## Boffins find 17,425,170-digit prime number

The Great Internet Mersenne Prime Search (GIMPS) has struck again, finding the largest-ever Mersenne prime number. The number, the 48th Mersenne prime found, is 17,425,170 digits long and therefore most comfortably represented as 257885161-1 . The previous record-holder was a mere 12,978,189 digits. If you want to read the whole …

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### Re: Here's a fun question for you

2, Shirley?

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### "I would go with 117"

One shiny upvote for AC 6/2/13 13:14, as promised. It's higher than you'd think, isn't it?

### damn

That's the password on my luggage.

### That's just perfect

Whenever 2^n - 1 is prime, the larger number (4^n - 2^n) / 2 is perfect, which means that its factors add up to the number itself. n=2 gives 6 = 1+2+3, n=3 gives 28 = 1+2+4+7+14, etc.

This new Mersenne prime gives a new perfect, which will have approx twice as many digits as the prime itself.

### an i7 ?

When i was a young'un in the 80s my pa was working for Cray at the time they found the 32nd Mersenne prime.

That was a Cray 2 - the liquid cooled the size of a large fridge.

And now they're finding these exponentially larger numbers on core 2 duos and i7's like we have in our desktop machines.... which we use for reading email and playing farmville????

Windows

### Re: an i7 ?

It's also because in the meantime someone realized that

PRIMES is in P

### is it just me?

But finding 48 primes out of a set of 56 million doesn't seem that much better than random?

### Re: is it just me?

Mersenne prime number; not just a prime number

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

### Re: is it just me?

Quite. It's trivial to find enormous primes.

googolplex! -1

and

googolplex! + 1

are both rather larger than this.

### Re: is it just me?

> Quite. It's trivial to find enormous primes.

True (for levels of confidence < 1.0) ....

> googolplex! -1, googolplex! + 1

> are both rather larger than this.

True; but is this a non-sequitir or are you suggesting that these are prime?

NB 4!+1 = 25, 5!-1=119 (7*17), 5!+1 = 121 (11*11)

### Re: is it just me?

It's just you. You have the algorithm wrong.

The real algorithm, which is the proof of the assertion "there is no largest prime", goes like this:

Assume there is some largest prime P.

Multiply all the primes <=P to create Q. (that's one of the steps you got wrong - it's not all the numbers, it's all the primes, so you cannot just use factoral).

By construction, Q is divisible by any of the primes up to and including P.

Subtract (or add) 1 to Q to yield R. R is NOT divisible by any prime less than or equal to P, by construction.

Therefor, R is either prime itself, or has one or more prime factor >P. (that's the second bit you got wrong. There's no guarantee R is prime.)

Ergo, P cannot be the largest prime.

### \$50K for the 100M digit prime

How much would the electricity and the use of a good enough computer cost?

### Re: \$50K for the 100M digit prime

Each test at that size takes about ten days on a \$1500 computer which uses about \$300 of electricity a year; so in a five-year lifetime it does about 200 tests and costs \$3000. The chance of success is about one in a million per test, so: yes, it would cost a lot more than \$50,000.

[ Blank stare ]

So basically there is no practical use for this discovery, other than nerd bragging rights. The boffins could be creating cold fusion, flying cars, or holographic 3D TV, but nooooooo. They use their so-called intelligence to find a big prime number while humanity suffers.

Intelligence is being able to build your own nuclear bomb in your garage. Wisdom is not using the bomb you just built to remove a stump in your backyard. I'd rather be wise than intelligent any day.

Yeah but, though but, when they find the "correct" prime number and analyse digits in just the "right" way, there will be the plans for this humungous machine for making the perfect pasta.

Now that has to be worth some time and money!

FYI, cold fusion has largely been dismissed as a hoax, flying cars would be impractical, principally because you wouldnt want them falling on top of you when the fleshware makes a mistake, and the concept of 'holographic 3D TV' demonstrates that you don't know what a hologram is.

Tha ability to follow instructions, and the clearance to obtain large quantities of radionuclides is being able to build a nuclear bomb in your garage. Common sense is not blowing up your back yard with a nuke. Wisdom comes from experience and the ability to learn from your mistakes, and those of others. Intelligence is the ability to work things out without the benefit of hindsight. I'd rather take the intelligence and not have to rely on canned quotes to make a point.

>> I'd rather be wise than intelligent any day.

I feel with you.

I'd rather be both - as indeed I am.

So basically there is no practical use for this discovery

depends, the number of calculations for this kind of thing are huge. so i suspect, the scientific drive to find these number does, in part, fund the research into making faster and faster computer systems. and eventually, that research filters down into the graphics cards that allow us to play such great looking games on our PCs and watching stunning CG fx in movies.

### Sexy

yes really they have sexy prime numbers....

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

I mean they had to right? No one who works out a prime number is getting it any other way.

The internet is full of filth. Sexy prime quadruplets.....

Put your 1 next to my 0.

### Re: Sexy

Quote: yes really they have sexy prime numbers....

That's just an extension of rule 34.

Must have been calculated on a PR1ME computer.

Shurely it would be easier[1] to simply download a JavaScript program that generated the required number, rather than transferring the 17 million digits verbatim?

[1] for small values of easier.

### Prize money distribution

Quote: A more likely reason for the ongoing pursuit of primes is the \$US50,000 prize on offer to the finder of the first 100-million-digit prime number.

So, if the GIMPS project finds the first 100m digit prime, would anyone whose computer was distributed a portion of that numbers workload be awarded a percentage of that?

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