45th and 46th Mersenne Primes Confirmed

kahunak writes to alert us that GIMPS has announced that the 45th and 46th Mersenne primes have been confirmed. The EFF's $100,000 award, for the first prime over 10 million digits in length, will probably be claimed. (We discussed no. 45 when it was announced.)

Re:So

[JustOK]

Hang on, I'm trying to type it in, but it takes longer because i'm using sms

Re:So

[felipekk]

The $100k award is not enough to cover the cost of sending the number through sms...

Re:So

[Naughty Bob]

The $100k award is not enough to cover the cost of sending the number through sms...

Even if sent in the form: (2^n)-1?

Re:

[rachit]

Yes, the rates the carriers charge for SMS's have risen *that* much...

Re:

[CommandoB]

Probably faster to just mail it [perfsci.com].

Re:So

[Thail]

You do realize that sending this prime number via SMS would require 62501 sms messages, using the standard US sms character limit of 160. Let's see... at the standard rate for SMS in the US of $.20, ( http://tech.yahoo.com/blogs/patterson/26695/congress-to-cell-carriers-why-have-sms-rates-doubled/ [yahoo.com] ) that comes out to, $12,500.20.

Now, assuming you can SMS at lightning speed and input 3 characters per second on a non qwerty keyboard (which is pretty dang fast if this story is to be believed http://www.engadget.com/2004/11/17/new-world-record-for-fastest-text-messaging/ [engadget.com] ) typing that out will take roughly 926 hours or 38.5 days.

Now I'm not a doctor, but you'd also have to factor in the chance for physical, and mental harm from this extended bout of texting. No sleep, no food or water, and definitly no slashdot for 38.5 days, not to mention the incedible amount of stress placed upon the joints, tendons, and muscles of your thumbs and arms.

I say no thank you sir, no thank you indeed. Good luck in your epic endeavor!

Re:

[JustOK]

hmmmm, think I'll outsource the job then.

Re:

[Drantin]

Don't forget accounting for human errors.

Re:So (OT)

[cnoocy]

Actio personalis monitur cum persona. (Dead men don't sue)

That should be moritur, with an r.

Re:

[Surt]

You can type numbers on a numeric keypad with one hand. So eating, drinking and other activities while smsing this message are still quite possible. Heck, sms is designed to be single-hand friendly.

Re:

[skjolber]

Add injury to insult: SMS messages are not required to arrive in-sequence... and you cannot use that many multipart sms ;)

Re:

[daveime]

Well in binary it's about 35 million '1's How difficult is that to type ? Only takes one keypress, and about 13 hours of holding down the key.

Re:

[rossdee]

Dr. Arroway to Michael Kitz: You want to classify the prime numbers?
(From Contact by Carl Sagan)

Re:Prime Post!

[QuickFox]

Not quite. In fact I will hereby reveal to the world the exact beginning and the exact ending of the 47th Mersenne prime (not just the 45th or the 46th, really the 47th!) as written in binary notation.

Not kidding, dead serious, this is the real thing:

11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 ... ... ... 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111

Mersenne numbers are by definition 2^n-1, which means that in binary notation every such number is a sequence of ones.

Re:

[Mprx]

Infinity of Mersenne primes isn't proven, you'll have to post the whole thing for us to believe you.

Re:

[Daimanta]

True, but it would be strange that there would be a limited amount of Mersenne primes using un unlimited amount of primes. But this could be the case. Still, we are at millions of digits now and we have 2 new ones so I am guessing that there are infinite.

Re:

[grimJester]

Mersenne numbers are by definition 2^n-1, which means that in binary notation every such number is a sequence of ones.

Since the length of the number in base-10 is a little more than 10 million digits, and 10^3 is roughly 2^10, does this mean n is as low as 33-35 million?

Re:

[grimJester]

Mersenne numbers are by definition 2^n-1, which means that in binary notation every such number is a sequence of ones.

Since the length of the number in base-10 is a little more than 10 million digits, and 10^3 is roughly 2^10, does this mean n is as low as 33-35 million?

Nevermind, checked Wikipedia. The largest currently known n is 32,582,657 so apparently my reasoning is correct.

Re:

[Daimanta]

(#24992811)

Prime factors:

3
2776979

fail

Re:

[19thNervousBreakdown]

(#24992811)

Prime factors:

3 2776979

UID.

fail

Sweet Christ, you managed to not only be wrong, but at the same time un-ironically use an awful 4chan meme to do it.

Re:

[Daimanta]

first: he was talking about the post not his UID

second:

His UID factors into

109 4127(semiprime)

you fail

troll

Re:

[Si-UCP]

He wasn't talking about any of that crap. He says "Prime Post" because his post is the second comment on THIS ARTICLE (a play on the First Post meme). 2 is, obviously, a prime. Are people just that oblivious, or am I the oblivious one not realizing that Mr. Daimanta and Mr. 19thNervousBreakdown here are trolling?

Re:

[Daimanta]

How the hell can he predict whether his post is the second one or not? Unless you struck a deal with /. admins or omniscient you can never know. But somehow you are capable of convienently forgetting this fact.

troll

Just missed the prize myself!

[bigtallmofo]

Well, last week I discovered the prime number 37. It was only a matter of time before I discovered one greater than 10 million digits.

Now these show-offs have gone ahead and spoiled it for the rest of us.

Why Mersenne Primes Matter

[RAMMS+EIN]

Not knowing why Mersenne primes matter, I looked it up on The Ultimate Source Of Truth [wikipedia.org]. From The Fine Article [wikipedia.org]:

Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether there is a largest Mersenne prime, which would mean that the set of Mersenne primes is finite. The Lenstra-Pomerance-Wagstaff conjecture asserts that, on the contrary, there are infinitely many Mersenne primes and predicts their order of growth. It is also not known whether infinitely many Mersenne numbers with prime exponents are composite, although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes.

Mersenne primes are used in pseudorandom number generators such as Mersenne Twister and ParkMiller RNG.

Mersenne primes were considered already by Euclid, who found a connection with the perfect numbers.

Mersenne numbers are very good test cases for the special number field sieve algorithm

Out of those, I only knew about the connection with pseudorandom number generators, which I became interested in after writing my deadbeef random number generator [inglorion.net].

This doesn't matter so much

[l2718]

I think this tell us a lot more about the potential power of distributed computing than about prime numbers. While Mersenne primes are interesting to number theorists, we'll never find enough to do statistics on -- they are mostly of interests to pure mathematicians for reasons of curiosity. Random prime numbers of about 1024 bits are much more useful (and easier to find). On the other hand, if these was ever a problem we really needed to solve (protein-folding screensavers come to mind) then we now know how much computation power we can harness.

Re:This doesn't matter so much

[kevinatilusa]

Knowledge of whether or not there are infinitely many Mersenne primes would probably not be interesting even to most pure mathematicians -- it's sort of a bizarre question that seems disconnected from the rest of mathematics. What would be interesting would be the actual methods used to prove this. In practice almost every question involving the existence/non-existence of certain types of primes is one we already know the answer to.

The reason for this lies in the prime number theorem, which says that the proportion of numbers less than N which are prime is about 1/Log(N). Unless there's some compelling reason to believe otherwise, you can guess the answer to many problems involving primes by replacing them with a set randomly chosen with the same probability.

For example, a randomly chosen number near 2^p-1 will be prime with probability about proportional to 1/p. Since the sum of 1/p diverges, we expect there to be infinitely many Mersenne primes (and can even guess their number, though this requires a bit more careful analysis to take care of the observation that Mersenne numbers don't have small prime factors, but this should only increase their number).

The same trick allows us to guess the answer for twin primes (sum diverges, so there should be infinitely many) and Fermat primes (primes of the form 2^(2^n)+1 -- the sum converges, so there should be only finitely many). But none of these are really rigorous proofs, because they're all based on the fundamental assumption that the primes are somehow pseudorandom.

Depending on the method of attack, a proof of the infinitude of Mersenne Primes may also shed light on how accurate or inaccurate the pseudorandomness assumption is. I would consider that to be a VERY interesting question.

Unfortunately these primes can't be published...

[the_humeister]

... because they coincidentally correspond to two of Britney Spears's songs encoded as mp3 files at 128kb and the RIAA won't allow such copyright infringement! Double ouch!

Re:

[volxdragon]

... because they coincidentally correspond to two of Britney Spears's songs encoded as mp3 files at 128kb and the RIAA won't allow such copyright infringement! Double ouch!

If that's the case, no great loss, we wouldn't want to see (or hear) them anyway!

Re:

[TheSpoom]

This just in: Britney Spears is actually a weapon sent by aliens to enslave the Earth through hidden prime number telepathic messages.

News at eleven.

Re:

[Fluffeh]

I don't think even the RIAA is sick enough to enforce copyright infringement on Britney's songs. I mean anyone *THAT* sick to download em is capable of much more hideous actions and even the RIAA is scared of some things.

poor bruce

[nachtkap]

Well that suxs for Bruce [geekz.co.uk]. Now he has to change the combination on his luggage again.