Here are the first digits of the newly identified prime number.
February 6th, 2013
01:01 PM ET

# Largest prime number yet discovered

By Elizabeth Landau, CNN

You know you're a geek if you felt all warm and fuzzy inside when you read that headline. If you got here by accident, here's the news: The biggest prime number yet has been discovered.

It is indeed massive, more than 17 million digits long. A text file of the entire number contains more than 22 megabytes of information.

[soundcloud url="http://api.soundcloud.com/tracks/78399855&#034; iframe="true" /]

For those who have been out of school for a while, let's review: A prime number is a positive integer that cannot be divided evenly by any number except itself and 1. The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

There is no clear pattern in these numbers, nor is there an easy formula to calculate the 11th prime number (31). And, as proven by the great mathematician Euclid, around 300 B.C., there are an infinite number of primes.

That means there are unfathomably large numbers that are prime. The newest find is 2 to the power of 57,885,161 minus 1. That means 2, multiplied by 2 more than 57 million times, minus 1. Don't try this on any ordinary calculator.

The lucky number-hunter who came upon it is Curtis Cooper of the Great Internet Mersenne Prime Search (GIMPS), a collaborative project involving thousands of volunteers who sift through numbers in search of primes.

Cooper, a professor at the University of Central Missouri, used his computer to identify the number through software developed by George Woltman, in Orlando, Florida, and the PrimeNet system written by Scott Kurowski, in San Diego, California.

The achievement was no easy task: According to GIMPS, it took 39 days of nonstop computing to prove the prime number is indeed prime.

This is the third time that Cooper and his university have uncovered a record prime number, according to GIMPS.

Prime-number hunters do get to reap some rewards. The new number is eligible for a \$3,000 prize from GIMPS. There's more money in even bigger numbers, though: The Electronic Frontier Foundation offers a cool \$250,000 to the first individual or group that snags a prime number of at least 1 billion digits. Neither of these purses is prime.

The particular kind of prime number that GIMPS collaborators look for is called a Mersenne prime, named after the French monk Marin Mersenne. The formula named after him is 2 to the power of "p" minus 1, where "p" is a prime number. This doesn't always yield a prime, but the result has a greater chance of being prime, and it's easier to verify whether it's prime.

Searching for prime numbers is sort of like looking for needles in haystacks, says Jordan Ellenberg, professor of mathematics at the University of Wisconsin. The Mersenne prime formula acts as a guide to a haystack showing where more needles (primes) are likely to be, so it's easier to tell where the needles are.

What relevance does the largest prime ever have on your life? Probably none. Although prime numbers are useful in cryptography, a field that studies ways to make communications and information secure, it's not as though cryptographers are running out of prime numbers already, Ellenberg said.

But it's an achievement in the sense that it shows modern computers are powerful and fast enough to run these calculations and processes, Ellenberg said.

"In some ways, this is more of triumph of engineering than a triumph of mathematics," he said.

 Post by: CNN's Elizabeth Landau Filed under: Math • On Earth
###### soundoff(267 Responses)
1. www

Thanks, this is the worst factor I’ve read www http://www.8768gug66ftf4.com

March 8, 2013 at 7:12 pm |
2. Eric

I'm still trying to figure out why a 17 million digit number requires a 22-megabyte file??? What's the 5-megabyte fluff?

February 12, 2013 at 12:05 pm |
• John

Eric, could it be that the 17 million + digits requires almost 5.7 million commas? I have been thinking about your reply for over twenty four hours, and this is the only reason I can think of why a text file of this number would require 22 megabytes. Please let me know what you think of my hypothesis. Thanks.

February 14, 2013 at 1:04 am |
• Wheatley

Remember that data isn't stored in those digits, it's stored in binary, so each of those more than 17,000,000 digits would take up at least 8 bytes of memory, not just one.

February 16, 2013 at 1:11 am |
• JNota

8 bits to a digit, buddy. 8 Bits is equal to one byte. Get your information correct before you correct someone. Also, its gotta be the comma's.

February 23, 2013 at 6:10 pm |
3. Eric

Needless to say, it ends in one of {1, 3, 7, 9}

February 12, 2013 at 12:04 pm |
• Mark Mooshagian

I think it ends in 1. I divided the exponent by 4 and found a remainder of 1. Because powers of two rotate in groups of four, this would indicate the composite number one greater than this prime must end in 2.

February 12, 2013 at 1:07 pm |
4. esbboston

I very carefuLLy transferred this largest prime number into a spreadsheet in order to do some work with it. My Firefox browser held it aLL but the copy paste process took 9 trips. I used the paste special to separate the number using the comma delimiters.

February 10, 2013 at 4:36 pm |
• Linda N.

So how do you publish this uber-lengthy finding in a scholarly mathematical journal?! I guess you've got to get into an online journal.

February 12, 2013 at 9:29 am |
• esbboston

I publish math stories, most of them silly, on my blog mixed with my other writings. I pulled in the large prime in order to calculate its condensed value, the process of repeatingly summing all the digits until you get just a single digit.. I haven't published that story yet.

February 12, 2013 at 8:46 pm |
5. Is j being censored on CNN, multiple comments never posted par let's golf

WOW, I printed out pi to one million digits for our school over a decade ago; How many pages would this consume?

February 9, 2013 at 11:34 pm |
• Mike Schwab

80 characters per line, 63 lines per page, 2 sides per page, 10,000 digits per page. 1,700 pages 3.4 reams of paper.
Add commas, 2,267 pages 4.5 reams of paper.

February 11, 2013 at 4:39 pm |
6. Kris Jackson

And here's one for you geeks. Here's a mathematical principle that can be neither proven nor disproven. All even numbers can be expressed as the sum of two prime numbers. Twelve is the sum of five and seven. Twenty-eight is the sum of 11 and 17. So on into the billions. No reason for it, it just is.

February 9, 2013 at 7:30 pm |
• Boyd Reed

Two things:
(1) Any even number greater than 4 can be expressed as the sum of two primes. (Remember, 1 is neither prime nor composite, so 4 doesn't work.) This is known as "Goldbach's Conjecture".
(2) There was a paper originally submitted in 2007 by Prof. Kent Slinker that purports to prove Goldbach's Conjecture. To date, I've not seen a refutation of it. Link here: http://arxiv.org/abs/0712.2381v11

February 12, 2013 at 10:59 am |
• Y Leung

Prove: The number 4 can be expressed as the sum of two prime numbers. In other words, 4 does work.

Suppose no two prime numbers can add up to 4. --( 1 )

2 is a prime.
2+2 = 4
Therefore, we have a contradiction with ( 1 ). Thus, 4 can be expressed as the sum of two primes. QED. 😀
(You can also check Wikipedia to verify this for Goldbach's conjecture.)

March 21, 2013 at 11:54 pm |
7. Maxwell

My brain exploded from the sheer epicness of this.

February 8, 2013 at 10:53 am |
8. marlowpowell

up to I looked at the paycheck saying \$6143, I didn't believe ...that...my mom in-law woz like truley bringing home money part-time from there computar.. there friends cousin has done this for only 11 months and resently repaid the morgage on their apartment and purchased a brand new Land Rover Defender. go to......... BIT40.ℂOℳ

February 7, 2013 at 5:53 pm |
9. Dana

It's called curiosity. Remember when you were little and you had some?

February 7, 2013 at 1:52 pm |
10. JohnW

So I guess the most logical step would be to try 2 raised to this number minus 1 to see if they can make a larger one.

February 7, 2013 at 1:30 pm |
• painkillr

except for the number 2, no even number is a prime number

February 7, 2013 at 4:08 pm |
• James McGraw

Eons ago when I had some math courses 2 was considered the smallest prime number as it fits the definition of a prime being a number with no factors other than itself and 1. Have I been deluded all of these years?

February 13, 2013 at 4:44 pm |
11. Bipul

Hey i really want t know how 100 is a prime no. ????

February 7, 2013 at 11:04 am |
• JohnW

It's not, where are you getting this idea?

February 7, 2013 at 1:31 pm |
12. Bipul

Hey, i really want to know how 100 is a prime no. ? Please help me !!!!!

February 7, 2013 at 11:02 am |
• dhondu

kasam se bhai ...... chutiya ho kaaaaa........

February 8, 2013 at 7:59 am |
13. The Cutting Crew

This is why you never share your prime rib. It can only be divided by one and itself.

February 7, 2013 at 10:36 am |
• Hungryhippo

Well played sir!

February 7, 2013 at 10:41 am |
14. Romney was our LAST HOPE

It doesn't matter. Nothing matters anymore. Obama is quickly murdering the planet and God has forsaken us.

February 7, 2013 at 10:35 am |
• palintwit

Bwa hahhahahha !!

February 7, 2013 at 10:44 am |
• Pepinium

If the world comes to an end tomorrow, one of the benefits will definitely be not having to share this planet with acephalic morons, of which sir, you are a "prime" example , :).

February 7, 2013 at 12:29 pm |
• constantine16621990

Lol!!!:) nicely said pepinium:)

February 8, 2013 at 10:53 am |
• Steveoh

Acephalic moron??? That, sir, is an impossibility. A moron is "a person affected with mild mental retardation". A person absent a head would be signifcantly more than mildly retarded ... don't you think???

February 15, 2013 at 8:41 pm |
15. boungiorno

just got to love it

February 7, 2013 at 10:20 am |
16. Christine

That is so cool!

February 7, 2013 at 10:11 am |
• constantine16621990

Ik me too, but i hate math, and i hate numbers:/

February 8, 2013 at 10:56 am |
17. Rich

The prizes really should be \$3,001 and \$249,989. How did a bunch of math geeks get that wrong?

February 7, 2013 at 10:10 am |
18. NooYawkah

Oh great, now China will find an even larger number, then once again we will take the lead, then China....where will it all end!?!

February 7, 2013 at 9:59 am |
19. Alex

I wish I could say I was impressed, but these days all you do is ask a computer to do all the work. It doesn't matter if it takes 39 days for it to do so – it's still a machine doing the work. You could write a program asking for a prime number 1 billion digits long and a computer will do it. (Though I'm surprised given the computing power at our disposal that it would take 39 days for what they did). Now if they were still calculating this by hand and the result came from years of math geeks sitting hunched over pad and pencil, then I'd be impressed. Now let's see a computer genius come up with a program that allows a computer to calculate that 1 billion digit prime number in 5 minutes. Now THAT would be impressive!

February 7, 2013 at 9:58 am |
• Computers are smart

In these days of asking a computer to do the work for you, I'm pretty sure you asked a computer to generate an intelligent comment for you to post.

February 7, 2013 at 10:54 am |
• Troy

And what do YOU do for a living?

February 7, 2013 at 10:59 am |
20. Matt Kauffman

Bring out the GIMPS!

February 7, 2013 at 9:48 am |
21. Oscar Pitchfork

Most of the comments here only drive home the fact that most clever, sharp-thinking narcissists (like the ones who post here) are so far away from actual critical thinking that they virtually guarantee the eventual downfall of the American way of life...

February 7, 2013 at 9:21 am |
• SixDegrees

If you mean the American way of life that promotes religion in place of science, hatred in place of tolerance and dogma in place of reason, I'll be glad to see it go.

February 7, 2013 at 9:54 am |
• Dana

Since when is that the American way of life? You've been listening to Faux News again, haven't you?

February 7, 2013 at 1:44 pm |
• Kris Jackson

Eau contraire mon frère! (Misspelling intentional, and accent grave added by IE or Gateway, I dunno.) Geeks love this stuff, all these answers (excepting those by the Republicans) have been pithy and apt. And we use this technology to come up with stuff that we dig and enhances our lives.

February 9, 2013 at 7:27 pm |
22. The little guy

What about all the prime numbers smaller than this that will remain undiscovered as we continue to search for even larger ones?

February 7, 2013 at 8:47 am |
23. palintwit

Tea Party Patriots from south to south and east to west are in a panic now that Sarah Palin has been broomed from Fake News. One has only to take a casual drive south of the Mason-Dixon line to hear the sound of bagger's heads exploding everywhere. POP... POP... POP !!

February 7, 2013 at 8:37 am |
• Jimmy

And the TEA partyhas what to do with this discussion???
BTW: If the POTUS doesn't like the TEA party he shouldn't have started it!
Without him the TEA party would not have reason to exist!

February 7, 2013 at 10:36 am |
• palintwit

Ahhh... the sweet sound of teabagger's heads exploding. POP... POP... POP !!

February 7, 2013 at 10:42 am |
24. Thomas

How long is a piece of string?

February 7, 2013 at 8:36 am |
• cedar rapids

half as long as when it was twice the size.

February 7, 2013 at 9:06 am |
• Stringman

Duh! Twice as long as from either end to the middle! Everyone knows that...

February 7, 2013 at 9:17 am |
• Guillaume

It depends how fast you are going.

February 7, 2013 at 10:07 am |
• Basho1644

Ahhh-ha-ha-ha! 🙂 Good one. I wonder how many people get that.

February 7, 2013 at 10:33 am |
25. Buck

One would think that CNN would report on NASA's latest Special Effects PR vs. a math quizz....

http://www.fountainsofthegreatdeep.com/IFS.htm

February 7, 2013 at 8:26 am |
• SixDegrees

I bet it hurts when you have to read big words.

February 7, 2013 at 9:58 am |
26. David M

Well, my life is now complete. What a burden has been lifted from my shoulders. Armed with this information I am certain I can now create world peace, solve hunger and poverty, and live happily ever after. After all, a number of such magnitude must be useful for something.

February 7, 2013 at 8:22 am |

PUD.... Pud Mcpudderson, Mcpud Pud

February 7, 2013 at 9:04 am |
27. john

And this benefits ... Who ? What ? Where and/or When ? Did this cure world hunger , greed, deaths by guns, cancer, aids ? nope .

February 7, 2013 at 8:22 am |

You sir are a Pud.

February 7, 2013 at 9:02 am |
• SixDegrees

Actually, there are a lot of practical applications for this, but you're too much of a dullard to understand them, given that you can't appreciate the discovery simply on its own merits.

February 7, 2013 at 9:56 am |
• asdrel

Can you provide just one example?

February 7, 2013 at 10:31 am |
• john

There was one right in the article. Cryptography depends on prime numbers. If any easy way to find primes were ever discovered modern cryptography would be obsolete over night. So yes, prime numbers are extremely relevant to your life, that is if you like using the internet, credit cards, cell phones, or any technology whatsoever.

February 7, 2013 at 11:05 am |
• USAUSA

When asked the same question, the mathematics Badger replied "probably none". You dope.

February 12, 2013 at 12:45 pm |
• MR

no, but it revealed your genius to the world – pity it's on such an obscure item...

February 7, 2013 at 10:41 am |
28. BEEP beep

Penny.....Penny.......Penny

February 7, 2013 at 7:49 am |
29. kai

So whats this about optimus prime?

February 7, 2013 at 5:31 am |
• Jgibb

Hahaha, shoot! I was just going to throw an optimus line out there. Nicely done

February 7, 2013 at 6:52 am |
30. Mario

It seems that the author of this article does not understand the discovery. This is NOT the biggest prime number discovered, this is the biggest Mersenne prime number discovered. Finding another bigger prime number is easy – finding another Mersenne prime number is difficult. It is not even known if the set of Mersenne prime numbers is finite or not. For "normal" prime numbers we know there is an infinite number of them.

February 7, 2013 at 5:13 am |
• paric2

February 7, 2013 at 6:56 am |

I believe this is the larges prime of any type yet discovered. Have you seen something about a larger non-Mersenne prime having been found? I haven't.

February 7, 2013 at 7:17 am |
• BEEP beep

Penny..... Penny......Penny.

February 7, 2013 at 7:46 am |
• third party

Any number that can be expressed as "2 to the power of n minus 1" is a Mersenne number. If it is also a prime number, then it is a Mersenne prime (some definitions also require that n be prime). This article is indeed about a Mersenne prime. Mersenne primes are a subset of all prime numbers, but very large Mersenne prime numbers may be easier to find than other very large prime numbers, due to a more efficient algorithm that thas been developed to verify whether or not a candidate is prime.

February 7, 2013 at 11:12 am |
31. howardfeinski

I can double the number of known prime numbers. Just put a negative sign in front.

February 7, 2013 at 2:28 am |
• Alyssa

Prime numbers by definition have to be positive integers. There are no negative prime numbers.

February 7, 2013 at 7:31 am |
32. catsnake

i wanna see how many animals are saved each year.

February 7, 2013 at 2:01 am |
33. cekubickimdt1950

..what's a prime number?

February 7, 2013 at 12:18 am |
• I love pi

I Love Pi, especially in the Z-order

February 7, 2013 at 1:04 am |
• Mr. Steve

If you didn't read above... it is a natural number larger than 1 whose only natural number factors are 1 and itself.

why these so-called math people use the set of integers instead of a simpler set is just silly.

February 7, 2013 at 8:32 am |
34. brian

i wonder how many crackpipes that would be...

February 7, 2013 at 12:06 am |
• MOCaseA

After the first you wouldn't care...

February 7, 2013 at 6:44 am |
35. TheBob

I much prefer to see article like this on CNN than about which bullsh** bimbo is getting banged by what d0uchebag.

February 7, 2013 at 12:02 am |
36. Dowgirl

This reminds me of the brilliant short story by AC Clark, The Nine Billion Names of God. A group of monks In Nepal were using supercomputers to search out all the names of God (e.g. God, HaShem, Allah.) What a great plot, I will not spoil the ending, but knowing that the number of primes is infinite makes me sleep better at night. Anyone else remember this story?

February 6, 2013 at 11:15 pm |
• Dru

Sure do. I loved that, and his other stories.

February 7, 2013 at 1:37 am |

Yep I remember this. Actually really freaked me out.

February 7, 2013 at 1:43 am |
• mbplato1

loved A C Clarkes books, both short stories and novels....the nine billion names of god was also a favorite

February 7, 2013 at 5:47 am |
37. Joe Math

Well, this is cute, but not that impressive. I'll be truly impressed when someone proves the Riemann hypothesis. And there is some real money that comes with that.

February 6, 2013 at 11:04 pm |
• Old Shoe

Finding a new very large prime number affects what?? A bra size is more intriguing.

February 7, 2013 at 10:16 am |

I'm sure I will never understand why people do this stuff.

February 6, 2013 at 11:00 pm |
• Lori

Think of it as any other person watching the best mystery movie of their lives over and over except for the fact that the tv goes out about 4 minutes before the end. The storyline is then continually running through their head and the ending is unknown. I think, to the people that work on these things, math holds the same intrigue and they can drive themselves crazy thinking about how the ending is.

February 7, 2013 at 8:56 am |
39. Mrq5

Now this is cool stuff!!! I must be a geek at heart:) I loved reading the comments here too, prime-rib is great!!! I do remember prime numbers being rather significant back in my college/calc days since they can not be factored or represented in smaller terms or numbers.

February 6, 2013 at 10:48 pm |
40. Timetraveler

At this very moment a group of conservative wackjobs is mobilizing to ban all research on prime numbers "cuz they is the seeds of the devil, and if the Bahble wanted us to know them prime numbers it woulda wrote 'em in the good book".

February 6, 2013 at 10:37 pm |
• Lori

it's funny you say that cuz on fox news, this story has twice as many likes and 3x as many shares/tweets and positive comments and for some reason, people here need to post about how crazy conservatives are freaking out. I'm a person of faith but a socially moderate/fiscal conservative one and I find this kind of stuff very cool. Not necessarily even the math part of it but the kind of mind that can mull over these things for so long in search of an answer to a question that most people never new was a question in the first place. Don't judge, just enjoy the wonder of the human mind.

February 7, 2013 at 9:06 am |
41. The Crazy Jew.

Wow! Somebody actually took time to do this! I'm impressed just with the tenacity of the people! Hating math myself (my field is history), I am glad, seriously, that people love this as much as I loved hearing about finding the body of Richard III. Any advancement of human knowledge is a good thing. I thought I'd read that this number was found by volunteers. But if tax dollars were used, its worthwhile. Certainly moreso than \$600 toilet seats and other boondoggles!

February 6, 2013 at 10:30 pm |
42. Rick Springfield

I saw that group of numbers above and thought right away it was the true cost of Obamacare in 3 years.

February 6, 2013 at 10:10 pm |
• pbernasc

no it is just the true stupidity coefficient associated with your brain, the bigger the coefficient , the stupidier your brain

February 6, 2013 at 10:17 pm |
• SciGuy

stupidier? oh, the irony.

February 7, 2013 at 12:05 am |
• pbernasc

think sude ... think

February 12, 2013 at 1:16 pm |
43. geeworker

I get it the pic with all the numbers is one of those computer generated images you know the ones that if you look at it at the right angle/stare past the numbers, you will see a hidden picture.

Nice pic of Beyonce with nothing on giving the finger to PETA

hint look at it from the the upper right looking down

February 6, 2013 at 10:02 pm |
44. Balancedbrain

Many engineers can't spell – and many English majors can't do math. We need both, so lighten up!!

February 6, 2013 at 9:25 pm |
• TheBob

Actually we only need engineers. Spellcheckers do a great job with spelling.

February 6, 2013 at 10:02 pm |
• SixDegrees

They due?

February 7, 2013 at 3:21 am |
• Alyssa

I humbly bow to SixDegrees.

February 7, 2013 at 7:33 am |
45. GCOM

It's all good.

February 6, 2013 at 8:43 pm |
46. SoCalMatt

"Great Internet Mersenne Prime Search (GIMPS), a collaborative project involving thousands of volunteers who sift through numbers in search of primes."

Sounds like a fun and exciting group of people.....sign me up! I hope they meet on Saturday nights!

February 6, 2013 at 8:28 pm |
47. Ken Sawyer

It really looks like the total on our national debt if you think of it except it does not keep gaing every second as our debt does.

February 6, 2013 at 8:23 pm |
• Caihlyn

Just to put this in perspective: The nation debt is around 16 trillion dollars, that is close to 2 to the power of 44. The prime they found is one less than 2 to the power of 57 million, 881 thousand, 161. Our national debt will not approach 2 to the 45th power, until it doubles...

February 6, 2013 at 10:36 pm |
• John

Ken was trying to be funny...and failing.

February 6, 2013 at 10:52 pm |
48. Ken Sawyer

It makes litte difference in the life of a normal person.

February 6, 2013 at 8:19 pm |
• willhaynes24

Actually, it does. Prime numbers are used in hundreds of different applications – including to protect your facebook password by encryption!

February 6, 2013 at 10:09 pm |
• The Thinker

But what if..it holds the key to the meaning of life...

February 6, 2013 at 10:11 pm |
• TheBob

No, that would be 42.

February 6, 2013 at 10:27 pm |
• Zaphod Beeblebrox

As all "The Hitchhiker's Guide to the Galaxy" fans know, this prime number has nothing to do with the meaning of life. The "Answer to the Ultimate Question of Life, the Universe, and Everything" is simply 42. (If you need proof, check the WIKI –> http://en.wikipedia.org/wiki/42_(number) <–)

February 6, 2013 at 10:38 pm |
49. Greenspam

A TEXT file with a 17M digits number is 22M large? Each digit is like 1-byte, so 17M digits is 17Mb...

I guess unless there is extra white space involved. So, 5M is added for 1 newline char.. but that doesn't make sense either. Because more than 1/3 of the space is devoted to newline (5M out of 22M), so that means a newline every other 3 chars?

What is going on here? The math is off!

February 6, 2013 at 8:09 pm |
• Jim

They probably included the commas in the text file. For every 3 numbers there will be a comma. 17/3. + 17 is 22.66

February 6, 2013 at 8:22 pm |
• Greenspam

May be... but what's the point of putting commas there?

February 6, 2013 at 10:56 pm |

February 7, 2013 at 7:20 am |
• Craig

1 byte is 8 bits, or 8 zeros and ones. This can represent a number up to 2^8=256. So 1 byte can represent a number on average up to 2.5 digits in base 10. 17M/2.5=7 Million bytes needed to store a 17 Million digit number.

February 7, 2013 at 1:39 am |
• painkillr

@craig the article says a "text file" which implies an ASCII format. surely you can represent all base 10 numbers with just 4 bits, but that would deviate from the convention of a computer text file where it reads all 8 bits as a byte

February 7, 2013 at 4:18 pm |
• Sciguy73

Hey Einstein, try looking at the picture. They're showing you the contents of the beginning of the file.

February 7, 2013 at 7:16 am |
• Sciguy73

Craig, they stored this number in ASCII. But if they had stored it in binary like you are saying, it would be 57,885,161 / 8 = 7,235,646 bytes long.

February 7, 2013 at 7:28 am |
50. EmmetEarwax

In a fan-fic I wrote ,a 500-year old cryptogram stubbornly resisted any & all solution -until the hero used the sequence of pi to extract the code, an ever-changing code. Suddenly he was able to find the answer to a major threat to all the universe !

Yet he couldn't explain this without boring his comrades.

February 6, 2013 at 7:51 pm |
51. JohnnyNoname

If there are infinite prime numbers then isn't it a wasted exercise to discover the largest prime number known? So what? There are still infinite more prime numbers larger than this one.

February 6, 2013 at 7:42 pm |
• Alex

The whole point is it is the largest known prime number...-.-

February 6, 2013 at 7:52 pm |
• Greenspam

Yes, there is an infinite number of prime numbers

February 6, 2013 at 7:57 pm |
• noodlebrain

Yet, we don't know what the next bigger one is. Nor the next one after that. Etc. Primes may be infinite but the ones we know are finite. That's the point.

And the finite subset: Primes We Know of the infinite set: All Primes has just increased by one; plus the new Prime We Know is now the largest of all the Primes We Know.

/nerd

February 6, 2013 at 8:48 pm |
• Bob

As computers and algorithms become faster we are able to factor larger numbers within a reasonable amount of time. The speed we can factor numbers affects the security of many encryption algorithms.

February 6, 2013 at 8:55 pm |
• oldprof

ENGINEERS AT Cray Research used to test Cray IIs before delivery by finding a new prime, or extending Pi

February 6, 2013 at 10:41 pm |
• TheBob

The largest prime number *KNOWN*, not the largest prime number in existence. Each new largest prime known that is discovered makes a greater challenge to discover the next one, hence the significance.

February 6, 2013 at 10:11 pm |
• The Thinker

That's infinitely obtuse.

February 6, 2013 at 10:12 pm |
52. Joe

Oh poo...I discovered that years ago!!!

February 6, 2013 at 7:35 pm |
• GPS Girl

Discovering your own old fecal deposits are nothing to really be that proud of. Just a'sayin...

February 6, 2013 at 7:42 pm |
• noodlebrain

Really? "Light years" ago? How long did it take you to travel that far? 🙂

February 6, 2013 at 8:49 pm |
53. southernwonder

if a number does not want to be divided, i am fine with that.

February 6, 2013 at 7:18 pm |
54. Cheech

Bet a lot of dudes would like to smoke that number.

February 6, 2013 at 7:04 pm |
55. Burbank

I hope this wasn't figured out on taxpayer grant money, but why do I get the sinking feeling that it was? I worked hard to make the money the government forcibly takes from me and I sure don't like seeing it squandered like this!

February 6, 2013 at 6:55 pm |
• Paul

If they did use tax money, I'll cover your share so you can stop crying about it.

February 6, 2013 at 7:02 pm |
• SixDegrees

Yes, I'm sure you'll miss that tiny fraction of a single cent it might have cost you.

February 6, 2013 at 7:12 pm |
• smalltownkafka

So instead of actually making some effort on your own, you made a comment whining about the possibility. You could have found out for yourself, but instead you chose to enter a comment all about you, your really shallow opinion and your whining belief that you working hard for your money makes you special among people.

February 6, 2013 at 7:36 pm |
• NUSC

I would rather a tiny fraction of a cent of my tax money be wasted on this project rather than on building a bridge to no where or all the pork projects that our politicians are so fond of just because they line their pockets directly and indirectly.

February 6, 2013 at 9:14 pm |
• GPS Girl

I'm glad your money was "taken" from you so that this number could be found.

In fact, just knowing that there are thousands of research projects being funded from "your" tax money really makes me warm and fuzzy inside...

February 6, 2013 at 7:39 pm |
• noodlebrain

GPS Girl, I think I love you.

February 6, 2013 at 8:51 pm |
• TheBob

You're my kinda girl.

February 6, 2013 at 10:15 pm |
56. Bart

Oops, that number is divisible by 7. Start over.

February 6, 2013 at 6:32 pm |
57. empresstrudy

Liberals are sad and angry at the elitism and exclusion of all the other numbers who's self esteem is crushed.

February 6, 2013 at 6:18 pm |
• JessThinkin

I'm sure that composite numbers are just as proud of their clan as prime numbers are of theirs.

February 6, 2013 at 9:12 pm |
• The Thinker

Liberals find the fact that these numbers refuse to be divided an inspiration! Long live prime numbers!
This just in...
Conservatives push to outlaw teaching of prime numbers in public schools citing the law of indivisibility as a construct of evolutionary teaching....hmmm

February 6, 2013 at 10:17 pm |
58. pubcathlon

There's gotta be a chuck norris math joke in here...

February 6, 2013 at 6:05 pm |
59. apothecary

So, one could, if so inclined, name this number Optimus Prime?

February 6, 2013 at 5:52 pm |
• Justin Case

That would be a violation of the Prime Directive.

February 6, 2013 at 6:01 pm |
• apothecary

LOL!!

February 6, 2013 at 6:29 pm |

I wonder if they could find if this prime has a twin in the Twin Prime Conjecture. THAT would interesting to me

February 6, 2013 at 5:45 pm |
• noodlebrain

Dammit! I just wore out my finger *and* blew up my calculator. Thanks. Thanks a bunch.

February 6, 2013 at 8:54 pm |
61. Owen Ward

They can get the next larger prime number by taking the factorial of the latest prime number and adding one. Now you've got a number such that one of it's prime factors is larger than the original one. Of course you've got to perform the prime factorization on it, which is expensive.

February 6, 2013 at 5:43 pm |
• Aloisae

I was wondering how expensive and if the \$3,000 prize actually covered the cost. Just looking at the 39 days of nonstop computing and considering the possibility of failed attempts, not to mention any costs associated with staff time put into the project, I was inclined to think that this isn't exactly a profitable pursuit.

February 6, 2013 at 6:13 pm |
• Shawn

"They can get the next larger prime number by taking the factorial of the latest prime number and adding one." – Whu? considering it is PRIME, the only factors are itself and 1. the factorial would be .. 1 and.. the number itself. Add 1 and that is the next prime number? I going to say Probably Not.

February 6, 2013 at 7:25 pm |
• Fmr Math Major

Shawn,
It sounds like you're not understanding the definition of the word "Factorial" (you seem to be confusing Factorial with Factoring). The factorial of a number N is 1 * 2 * 3 ... * N (e.g. Factorial of 3 is 3 * 2 * 1 = 6, Factorial of 4 is 4 * 3 * 2 * 1 = 24).

I'm not necessarily convinced that Factorial of (current largest prime number) + 1 is prime, but it's kind of an interesting thought, in a math-geek way.

February 6, 2013 at 8:07 pm |
• Brian

@Shawn, the FACTORIAL of a number is not the FACTORS of a number. The FACTORIAL is the product of all the numbers up to and including that number.

e.g. the FACTORIAL of 7 (written 7! ) is 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040.

5040 + 1 is 5041. See my note below to Fmr Math Major (whose reply to you is not showing in the normal view for some reason, but appears when I try to reply to you.)

@Fmr Math Major, It is known (from Euclid's proof of the Infinity of primes that the FACTORIAL of a prime + 1 is either prime itself, or has a prime factor which is not in the original list of products.

For example, using the factorial of 7 + 1 (noted above), you get 5041. This is not itself prime, but it has a prime factor of 71, which is not in the original list of numbers used to produce factorial 7 plus 1. You can then calculate 71 factorial plus 1 and get an even larger prime.

The real reason that this method is not generally followed for calculating larger primes is that is it very costly in terms of computation.

February 6, 2013 at 8:28 pm |
• endeavor43

@ Brian: Also, contrary to what Owen Ward says above, this method does not give you the NEXT LARGER prime number. In your example, the next prime number after 7 is 11, but 11 is not a divisor of 5041 = 7! + 1.

February 6, 2013 at 9:20 pm |
• Owen

@endeavor43, you are correct. It's not necessarily the next prime number, but it is a larger prime number, which is all we really care about.

February 6, 2013 at 9:41 pm |
• stanley

That is not true. Counterexample: 5 is prime. 5! + 1 = 121, which is not prime because it is 11*11.

February 7, 2013 at 3:26 am |
• GPS Girl

You mean, like (2^57,885,161 – 1)! + 1

That's a big ol' number...

February 6, 2013 at 7:46 pm |
• ritmocojo

Love it when you talk nerdy to me. Please don't stop.

February 7, 2013 at 9:41 am |
• Loubies

Why must every pursuit be monetarily profitable to be worthwhile? That's what's wrong with this country. Too many people believe that if it doesn't make you money then it's not worth it.

February 6, 2013 at 8:01 pm |
• Sciguy73

Like

February 7, 2013 at 7:22 am |
• sharoom

Your method doesn't always work. Let's take a smaller prime as an example such as 5.

5! + 1 = 5x4x3x2x1 + 1 = 120 + 1 = 121

121 is not prime. It is divisible by 11.

Q.E.D.

February 6, 2013 at 8:51 pm |
• Owen

The (factorial + 1) is not necessarily prime. But one of its prime factors is guaranteed to be larger than the original one.

February 6, 2013 at 9:02 pm |
• The Thinker

This is my favorite posting thread EVER!

February 6, 2013 at 10:19 pm |
• Owen

I realized after posting that my method is not practical. Without a working quantum computer, factoring large numbers like this with today's computers would take longer than the age of the universe. That's why modern encryption techniques are based on the product of two large prime numbers.

February 6, 2013 at 8:58 pm |
• Theo

In fact it is not known whether there exist an efficient algorithm to factor numbers. If someone discovers one this would be a big hit to the current algorithms used in internet security (which use products of two very large primes).

February 7, 2013 at 11:41 am |
62. R

If there are infinite prime numbers, Statistically, You can start typing randoms numbers in any order up to 100 or 1000 digits and that would be initial digits of a prime number. Think about it. Quite Interesting!

February 6, 2013 at 5:38 pm |
• stanley

Your statement about statistics isn't true. The prime number theorem says that the probability of a randomly-selected number N being prime is 1/ln(N). If you randomly type lots of digits, N will be huge, so 1/ln(N) will be tiny.

February 7, 2013 at 3:30 am |
63. Kris Warloe

There is an error in the given definition of a prime number. According to the given definition one is a prime number since it is divisible by one and itself. the definition needs to say that a prime number has exactly two DISTINCT factors.

February 6, 2013 at 5:36 pm |
• endeavor43

I think that the usual definition specifies that a prime number must be greater than one, but actually I think that your definition is more mathematically satisfying, so long as you are allowing primes to be negative.

February 6, 2013 at 7:07 pm |
• John

...two distinct positive integer factors.

February 6, 2013 at 10:41 pm |
64. ZeroSix

Sheight.

February 6, 2013 at 5:02 pm |
65. wang tassinari

before I saw the check 4 \$7296, I did not believe that my sister was like they say actualey erning money part-time on their computer.. there sisters roommate haz done this less than eleven months and by now took care of the mortgage on there cottage and got a great Cadillac. read more at............ BIT40.ℂOM

February 6, 2013 at 4:59 pm |
• rc roeder

If it looks like spam, if it sounds like spam it it tastes like spam it is SPAM.

February 6, 2013 at 5:10 pm |
• tastes like spam

Hate to tell you, Buddy, but that's not how your sister earned all that money. . .

February 6, 2013 at 5:55 pm |
• ThereIsNoGod

February 6, 2013 at 6:52 pm |
• The_ref

Only 992,704 more clients and she'll be a millionaire.

February 6, 2013 at 8:37 pm |
• moose2823

Thats NOT a prime number! Get back on the topic of the article!!

February 6, 2013 at 10:21 pm |
• The_ref

OK. Only 992,707 more clients and she'll have \$1,000,003. The smallest prime number greater than 1,000,000.

February 7, 2013 at 8:55 am |
66. God

I know a few larger ones....

February 6, 2013 at 4:53 pm |
• bobk52

The biggest Prime # is on my wife's credit card!

February 6, 2013 at 7:31 pm |
67. Jokesterer

This is my favorite number. What a coincidence.

February 6, 2013 at 4:51 pm |
68. notsogeeky

Awsome! Keep on posting more on numbers. They are fun and cheap.

February 6, 2013 at 4:41 pm |
• EuphoriCrest

Oh sure, they may look cheap at first, but they can add up really fast!

February 6, 2013 at 7:43 pm |
69. Rob

Oh, at first glance I thought it was the national deficit!

February 6, 2013 at 4:35 pm |
• K

this number is so big that it took 59.02 MINUTES to scroll down continuously from top to bottom.

February 6, 2013 at 4:40 pm |
70. W.

When I had fallen 60 feet, breaking my body badly and suffering a spinal cord injury, I would add up all the prime numbers backwards from 100 to 2 and take the square root of that value, while laying paralyzed in ICU with tubes out of every orifice and experiencing extreme, ubiquitous pain: staring at the ceiling. I never got the answer right and I never expected to. It did, however keep me alive by the preoccupation of my mind away from the profound injuries I was enduring. As inconsequential as this seems to the lead story, sometimes prime numbers can save a life, they did mine. Now I am a paraplegic and sequestered to the isolation of my home. I am working on axiomatic formulations of Godel numbers and their implications to recursive synthetic DNA transitional computations. Paucity is a fundamental to probity. I only wish I had gone to school.

February 6, 2013 at 4:25 pm |
• Anne

W. Thank you for making my day with this comment. That is all.

February 6, 2013 at 4:43 pm |
• enkaynj

Agreed. Mostl of the time, the comments are more interesting than the lead story itself.

February 6, 2013 at 8:13 pm |
• sreeni

amazing story !

February 6, 2013 at 4:48 pm |
• aknartrebna

Best. Post. Ever.
In other news, 2^2^9 – 1 is still my favorite

February 6, 2013 at 4:56 pm |
• Poltergeist

Stuff like this should be in the news. That's inspiring.

February 6, 2013 at 5:19 pm |
• elandauCNN

W – Thanks so much for sharing!

Elizabeth Landau, CNN

February 6, 2013 at 5:33 pm |
• moose2823

I brought you chocolates.....I ate some

February 6, 2013 at 10:22 pm |
71. Slowpoke Rodriguez

Great, now everyone knows my email password.

February 6, 2013 at 4:17 pm |
• Nobody Knows

not to mention my youtube my minecraft my computer and my phone ........stupid scientists >_<

February 6, 2013 at 5:20 pm |
72. svann

The best prime is prime rib.

February 6, 2013 at 4:08 pm |
• Lizrod

I like my prime numbers, with a side salad and steak fries.

February 6, 2013 at 4:23 pm |
73. Ilam

Just don't forget to carry the 1.

February 6, 2013 at 3:48 pm |
74. Mimi

B I N G O !!!

February 6, 2013 at 3:35 pm |
75. Charles

All integers have the numeral 3 in them.

http://www.cut-the-knot.org/do_you_know/digit3.shtml

February 6, 2013 at 3:19 pm |
• apstar

Don't they have more productive things to do with all that CPU power? We know there will always be a bigger prime number that can be "discovered" so enough already.

February 6, 2013 at 3:27 pm |
• MrBo

Watch out, Grumpy Cat is on the loose.

February 6, 2013 at 3:31 pm |
• Eman

Yes, like surfing Facebook or downloading pictures of cats dressed like pirtaes. It's not like they were diverting power from a hospital's ICU to do this. Geez.

February 6, 2013 at 3:39 pm |
• inimrepus

Actually, prime numbers are vital in computer security.

February 6, 2013 at 4:09 pm |
• Roger

If all humans had your level of intellectual curiosity, we might have learned to plant grain by now. And then again, maybe not.

February 6, 2013 at 11:15 pm |
• orange

Um. 4, 5, 26,

February 6, 2013 at 4:29 pm |
76. dc

It's close to the number of times Microsoft tells me it has updates to do every time I shut down! =o)

February 6, 2013 at 3:03 pm |
77. Jeff Cox

They're just discovering that? I'm pretty sure that's how much my ex-wife ran up on our credit cards just before the divorce ...

February 6, 2013 at 3:02 pm |
78. Hoss

I'm pretty sure the number 2 will go into it. Can someone check my math?

February 6, 2013 at 2:59 pm |
• HenryMiller

You can check it yourself–click on the link, wait a longtime, and look to see if the least significant digit is even.

February 6, 2013 at 3:55 pm |
• Dave

No, it won't be even; that's where the minus 1 comes in.

February 6, 2013 at 4:36 pm |
• Steve

Incorrect, by definition, both 2 times any number is even, and any even number minus 1 is odd.

Since this number is equal to 2^57,885,161 – 1, this number is odd, which means, again, by definition, it is not divisible by 2.

February 6, 2013 at 4:40 pm |
• elandauCNN

Steve is correct. 2 raised to any power, minus 1, will be odd.

Elizabeth Landau, CNN

February 6, 2013 at 5:31 pm |
• noodlebrain

Does nobody here get "tongue in cheek" comments? :/

February 6, 2013 at 9:03 pm |
79. ritmocojo

"Feel like a number, feel like a number"

February 6, 2013 at 2:53 pm |
80. kurtinco

I don't know why this is fascinating, but it is. It is a little mind boggling to think that integers with billions of digits are still able to be prime numbers.

When the author talked about applications of this knowledge, it reminded me of the movie "Contact". In that movie, a recitation of the prime numbers up to a certain point was used to show a signal received from space was of intelligent origin.

Perhaps one day we'll come to look at prime numbers as a way of judging whether alien species understand mathematics. Regardless, this is still pretty impressive stuff to calculate.

February 6, 2013 at 2:52 pm |
81. Korm

Still not as big as Michelle Obama's butt.

February 6, 2013 at 2:52 pm |
• hingedlwnb

You're right. MO's butt is indeed prime.

February 6, 2013 at 3:03 pm |
• Korm

It's her face that is scary.

February 6, 2013 at 4:16 pm |
• Venusman

I didn't know that they let three-year-olds write comments.

February 6, 2013 at 3:07 pm |
• Korm

Did you come up with that all by yourself? You deserve a gold star.

February 6, 2013 at 4:17 pm |
• palintwit

February 6, 2013 at 3:17 pm |
82. Optimus Prime

It's Prime Time for find prime numbers.

February 6, 2013 at 2:51 pm |
83. are122

What relevance does the largest prime ever have on your life? Probably none. <~~Huh. He's right.

February 6, 2013 at 2:46 pm |
• Howard

Great! They found the largest prime number yet. Ooooo-kay, so now that they found it ... what are they going to do with it?

February 6, 2013 at 2:52 pm |
• EmmetEarwax

The higher we go with numbers, the more resistant and intractible they are to factoring. The above monster is beyond the human brain to handle, and only monolithic super-computers could have computed the number being discussed.

It HAS been proven that a number divided by the number of primes up to (and including it,if its prime) is approximated by its natural logarithm.

But when will math discoveries lead to the eradication of disease, of social disorder, of political & religious tyranny, and of all other ills ?

February 6, 2013 at 7:45 pm |
• SixDegrees

The ability to factor large numbers is an integral part of the search for large primes. Finding fast methods for factorization has a direct impact on the security of all current encryption algorithms.

February 6, 2013 at 3:26 pm |
• sameeker

I would much rather read about this then some scandal involving the Kardashians or a football player with a fake girlfriend. People like this poster eat up that drivel, while shunning math and science. Oh the state of America today.

February 6, 2013 at 3:47 pm |
• SixDegrees

Some people think that Kim has prime boobs. I think they're just odd.

February 6, 2013 at 4:46 pm |
84. File Format

If a text file contains 22MB of information then the size of the number must be more than 17M digits.

February 6, 2013 at 2:19 pm |
• MS

It was probably a Microsoft Word file. And don't forget the commas!

February 6, 2013 at 2:26 pm |
• asdf

I guess it would depend on what the base system is but true under decimal systems where at most you only need 4 bits to represent a digit.

February 6, 2013 at 2:37 pm |
• asdf

decimal system, stupid typo

February 6, 2013 at 2:43 pm |
• Sciguy73

4 bits per digit is only true if you're representing it in hexadecimal. In decimal it is closer to 3.4 bits per digit.

February 7, 2013 at 7:42 am |
• Mike

Not if he used pkzip. 🙂

February 6, 2013 at 2:46 pm |
• Digital Joe

You are correct, but it could take 22MB to house the file, if the data sectors are off. Large files like large sectors, less overhead on the disk.

February 6, 2013 at 2:53 pm |
85. palintwit

And mathematicians at prestigous Sarah Palin University have perfected the abacus.

February 6, 2013 at 2:08 pm |
• Dude

Dont u think its time to give it a rest ? Its stale already...

February 6, 2013 at 2:28 pm |
• asdf

Sarah who? Oh that chick I wack off too at the beginning of The Undefeated. You have to get your business done in the first five minutes or the dialog starts to make you vomit.

February 6, 2013 at 2:39 pm |
• manyote

And don't omit the 'Redneck Palm Pilot' she invented.

February 6, 2013 at 2:51 pm |
• palintwit

Good one.

February 6, 2013 at 3:18 pm |
• Dean100343

Would be willing to wager that she has a little more money in the bank than you and is probably a whole lot better looking also.

February 6, 2013 at 3:18 pm |
• palintwit

Neither of which is a measure of success.

February 6, 2013 at 3:21 pm |
• Engineer

Abacus' are actually a lost art and extremely useful. Today's calculators are a crutch for students, and hinder them from truly understanding and enjoying mathematics. Yes, Math is important. The stuff you said "I'll never need this, this has no practical application" is the reason you have most of the things you rely on for everyday life.

February 6, 2013 at 3:38 pm |
• Engineer

February 6, 2013 at 3:42 pm |
• svann

I dont know about abacus, but I guess I must have been in the last class to learn slide rule.

February 6, 2013 at 4:12 pm |
• Montello

I remember way back in the 50's when a guy came up with a way to do square roots on an abacus, and actually beat a computer at it! We've come a long way, baby.

February 6, 2013 at 5:20 pm |
• Speller

Abacuses, not abacus'. Learn to make plurals correctly, Engineer.

February 6, 2013 at 5:24 pm |
• Roger

Hey Svann,

Were you the kid with the brown horn rim glasses and long blonde hair? I was two chairs behind you.

February 6, 2013 at 11:21 pm |
• Eric

Abacii?

February 12, 2013 at 12:19 pm |

### Contributors

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