New Mersenne Prime Discovered, Largest Known Prime Number: 2^74,207,281

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New Mersenne Prime Discovered, Largest Known Prime Number: 2^74,207,281 - 1 (mersenne.org)

Posted by Soulskill on Tuesday January 19, 2016 @03:01PM from the that's-my-phone-number dept.

Dave Knott writes: The Great Internet Mersenne Prime Search (GIMPS) has discovered a new largest known prime number, 2^74,207,281-1, having 22,338,618 digits. The same GIMPS software recently uncovered a flaw in Intel's latest Skylake CPUs, and its global network of CPUs peaking at 450 trillion calculations per second remains the longest continuously-running "grassroots supercomputing" project in Internet history. The prime is almost 5 million digits larger than the previous record prime number, in a special class of extremely rare prime numbers known as Mersenne primes. It is only the 49th known Mersenne prime ever discovered, each increasingly difficult to find.

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PrimeCoins by darkain · 2016-01-19 15:05 · Score: 2

Are these people mining PrimeCoins? What's the motivation to be part of this network? Just curious is all.
1. Re:PrimeCoins by Anonymous Coward · 2016-01-19 15:08 · Score: 1
  
  Don't ask why people are doing math, even they don't know.
2. Re:PrimeCoins by dasunt · 2016-01-19 15:12 · Score: 3, Funny
  
  You were the first comment, and you didn't take the opportunity to say "prime post!" :p
3. Re:PrimeCoins by Anonymous Coward · 2016-01-19 15:14 · Score: 1
  
  Once you have enough for food, shelter and healthcare, only the most boring people do things for money.
4. Re:PrimeCoins by Anonymous Coward · 2016-01-19 15:18 · Score: 0
  
  There is a US$3000 award for the finder.
5. Re:PrimeCoins by suso · 2016-01-19 15:25 · Score: 4, Insightful
  
  There is a US$3000 award for the finder.
  And a $3000 power bill for those who don't find it.
6. Re:PrimeCoins by Anonymous Coward · 2016-01-19 15:30 · Score: 1
  
  Why do anything? Nothing really matters if you stand back far enough.
  If we're going to nitpick what others do though, I think they should concentrate their efforts on finding a formula instead of brute forcing new numbers.
7. Re: PrimeCoins by Anonymous Coward · 2016-01-19 15:47 · Score: 1
  
  What's the motivation? Apart from basic human curiosity and wanting to be part of something bigger than yourself, however pointless?
  Not much.
  But however pointless this may seem they still have a) discoverd a new prime number and b) uncovered bugs in hardware, so it's not a complete waste of time.
8. Re:PrimeCoins by freeze128 · 2016-01-19 15:51 · Score: 0
  
  Another prime number found means another prime number that can be used in encryption... and since this is the largest prime yet, that means it's just going to be harder to brute force, which means better security (aside from any quantum computing breakthroughs).
9. Re:PrimeCoins by Livius · 2016-01-19 15:53 · Score: 5, Funny
  
  Obviously prime posts start with the second one.
10. Re: PrimeCoins by ememisya · 2016-01-19 16:02 · Score: 1
  
  I wanna be a perfect number! 2^74,207,281 - 1, you're so fucking special. Hahaha! That ol' monk got more credit than he deserved didn't he?
11. Re:PrimeCoins by agm · 2016-01-19 16:08 · Score: 0
  
  Only if you fall for the dubious exception to the definition of "prime" that excludes 1 because it makes maths more convenient. :-)
12. Re:PrimeCoins by DesertNomad · 2016-01-19 16:11 · Score: 4, Informative
  
  this is likely true as the number 1 is not a prime number. https://primes.utm.edu/notes/f...
13. Re:PrimeCoins by chmod+a+x+mojo · 2016-01-19 16:13 · Score: 1
  
  1: to help, kind of like SETI / FOLDING@Home / et al.
  2: finding a large prime that hasn't been found yet pays ~$5k
  3: finding million digit+ primes can pay out up to ~$50K when verified.
  4: they have an old PC just hanging around and feel like helping out the math fields.
  
  --
  To err is human; effective mayhem requires the root password!
14. Re:PrimeCoins by Njorthbiatr · 2016-01-19 16:24 · Score: 1
  
  Who is paying for prime numbers!!!
15. Re:PrimeCoins by armanox · 2016-01-19 17:15 · Score: 1
  
  No coins. Just bragging rights.
  
  --
  I'm starting to think GNU is the problem with "GNU/Linux" these days.
16. Re:PrimeCoins by WalksOnDirt · 2016-01-19 18:02 · Score: 3, Insightful
  
  There are only 49 of these known. I don't see how it can be used in encryption.
  
  --
  a,e,i,o,u and sometimes w and y (at be if of up cwm by)
17. Re:PrimeCoins by fahrbot-bot · 2016-01-19 18:25 · Score: 3, Funny
  
  Who is paying for prime numbers!!!
  Mexico.
  
  --
  It must have been something you assimilated. . . .
18. Re:PrimeCoins by 91degrees · 2016-01-19 19:32 · Score: 1
  
  If we only use Mersenne primes in encryption, we'd be trivially easy to crack. Even without a list of the primes, you only need to work through a few million of them. That doesn't take long even for a desktop PC. And you'd need a key almost a megabyte long!
19. Re:PrimeCoins by SuricouRaven · 2016-01-19 20:09 · Score: 1
  
  4b: Also a parent/college/workplace paying the power bill.
20. Re: PrimeCoins by wonkey_monkey · 2016-01-19 21:11 · Score: 3, Insightful
  
  I wanna be a perfect number!
  I'd rather be happy than perfect.
  
  --
  systemd is Roko's Basilisk.
21. Re:PrimeCoins by sectokia · 2016-01-19 23:59 · Score: 2
  
  Prime numbers are very useful for puesdo random number generators, In this case the merssene twister. The is a huge benefit in making good rng from prime, because it can be made with an incredible simply algorithm that can run fast etc.
22. Re:PrimeCoins by jafiwam · 2016-01-20 00:12 · Score: 2
  
  4b: Also a parent/college/workplace paying the power bill.
  4c: Resistance electric heating where the "extra" power goes to something you gotta do anyway.
  4d: Testing a new rig.
  4e: Annoys the sanctimonious douchebags in the audience.
23. Re: PrimeCoins by JonahsDad · 2016-01-20 02:15 · Score: 1
  
  I wanna be a perfect number! 2^74,207,281 - 1, you're so fucking special. Hahaha! That ol' monk got more credit than he deserved didn't he?
  Largest known perfect number found (credit to Euclid).
  (2^74,207,281 - 1) * 2^74,207,280.
24. Re:PrimeCoins by Bob+the+Super+Hamste · 2016-01-20 02:51 · Score: 1
  
  4d: Testing a new rig.
  Glad to see I'm not the only one who does this. Let it run full on for a few days then after that let it blast away at night when not in use for a week or 2 to make sure everything is good and doesn't have problems.
  
  --
  Time to offend someone
25. Re:PrimeCoins by hendrips · 2016-01-20 03:34 · Score: 1
  
  There is nothing dubious about it. Primes are defined this way because of the Fundamental Theorem of Arithmetic. If primes were defined to include 1, there would be no such thing as a unique factorization into primes, and if that did not exist, there would be no point to the concept of primes at all.
  More generally, one of the principles of abstract algebra is that units (elements with a multiplicative inverse) can never be primes in any unique factorization domain (i.e., any ring that follows the Fundamental Theorem of Arithmetic).
26. Re:PrimeCoins by Anonymous Coward · 2016-01-20 05:21 · Score: 0
  
  How do you pay for plane/train/bus tickets to travel the world?
27. Re:PrimeCoins by slew · 2016-01-20 06:54 · Score: 1
  
  Prime numbers are very useful for puesdo random number generators, In this case the merssene twister.
  The is a huge benefit in making good rng from prime, because it can be made with an incredible simply algorithm that can run fast etc.
  Kinda, but not really. The real requirement for making a good generalized linear congruent pseudo-random number generator with a long period is to find a large galois field matrix that has a *primitive* characteristic polynomial. As it turns out it is easier to *test* if a trinomial (polynomial with 3 non-zero terms) is primitive if it is generated from a parameter related to a Merssene prime number decomposition (2^k-1). This does not guarantee that any of the trinomials generated by this parameter is primitive, only that it is easy to test (some Merssene primes like M40 do not generate any usable trinomials).
  Primitive trinomials are good for fast pseudo-random number generators because they will have the long period set by the primitive, yet be easier to compute because there will be lots of zero terms in the matrix (instead of a dense matrix).
  However regardless of the difficulty of the mechanism to validate that the matrix is primitive, they computation that you do to *generate* random number is completely independent of the prime-ness of the parameter (and you don't really want a prime number if it isn't a Merssene prime because the slow way of testing can be sped up by factoring the parameter) only the density of the matrix. Matrices with primitive polynomials (or specifically trinomials) not generated by Merssene primes will have the same computation time.
  You can kind of think of primitive polynomials as being kind of a generalization of a prime number to galois polynomials, but it's not really the same thing except in the case where your matrix is a simple scalar (e.g. the classic linear congruent scalar pseudo random number generator you learned in school).
28. Re:PrimeCoins by Anonymous Coward · 2016-01-20 07:26 · Score: 0
  
  I pay for all my glut and luxury through imperceptibly distributed exploitation of commoners.
29. Re:PrimeCoins by agm · 2016-01-20 10:50 · Score: 1
  
  Ok, you win. :-)
30. Re:PrimeCoins by TeknoHog · 2016-01-20 13:14 · Score: 1
  
  And a $3000 power bill for those who don't find it.
  News flash: it takes energy and money to do research.
  
  --
  Escher was the first MC and Giger invented the HR department.
31. Re:PrimeCoins by AthanasiusKircher · 2016-01-20 13:43 · Score: 1
  
  There is nothing dubious about it. Primes are defined this way because of the Fundamental Theorem of Arithmetic.
  While, I completely agree with you, lighten up a bit. Also, realize that in the real world the word "prime" comes from Latin primus, meaning first... hence prime steak, prime meridian, Optimus Prime, etc. And thus while in the mathy definition you're right, the real-world definition allows significant wordplay in this specific thread -- the first post is by definition a prime post, but in another sense (your sense), it's not.
32. Re:PrimeCoins by cold+fjord · 2016-01-20 17:01 · Score: 1
  
  For purposes of encryption the fact that it is prime number is relevant, the fact that it is a Mersenne prime isn't. It can be used just like any other prime number. (Assuming the encryption software is written with the capacity to accommodate such a large prime which I wouldn't take as a given.)
  
  --
  much of left-wing thought is a kind of playing with fire by people who don't even know that fire is hot - George Orwell
33. Re:PrimeCoins by cold+fjord · 2016-01-20 17:27 · Score: 1
  
  Haven't you ever been curious about something? The urge to explore? The desire to contribute to expanding the knowledge of humanity? The desire to contribute to developing useful knowledge for an important field like mathematics? The possibility of arriving at that important result yourself? The possibility of doing something useful?
  Not everyone shares those interests, especially for something as abstract as math in general, and searching for a particular form of prime number in particular.. There are probably other reasons as well.
  This is actually one of the mass participation projects that I've considered contributing to over the years. I actually have contributed to folding@home.
  
  --
  much of left-wing thought is a kind of playing with fire by people who don't even know that fire is hot - George Orwell
34. Re:PrimeCoins by WalksOnDirt · 2016-01-20 19:22 · Score: 1
  
  If it weren't so uselessly large it would definitely be in my list of famous prime numbers to try. That makes it an incredibly poor choice.
  
  --
  a,e,i,o,u and sometimes w and y (at be if of up cwm by)
35. Re: PrimeCoins by Anonymous Coward · 2016-01-22 17:42 · Score: 0
  
  Unique Factorization would still apply. Namely, 1 factorizes as 1*1, which factorizes as 1*1*1, which factorizes as 1*1*1*1, etc... thus every number uniquely factorizes as 1*1*1*...* [rest of the prime factors here]. If you want a shorter definition then define a new constant O_ne = 1*1*1*...*1 (please forgive the mathematical humor). Then, any number uniquely factorizes as O_ne * [rest of prime factors].
Obviously by Anonymous Coward · 2016-01-19 15:07 · Score: 0

That's a pretty large number, but they still haven't found your mom's number.
1. Re:Obviously by 93+Escort+Wagon · 2016-01-19 16:47 · Score: 1
  
  That's a pretty large number, but they still haven't found your mom's number.
  That's surprising, since so many guys have it already.
  
  --
  #DeleteChrome
Damn by Anonymous Coward · 2016-01-19 15:17 · Score: 0

Just when I'm done encrypting my data with the two largest known primes, someone finds one that is bigger.
Mental note by aaarrrgggh · 2016-01-19 15:22 · Score: 4, Funny

Thanks, now I need to change private key.
1. Re:Mental note by Anonymous Coward · 2016-01-19 17:13 · Score: 1
  
  I was going with the combination on my luggage.
2. Re:Mental note by Etherwalk · 2016-01-19 18:59 · Score: 2
  
  "2^74,207,281-1? That sounds like the combination an idiot would put on his luggage."
  --Spaceballs 2: The Search for More Money
3. Re:Mental note by LordHighExecutioner · 2016-01-20 03:48 · Score: 1
  
  And of course you memorized it, isn't it ?!?
"each increasingly difficult to find." by Anonymous Coward · 2016-01-19 15:28 · Score: 1

How the fuck do we know that? Maybe after the next one they get super easy, we have no fucking idea lol.
1. Re: "each increasingly difficult to find." by Anonymous Coward · 2016-01-19 15:32 · Score: 0
  
  I guess it's a trend. Although the next one could be found tomorrow, it's been taking years between each one found despite the continuous improvements in computing power.
2. Re:"each increasingly difficult to find." by Pseudonym · 2016-01-19 15:40 · Score: 4, Informative
  
  Here you go: S. Wagstaff, "Divisors of Mersenne numbers," Math. Comp., 40:161 (January 1983) 385--397. MR 84j:10052
  It's true that we don't know for sure, but it's not true that we have no fucking idea.
  
  --
  sub f{($f)=@_;print"$f(q{$f});";}f(q{sub f{($f)=@_;print"$f(q{$f});";}f});
3. Re: "each increasingly difficult to find." by Anonymous Coward · 2016-01-19 17:27 · Score: 0
  
  So start testing the primality of ulta large mersenne exponents and show is how easy it is. Better yet you should come up with a formula to predict these ultra large easy to find prime numbers
4. Re:"each increasingly difficult to find." by m.alessandrini · 2016-01-19 20:29 · Score: 1
  
  Math is fascinating because it can prove that a thing is possible or impossible, even if it has no idea what that thing is like. Take for example the proof that you cannot find an algebraic formula to solve equations of degree 5 or higher.
5. Re:"each increasingly difficult to find." by Anonymous Coward · 2016-01-20 03:02 · Score: 0
  
  Math is fascinating because it can prove that a thing is possible or impossible
  Mr. Gödel and Mr. Tarski would like to have a word with you...
6. Re:"each increasingly difficult to find." by Petronius+Arbiter · 2016-01-20 03:57 · Score: 4, Informative
  
  Math is also fascinating because of how it can often work around impossibility proofs.
  E.g., what class of polynomials is solvable depends on what elementary functions are allowed. With Jacobi theta functions, you can exactly solve quintics.
  http://mathoverflow.net/questi...
  For another example, with cosine and acos, you can exactly solve cubic polynomials, w/o using cube roots. Better, if the solutions are real, then the solution does not require imaginary numbers, unlike if you solve with cube roots.
Rare Primes? by TechyImmigrant · 2016-01-19 15:32 · Score: 1

>In a special class of extremely rare prime numbers known as Mersenne primes.
I understood that Mersenne primes are not rare, they are common compared to primes that don't fit the 2^n -1 form. Hence searching for Mersenne primes is a more efficient way of finding big ones.

--
I should use this sig to advertise my book ISBN-13 : 978-1501515132.
1. Re:Rare Primes? by Anonymous Coward · 2016-01-19 15:52 · Score: 0
  
  Common compared to other primes? What an ignorant statement!
  A proportion of approximately 1/log(x) of the natural numbers less than x is prime.
  There are well over 2^74000000 primes less than this newly-discovered one, but only 48 of them (assuming none between the previously-discovered one and the new one) are Mersenne primes.
2. Re:Rare Primes? by TechyImmigrant · 2016-01-19 16:12 · Score: 0
  
  Common compared to other primes? What an ignorant statement!
  A proportion of approximately 1/log(x) of the natural numbers less than x is prime.
  There are well over 2^74000000 primes less than this newly-discovered one, but only 48 of them (assuming none between the previously-discovered one and the new one) are Mersenne primes.
  Right, but pick a specific form that you can search along. If you searched along the odd numbers, incrementing by two each time, you would search through more cases than searching through (2^n)-1 increasing n by one each time. (2^n)-1 is a rich vein compared to say (2^n)-3 for incrementing n, or n_(i+1) = (n_i) + 2 for incrementing i.
  
  --
  I should use this sig to advertise my book ISBN-13 : 978-1501515132.
3. Re:Rare Primes? by complete+loony · 2016-01-19 16:23 · Score: 3, Informative
  
  No, absolutely not.
  Out of 74,207,281(-ish) tested values for n, this is only the 49th prime found. If you tested the first 74,207,281 odd numbers you would have found more that 5 million primes.
  
  --
  09F91102 no, 455FE104 nope, F190A1E8 uh-uh, 7A5F8A09 that's not it, C87294CE no. Ah! 452F6E403CDF10714E41DFAA257D313F.
4. Re:Rare Primes? by Anonymous Coward · 2016-01-19 16:25 · Score: 5, Informative
  
  It's not so much that Mersenne numbers are much more likely to be prime than other odd numbers of their size. It's that there is a special-purpose primality test just for Mersenne numbers that is tons more efficient than verifying other primes of similar size.
5. Re:Rare Primes? by TechyImmigrant · 2016-01-19 17:44 · Score: 1
  
  Thank you. That makes sense. I learned something.
  
  --
  I should use this sig to advertise my book ISBN-13 : 978-1501515132.
6. Re:Rare Primes? by Anonymous Coward · 2016-01-19 20:20 · Score: 4, Insightful
  
  Uninteresting fact.
  If 2^n-1 is represented in binary then n will be the number of set bits.
  That means that if n can be divided by m then 2^n-1 can be divided by 2^m-1. (For example 2^15-1 = 32767 and can be divided by 2^3-1 and 2^5-1.)
  From the headline we can tell that 74,207,281 is a prime, otherwise 2^74,207,281-1 wouldn't be a prime.
7. Re:Rare Primes? by Anonymous Coward · 2016-01-20 05:02 · Score: 0
  
  Learning something by making stuff up in a forum and waiting for people to correct it has a high social cost. Please find another way to learn.
8. Re:Rare Primes? by TechyImmigrant · 2016-01-21 14:18 · Score: 1
  
  Learning something by making stuff up in a forum and waiting for people to correct it has a high social cost. Please find another way to learn.
  There's only a high social cost if you care what other people think. I had confused that series with . An AC did eventually explain the reason for searching for Mersenne primes being the efficiency of the primality test. I'm very familiar with primality tests for key search algorithms, which need to select uniformly amongst primes for the security of the keys to be maintained, because I'm an implementor of crypto.
  Many of the other commenters just showed their smug attitude by saying "You're wrong" without bothering to put in the effort to explain the efficient primality test as the reason.
  
  --
  I should use this sig to advertise my book ISBN-13 : 978-1501515132.
9. Re:Rare Primes? by TechyImmigrant · 2016-01-21 14:19 · Score: 1
  
  Argh. My html got messed up. For shame! For shame!
  
  --
  I should use this sig to advertise my book ISBN-13 : 978-1501515132.
10. Re:Rare Primes? by TechyImmigrant · 2016-01-26 05:59 · Score: 1
  
  No. It's interesting.
  
  --
  I should use this sig to advertise my book ISBN-13 : 978-1501515132.
It's not new by Anonymous Coward · 2016-01-19 15:45 · Score: 1

It's not new. Chuck Norris discovered in with this pocket calculator which measuring the circumference of his biceps.
1. Re:It's not new by invictusvoyd · 2016-01-19 18:41 · Score: 1
  
  Which was after he smacked your head . That explains why your statement does not make sense .
2. Re:It's not new by Bob+the+Super+Hamste · 2016-01-20 03:00 · Score: 1
  
  Lies we all know it was first known to Bruce Schneier who long ago found all Mersenne Primes in O(1) time.
  
  If you are going to use a internet meme at least pick the right one.
  
  --
  Time to offend someone
i thought Optimis Prime was the ultimate prime by Anonymous Coward · 2016-01-19 16:40 · Score: 0

Is this like infinity to the power of infinity - 1? How much paper would it take to print that number? What if I threw in a vowel like 2^really huge number + u?
1. Re: i thought Optimis Prime was the ultimate prime by Anonymous Coward · 2016-01-19 16:44 · Score: 0
  
  Lol, damn I guess it's Optimissed Prime ðY
2. Re:i thought Optimis Prime was the ultimate prime by cfalcon · 2016-01-19 17:13 · Score: 1
  
  Well, printing it in binary would be 74,207,280 numeral "1"s, so if you go that way it would be pretty big!
3. Re: i thought Optimis Prime was the ultimate prime by Anonymous Coward · 2016-01-19 17:29 · Score: 0
  
  That would be optimus prime you fake nerd
4. Re:i thought Optimis Prime was the ultimate prime by Jeremi · 2016-01-19 18:01 · Score: 2
  
  Well, printing it in binary would be 74,207,280 numeral "1"s, so if you go that way it would be pretty big!
  binary is for pikers. Real mathematicians print it out in unary.
  
  --
  
  I don't care if it's 90,000 hectares. That lake was not my doing.
5. Re:i thought Optimis Prime was the ultimate prime by Anonymous Coward · 2016-01-19 20:24 · Score: 0
  
  I think you forgot one "1" there.
6. Re: i thought Optimis Prime was the ultimate prime by TheRealMindChild · 2016-01-20 00:43 · Score: 1
  
  Omega prime
  
  --
  
  "When life gives you lemons, don't make lemonade. Make life take the lemons back!" -- Cave Johnson
7. Re:i thought Optimis Prime was the ultimate prime by Anonymous Coward · 2016-01-24 07:53 · Score: 0
  
  Dumbass
  Infinity is not a number so infinity to the power of infinity is ignorant blather.
This is amazing! by Anonymous Coward · 2016-01-19 16:52 · Score: 0

I think this is Bruce Schneier's phone number... or possibly the combination to his luggage!
It's small. by Kwyj1b0 · 2016-01-19 17:05 · Score: 5, Funny

It's still smaller than the box Amazon Prime uses to send me a toothpick.
Hold on, let me doublecheck in Mathematica: by Brannon · 2016-01-19 17:20 · Score: 1

In1> PrimeQ[2^74207281-1]
Now we wait.
1. Re:Hold on, let me doublecheck in Mathematica: by Anonymous Coward · 2016-01-19 19:26 · Score: 1
  
  Heh, i would expect they make a hardcoded list for them.
22,338,618 digits by mejustme · 2016-01-19 17:21 · Score: 5, Interesting

How "big" is 22,338,618 digits? Text file containing the prime is 22.8 MiB in size. http://www.mersenne.org/primes...
1. Re:22,338,618 digits by craigm4980 · 2016-01-19 17:38 · Score: 4, Insightful
  
  The number is 2^74,207,281-1, thus its exactly 74,207,280 bits long and all those bits are 1. That's 9,275,910 bytes, or roughly 9MiB. When talking about mersenne primes on a tech site, using base 10 versions encoded as ascii (or utf-8, its the same for that subset) seems like an odd measure of size.
2. Re:22,338,618 digits by mejustme · 2016-01-19 17:49 · Score: 1
  
  I was looking for a text file showing the number since obviously this prime wont fit in a uint32_t. 74,207,280 bits means nothing to me due to the size. Seeing a 22.8 MiB text file filled with digits gave it some scale.
3. Re:22,338,618 digits by Anonymous Coward · 2016-01-19 20:34 · Score: 0
  
  2^8-1 is 8 bits long. 2^32-1 is 32 bits long.
  The number 2^74,207,281-1 is 74,207,281 bits long. You would need 9,275,911 bytes.
4. Re:22,338,618 digits by Anonymous Coward · 2016-01-19 20:59 · Score: 0
  
  and you will not be able to read it, or only see a series of FFF....FFF inside.
  Stay with the 22MB decimal printing, it is better :P
5. Re:22,338,618 digits by Anonymous Coward · 2016-01-19 22:47 · Score: 0
  
  > this prime wont fit in a uint32_t
  You need an uint74207281_t
6. Re:22,338,618 digits by Anonymous Coward · 2016-01-19 22:59 · Score: 0
  
  With fewer than 10^(22.4 million) exceptions, almost all other primes are bigger than it. So relatively speaking, this is one of the tiniest primes! There are only finitely many primes smaller than it, and infinitely many greater than it.
7. Re:22,338,618 digits by Anonymous Coward · 2016-01-19 23:08 · Score: 0
  
  and you will not be able to read it, or only see a series of FFF....FFF inside.
  Stay with the 22MB decimal printing, it is better :P
  You can most certainly read it. The series of FFF....FFF is the exact number.
  Tosser.
8. Re:22,338,618 digits by Anonymous Coward · 2016-01-19 23:55 · Score: 0
  
  "How "big" is 22,338,618 digits? Text file containing the prime is 22.8 MiB in size"
  3 Interesting? Really?
  You dumb shit, a digit in ASCII (or UTF8) is 1 byte. What are you doing on slashdot?
9. Re: 22,338,618 digits by Anonymous Coward · 2016-01-20 01:09 · Score: 0
  
  Yeah, that's another low point for slashdot... Rolled my eyes and came here to comment that as unnerdy as the commenter was, the upvotes were worse. Part of me hoped to find hints it was a joke...
10. Re:22,338,618 digits by Anonymous Coward · 2016-01-20 02:29 · Score: 0
  
  and you will not be able to read it, or only see a series of FFF....FFF inside.
  That is if I use an editor that decides to display the number with hexadecimal notation.
  In iso-latin-1 it would be a series of ÿ.
  Even with hexadecimal notation there will be a leading or trailing 1 depending on if network or Intel byte order is used.
  If I use a specialized editor to display the data I could use one that displays it in decimal.
11. Re:22,338,618 digits by Anonymous Coward · 2016-01-20 02:32 · Score: 0
  
  python -c "with open('prime.txt','w') as f: f.write('%d' % (2**74207281-1))"
12. Re: 22,338,618 digits by Cederic · 2016-01-20 03:54 · Score: 1
  
  It wasn't a joke. I can tell because they also used MiB, which tells you immediately they don't know what they're talking about.
13. Re:22,338,618 digits by shawn2772 · 2016-01-20 04:23 · Score: 1
  
  python -c "with open('prime.txt','w') as f: f.write('%d' % (2**74207281-1))"
  That's gonna take a while. This is much faster:
  python -c "with open('prime.txt','w') as f: f.write('0x' + 'F' * 9275910))"
14. Re:22,338,618 digits by shawn2772 · 2016-01-20 04:26 · Score: 1
  
  python -c "with open('prime.txt','w') as f: f.write('%d' % (2**74207281-1))"
  That's gonna take a while. This is much faster:
  python -c "with open('prime.txt','w') as f: f.write('0x' + 'F' * 9275910))"
  Oop, but wrong. It leaves out one bit.
  python -c "with open('prime.txt','w') as f: f.write('0x1' + 'F' * 9275910))"
  That one is right.
15. Re:22,338,618 digits by shawn2772 · 2016-01-20 04:28 · Score: 1
  
  (Note to self: test before posting)
  python -c "with open('prime.txt','w') as f: f.write('0x1' + 'F' * 9275910)"
16. Re:22,338,618 digits by Anonymous Coward · 2016-01-20 05:20 · Score: 0
  
  Given the density of primes, you'll find (ignoring the difficulty of searching and verifying) primes whose binary representation (big endian) is valid .mp4 porn. Rule 34 exists, even with mathematics.
17. Re:22,338,618 digits by ChrisMaple · 2016-01-20 06:16 · Score: 1
  
  Actually, the most significant hexadecimal digit is 1.
  
  --
  Contribute to civilization: ari.aynrand.org/donate
18. Re:22,338,618 digits by skastrik · 2016-01-20 06:49 · Score: 1
  
  But only 11 mb in packed decimal, which will be more or less as efficient when you write the number to the terminal.
More, later ... by Anonymous Coward · 2016-01-19 17:49 · Score: 0

I have discovered a truly remarkable proof of this, but the margin of the web page is too narrow to contain it.
OMG, who cares! by footNipple · 2016-01-19 18:04 · Score: 1

Isn't knowing the definition of a prime number enough?
1. Re:OMG, who cares! by jandersen · 2016-01-19 21:40 · Score: 3, Informative
  
  Isn't knowing the definition of a prime number enough?
  Enough - for what? The definition of prime numbers is deceptively simple, but we still don't know a general way to construct all prime numbers - we don't even know if there is one. The same can be said for many other classes of numbers, I suppose, but prime numbers have turned out to be useful for our understanding of numbers and other things.
  Compare with vector spces: a vector space is, to put it simply, a space with 'dimension': every point in a vector space can be represented as a tuple of numbers: a = (a1, a2, a3, ...., aN). The first thing you want to find in a vector space is the basis: a set of N vectors that point out the independent coordinate axes of the space think of R^2 or R^3, the 2- and 3-dimensional spaces we are familiar with. Every natural number has a slightly similar property: it can be written as a product of prime numbers - the prime factors. This can useful when you calculate things - if you know that 30030 = 2*3*5*7*11*13 and 136367 = 7*7*11*11*23, then it is easy to see that 136367/30030 = 2*3*5*13/7*11*23; sometimes it is easy to find prime factors, at least if you know what the prime numbers are.
  Also, in the theory for finite groups, if p is a prime number, then any group with p elements is cyclic and any group with p^2 is Abelian (wikipedia is your friend, if you want to know more); cryptic, I know, but it has profound consequences.
2. Re:OMG, who cares! by PvtVoid · 2016-01-19 22:03 · Score: 1
  
  Isn't knowing the definition of a prime number enough?
  Totally. It's not like prime numbers can be applied to anything useful like cryptography.
3. Re:OMG, who cares! by ChrisMaple · 2016-01-20 06:37 · Score: 1
  
  The Sieve of Eratosthenes is a general method to find all prime numbers. To the best of my knowledge, there is no algebraic function that given an integer input always produces a prime.
  
  --
  Contribute to civilization: ari.aynrand.org/donate
4. Re:OMG, who cares! by Anonymous Coward · 2016-01-20 07:12 · Score: 0
  
  Math geeks care, you philistine.
  Your lack of curiosity will keep you stupid. Your stupidity will make you a danger to yourself and others. Your derisive attitude towards those who love knowledge will not improve your situation.
  A clue can be a valuable thing.
5. Re:OMG, who cares! by Anonymous Coward · 2016-01-20 07:37 · Score: 0
  
  To the best of my knowledge, there is no algebraic function that given an integer input always produces a prime.
  f(n) = 2
6. Re:OMG, who cares! by Anonymous Coward · 2016-01-20 09:32 · Score: 0
  
  > there is no algebraic function that given an integer input always produces a prime.
  f(x) = 3
2^74,207,281-1 by Anonymous Coward · 2016-01-19 18:16 · Score: 0

Isn't 2^74,207,281-1 the same as 2^74,207,280?!?
1. Re: 2^74,207,281-1 by Anonymous Coward · 2016-01-19 19:09 · Score: 0
  
  It subtracts from the final number, not off the exponent. 2^2 -1 is 4-1=3. 2^3 -1 is 8-1=7. The exponent changes the number much greater than the single -1 does. If you subtract from the exponent, the number will be significantly smaller. It would also be a factor of two which means it isn't prime.
2. Re:2^74,207,281-1 by Anonymous Coward · 2016-01-19 19:17 · Score: 0
  
  no, the -1 applies to the 2^74,207,281, not the 74,207,281 so it's (2^74,207,281)-1
I don't get it by JustNiz · 2016-01-19 19:03 · Score: 1

So what is the big deal? I mean how will this actually change anything?
1. Re:I don't get it by Anonymous Coward · 2016-01-19 19:29 · Score: 1
  
  They want to determine the bucket count for the hash map of the cosmic simulator.
2. Re:I don't get it by Anonymous Coward · 2016-01-19 21:32 · Score: 0
  
  Can you imagine the performance impact of what it must be? I wonder how much faster the universe would run if it was lessened just a bit?
3. Re:I don't get it by Anonymous Coward · 2016-01-19 22:47 · Score: 0
  
  So what is the big deal? I mean how will this actually change anything?
  Well, for a start, the effort helped them discover a bug in certain processors. In most applications rare processor bugs like that are hard to detect. One might just accept an incorrect result, or assume the problem is something else in the code. But with highly systematic mathematical work like this, processor bugs become a bit easier to pin down.
  Whether finding large primes like this will lead to deeper mathematical insights about primes is still unknown. But if there is a so far undiscovered patterns to the primes, efforts like this may very well be an key step towards finding them.
4. Re:I don't get it by david_thornley · 2016-01-21 04:18 · Score: 1
  
  Or if it wasn't hastily hacked in Perl mostly on the Seventh Day (the one that God put a sign on the door saying "Resting - Do Not Disturb").
  
  --
  "When you have eliminated the unacceptable, whatever is left, however improbable, must be the truthiness" - Holmes
Re:Better link by Anonymous Coward · 2016-01-19 19:14 · Score: 1

I'm pretty sure the press release is more relevant to the news of a new Mersenne Prime discovery then a link to generic information of primes of that type.
You think that's a big prime, huh? by Anonymous Coward · 2016-01-19 20:16 · Score: 0

Then you should have seen the prime number I shot out in the Bayou last summer. That sucker almost flipped the boat before Billy Bob shot 'im dead. Them prime nummers just keep growing bigger every year, soon we'll have to get a bigger machine gun to keep them off the porch.
The biggest utility of mersenne primes by Anonymous Coward · 2016-01-19 20:53 · Score: 0

The biggest utility of mersenne primes, and why it is exceptionally rewarding to look for them, is that any time one is found, you can read on the web what a lot of idiots who have no idea about the subject comment about the finding and about mersenne primes' utility.
Vs. by Anonymous Coward · 2016-01-19 21:25 · Score: 0

So what's the different between GIMP and GIMPS? I don't get it?
These are insanely large by 140Mandak262Jamuna · 2016-01-20 00:15 · Score: 2

The number of subatomic particles in the known universe is estimated to be less than 1.0e99. So if tag each subatomic particle with an integer you would run out of subatomic particles before you reach even one googol.

--
sed -e 's/Chuck Norris/Rajnikant/g' joke > fact
1. Re:These are insanely large by Anonymous Coward · 2016-01-24 05:00 · Score: 0
  
  I believe the amount of particles is estimated to be 1.0e82, with the mass of the universe at around 1e53kg.
Not to be confused with... by Anonymous Coward · 2016-01-20 00:44 · Score: 1

...the very short paper: W. Sagstaff, "Divisors of Mersenne Prime numbers," Math. Comp., 41:161 (February 1983) 261--261. MR 84j:10053
luggage combination by esperto · 2016-01-20 01:05 · Score: 2

Great, now i have to change my luggage lock combination.
1. Re:luggage combination by Anonymous Coward · 2016-01-20 02:41 · Score: 0
  
  This joke was horrible the first two times it was posted in this thread. Good thing you posted it a third time.
2. Re:luggage combination by Anonymous Coward · 2016-01-20 05:35 · Score: 0
  
  Great, now I have to change my luggage lock combination.
In Soviet Russia... by Anonymous Coward · 2016-01-20 02:32 · Score: 0

Mersenne discovers YOU!
Re:Better link by Anonymous Coward · 2016-01-20 02:40 · Score: 0

Why link to primes.utm.edu instead of Wikipedia?
That's my phone number by Anonymous Coward · 2016-01-20 04:46 · Score: 0

They should have asked me. That's my phone number (274) 207-2811. Thinking of changing it now.
Or factoradically. by Anonymous Coward · 2016-01-21 20:31 · Score: 0

The Factorial Number System: https://en.wikipedia.org/wiki/Factorial_number_system
2^74,207,281-1, that is about 24!. So with an alphabet of 24! code points (which begs for UTF-8!), you can write it down in about 24 characters.
For Science!! by billstewart · 2016-01-24 17:06 · Score: 1

We've been running things like this for a couple of decades, just as SETI@Home searches for little green men, etc. I ran the GIMPS Mersenne prime search software for a couple of years on my work laptop, but it really chewed through battery life, and eventually the desktop CPUs (and GPUs, once those were supported) became enough faster that it wasn't worth contributing.

--

Bill Stewart
New Fast-Compression-only CPR http://preview.tinyurl.com/dy575ks