Largest Twin Prime Yet Discovered

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."

Comments

Are you kidding?

[greg_barton]

A twin prime is a pair of prime numbers separated by the integer two.

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

Re:Are you kidding?

[EmagGeek]

You mean like this?

137

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

Re:Are you kidding?

[fredmosby]

How about 2 and 5.

Re:Are you kidding?

[Peter Cooper]

Sorry to take a dump on a cute joke with pedantry, but 1 isn't a prime.

Re:Are you kidding?

[proverbialcow]

Very good. Now try finding two primes whose difference is 7.

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?

[cperciva]

Now try finding two primes whose difference is 7.

How about 5 and (-2)?

Re:Are you kidding?

[Secret Rabbit]

To join this little debate (replying to you as I don't want to reply to two different people with the same post):

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?

[Record Keeper]

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

Noted.

Good example of a /. story.

[Ninjaesque One]

Succinct, on a subject undeniably nerdy, and mostly devoid of spelling mistakes. Also, not 'edited' by Zonk.

How is this meaningful?

[JimMcc]

Seriously. I'm not a math major, etc. But I'm curious, is this of value? Other than of course as a curiosity.

Re:How is this meaningful?

[0rionx]

This article is a pretty good summary of the reasons behind the search for large primes. Although finding a new large prime doesn't necessarily have any specific, short term "benefits", it serves to deepen our understanding of mathematics. As extremely large primes are of importance in cryptography, the ability to find and work with large primes has a great deal relevancy in IT, as well. The more we discover large primes the more we learn about ways to factor them quickly and efficiently.

Re:How is this meaningful?

[TravisW]

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)

Re:How is this meaningful?

[QuantumG]

scoff all you want. You wouldn't believe the kinds of math that have been applied to gnome sequencing.. stuff that was discovered in completely different domains. That's the beauty of math.

Re:How is this meaningful?

[heinousjay]

I usually just line the gnomes up by height.

Re:Don't seem too excited

[odasnac]

generally, yeah. most prime numbers are odd.


...

i'm so sorry.

Re:Huh? What?

[tepples]

Actually, a twin prime is a pair of numbers n + 1 and n - 1 such that both are prime. For example, 41 and 43 are twin primes. Incidentally, if n is greater than 4, then n is always a multiple of 6; this is fairly easy to prove to yourself.

Re:I am a math major...

[Anonymous Coward]

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!"

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

Re:Don't seem too excited

[cgibbard]

Finding twin primes like this is mostly just an elaborate computational game which doesn't really tell much about the mathematical structure of twin primes. It doesn't help at all with knowing whether there are infinitely many or not, for example. The same goes for other searches for large primes.

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. ;)

Minor correction

[Zadaz]

"The discoverer was a computer in France, owned by Eric Vautier."

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.

Good for security.

[r00t]

Now we all know the best numbers to use for a PGP key.

Re:Don't seem too excited

[Danny Rathjens]

most prime numbers are odd.

Only on slashdot would the parent get moderated as "informative"...

Do you know why 2 is odd?

It's the only even prime number. :)

Re:Huh? What?

[XaXXon]

Let's see if it really is fairly easy :)

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 :)

Why call them twin primes...

[sehlat]

and not prime mates?

But... aren't all odd numbers prime ?

[dargaud]

Time for an old classic: How to prove that all odd numbers are prime?
Well, this problem has different solutions whether you are a: Mathematician: 3 is prime, 5 is prime, 7 is prime, and by induction we have that all the odd integers are prime. Physicist: 3 is prime, 5 is prime, 7 is prime, 9 is an experimental error... Engineer: 3 is prime, 5 is prime, 7 is prime, 9 is prime... Chemist: 3 is prime, 5 is prime... hey, let's publish! Modern physicist using renormalization: 3 is prime, 5 is prime, 7 is prime, 9 is ... 9/3 is prime, 11 is prime, 13 is prime, 15 is ... 15/3 is prime, 17 is prime, 19 is prime, 21 is ... 21/3 is prime... Quantum Physicist: All numbers are equally prime and non-prime until observed. Professor: 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student. Confused Undergraduate: Let p be any prime number larger than 2. Then p is not divisible by 2, so p is odd. QED Measure nontheorist: There are exactly as many odd numbers as primes (Euclid, Cantor), and exactly one even prime (namely 2), so there must be exactly one odd nonprime (namely 1). Cosmologist: 3 is prime, yes it is true.... Computer Scientist: 10 is prime, 11 is prime, 101 is prime... Programmer: 3 is prime, 5 is prime, 7 is prime, 9 will be fixed in the next release, ... C programmer: 03 is prime, 05 is prime, 07 is prime, 09 is really 011 which everyone knows is prime, ... BASIC programmer: What's a prime? COBOL programmer: What's an odd number? Windows programmer: 3 is prime. Wait... Mac programmer: Now why would anyone want to know about that? That's not user friendly. You don't worry about it, we'll take care of it for you. Bill Gates: 1. No one will ever need any more than 3. ZX-81 Computer Programmer: 3 is prime, Out of Memory. Pentium owner: 3 is prime, 5 is prime, 7 is prime, 8.9999978 is prime... GNU programmer: % prime
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'' Unix programmer: 3 is prime, 5 is prime, 7 is prime, ...
Segmentation fault, Core dumped. Computer programmer: 3 is prime, 5 is prime, 7 is prime, 9 is prime, 9 is prime, 9 is prime, 9 is ...
Oops, let's try that again:
3 is prime, 5 is prime, 7 is prime, 9 is ... 3 is prime, 5 is prime, 7 is prime, 9 is ... 3 is ...
Um, right. Okay, how about this:
3 is not prime, 5 is not prime, 7 is not prime, 9 is not prim