berkeley.edu] , the classic one, they explicitly told people not to let computers running for the sole purpose of calculation, even asking them to turn them of when you guys in the US had a power crisis. There are people running farms of computers just for the fun of it. *sigh*

seti, primes and stuff might be important, but I'd like to still have some power left to radio a reply to E.T.

## Prime twins (1)

## DavidV (167283) | more than 7 years ago | (#17643844)

## what a coincidence! (1)

## speculatrix (678524) | more than 7 years ago | (#17644084)

The pair discovered on January 15th was 2003663613 * 2195,000 ± 1.what a coincidence! that's the combination to my luggage!