12M Digit Prime Number Sets Record, Nets $100,000

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12M Digit Prime Number Sets Record, Nets $100,000

Posted by CmdrTaco on Thursday October 15, 2009 @03:43AM from the that's-a-lotta-bits dept.

coondoggie writes "A 12-million-digit prime number, the largest such number ever discovered, has landed a voluntary math research group a $100,000 prize from the Electronic Frontier Foundation (EFF). The number, known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1 . A Mersenne number is a positive integer that is one less than a power of two, the group stated. The computing project called the Great Internet Mersenne Prime Search (GIMPS) made the discovery on a computer at the University of California, Los Angeles (UCLA) Mathematics Department."

232 comments

Actually the 47th by eldavojohn · 2009-10-15 03:45 · Score: 4, Informative

The number known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1
Wikipedia lists it as the 47th known prime.

--
My work here is dung.
1. Re:Actually the 47th by Anonymous Coward · 2009-10-15 03:47 · Score: 0
  
  Doesn't that make the 48th Mersenne prime 2 to the power of 43,112,610 minus 1? Can I have my $100,000 now please?
2. Re:Actually the 47th by eldavojohn · 2009-10-15 03:51 · Score: 3, Informative
  
  Doesn't that make the 48th Mersenne prime 2 to the power of 43,112,610 minus 1? Can I have my $100,000 now please?
  No, because not all Mersenne numbers are prime numbers. Example: 2 ^ 4 - 1 = 15 And 15 is divisible by both 3 and 5. It's highly unlikely for two Mersenne primes to be adjacent to each other as Mersenne numbers but not impossible. If you could verify your assertion, you might just be eligible. I'm guessing it's already been checked by no by GIMPS though.
  
  --
  My work here is dung.
3. Re:Actually the 47th by Anonymous Coward · 2009-10-15 03:51 · Score: 0
  
  That one isn't prime.
4. Re:Actually the 47th by Anonymous Coward · 2009-10-15 03:51 · Score: 0
  
  Unless of course it's not prime... you have to prove it first.
5. Re:Actually the 47th by armanox · 2009-10-15 03:51 · Score: 1
  
  If you can prove it.
  
  --
  I'm starting to think GNU is the problem with "GNU/Linux" these days.
6. Re:Actually the 47th by MathFox · 2009-10-15 03:53 · Score: 1
  
  No, 2^43,112,610-1 can be divided by 3.
  
  --
  extern warranty;
  main()
  {
  (void)warranty;
  }
7. Re:Actually the 47th by Neon+Spiral+Injector · 2009-10-15 03:55 · Score: 1
  
  No. Mersenne primes are numbers which fit into the 2^n-1, but not every 2^n-1 is prime. Try, 2^4-1 = 15
  Quite often though, when 2^n-1 is prime for the same n, 2^n+1 is also prime, but not always.
8. Re:Actually the 47th by gnasher719 · 2009-10-15 03:58 · Score: 5, Informative
  
  No, because not all Mersenne numbers are prime numbers. Example: 2 ^ 4 - 1 = 15 And 15 is divisible by both 3 and 5. It's highly unlikely for two Mersenne primes to be adjacent to each other as Mersenne numbers but not impossible. If you could verify your assertion, you might just be eligible. I'm guessing it's already been checked by no by GIMPS though.
  
  Here's the complete list of all consecutive Mersenne numbers that are both primes: 3 = 2^2-1 and 7 = 2^3-1.
  
  2^n-1 can only be a prime if n is a prime, because 2^(ab) - 1 is divisible by 2^a - 1 and 2^b - 1. And (2, 3) are the only two consecutive primes.
9. Re:Actually the 47th by Ann+Coulter · 2009-10-15 04:02 · Score: 1
  
  2^43112610-1 is definitely composite. 2^(2*m)-1 = (2^m-1)*(2^m+1)
  So, 2^43112610-1 = (2^21556305-1)*(2^21556305+1)
10. Re:Actually the 47th by commodore64_love · 2009-10-15 04:26 · Score: 2, Funny
  
  Hmmmm.
  Will knowing these numbers help me procreate before I die?
  
  --
  "I disapprove of what you say, but I will defend to the death your right to say it." - historian Evelyn Beatrice Hall
11. Re:Actually the 47th by Nadsat · 2009-10-15 04:26 · Score: 1
  
  It is the second largest prime: Both of all primes and Mersennes. It is not, as the summary states, the "largest such number ever discovered"
  
  --
  
  The Custom Mary
12. Re:Actually the 47th by tholomyes · 2009-10-15 04:31 · Score: 4, Funny
  
  Hmmmm.
  Will knowing these numbers help me procreate before I die?
  I don't know about the three or the seven, but the two certainly will... after all, it takes two to tango.
  
  --
  When did the future switch from being a promise to a threat? -C. Palahniuk
13. Re:Actually the 47th by Anonymous Coward · 2009-10-15 04:45 · Score: 1, Interesting
  
  It's the 47th by size; 45th by order of discovery. Two smaller Mersenne primes were discovered after the current record-holder. One was discovered within a couple of days of the discovery of the prize-winner-- and it was, itself, large enough to claim the EFF prize ($100k for 10M digits).
14. Re:Actually the 47th by tool462 · 2009-10-15 04:56 · Score: 1
  
  Yes, but only at your prime.
15. Re:Actually the 47th by Arthur+Grumbine · 2009-10-15 05:07 · Score: 0, Redundant
  
  Your single-minded obsession with achieving immortality through the propagation of your genes is quaint and soon to be irrelevant.
  
  --
  Now that I think about it, I'm pretty sure everything I just said is completely wrong.
16. Re:Actually the 47th by justdaven · 2009-10-15 05:08 · Score: 2, Funny
  
  It is probably more of a contraceptive...
17. Re:Actually the 47th by mcgrew · 2009-10-15 05:21 · Score: 4, Funny
  
  Unfortunately, I'm afraid that knowing these numbers will prevent you from procreating before you die.
  
  --
  Free Martian Whores!
18. Re:Actually the 47th by Anonymous Coward · 2009-10-15 05:37 · Score: 0
  
  Quick, someone test if 2^(2^43,112,609 - 1) - 1 is prime. If so, please make out the check for $100,000 to Cash. I'll be by to pick it up after I pick up my $1,000,000 from the Clay Institute for proving P=NP when N=1 or P=0.
19. Re:Actually the 47th by ShecoDu · 2009-10-15 05:47 · Score: 1
  
  I have a question, if 2^n-1 can only be a prime if n is a prime... would using the new 12M digit prime in the article as n, result in a new bigger prime? can it be repeated?
20. Re:Actually the 47th by onemorechip · 2009-10-15 05:50 · Score: 1
  
  And it's easily proven:
  If 2^x - 1 is prime, then neither 2^x - 1 nor 2^x is divisible by 3. Of any 3 consecutive integers, one must be divisible by 3. Therefore 2^x + 1 is divisible by 3.
  Therefore 2*(2^x+1) = 2^(x+1) + 2 is divisible by 3, and so is 2^(x+1) - 1.
  
  --
  But, I wanted socialized health insurance!
21. Re:Actually the 47th by onemorechip · 2009-10-15 05:52 · Score: 4, Funny
  
  It is the second largest prime: Both of all primes and Mersennes.
  Wow, does that mean we're close to discovering the largest prime?
  
  --
  But, I wanted socialized health insurance!
22. Re:Actually the 47th by Austerity+Empowers · 2009-10-15 05:54 · Score: 1
  
  Folie a deux, menage a trois.
23. Re:Actually the 47th by Vovk · 2009-10-15 05:59 · Score: 2, Informative
  
  no. for instance, 2^11 = 2048. 2048 - 1 = 2047 which is divisible by 23. n HAS to be prime, but not every prime n will give a prime result
24. Re:Actually the 47th by sarahbau · 2009-10-15 06:04 · Score: 1
  
  2^n-1 can only be prime if n is prime. It doesn't mean that it must be prime if n is prime. For example, 11 is prime, but 2^11-1 = 2047, which is not prime (2047/23 = 89)
25. Re:Actually the 47th by Anonymous Coward · 2009-10-15 06:05 · Score: 0
  
  He said 2^n-1 can only be a prime if n is a prime. He didn't say the converse was true.
26. Re:Actually the 47th by coolsnowmen · 2009-10-15 06:15 · Score: 1
  
  That is kind of a bad number to pick, because 4 isn't prime (2*2). And then go on to say that it is highly unlikely that 2 neighboring primes are mersenne primes when, the first 4 primes (2,3,5,7) are all mersenne primes, and then 13,17,19 are all in a row again.
27. Re:Actually the 47th by esrobinson · 2009-10-15 06:20 · Score: 1
  
  And it's easily proven:
  If 2^x - 1 is prime, then neither 2^x - 1 nor 2^x is divisible by 3. Of any 3 consecutive integers, one must be divisible by 3. Therefore 2^x + 1 is divisible by 3.
  Therefore 2*(2^x+1) = 2^(x+1) + 2 is divisible by 3, and so is 2^(x+1) - 1.
  A (completely useless) counterexample: Let x = 2.
28. Re:Actually the 47th by AmberBlackCat · 2009-10-15 06:25 · Score: 1
  
  What are these numbers good for? Is there a reason, other than the love of math, that a non-profit which accepts donations would pay $100,000 for this?
29. Re:Actually the 47th by Anonymous Coward · 2009-10-15 06:47 · Score: 0
  
  what I'd pay for an abacus that could solve that problem...
30. Re:Actually the 47th by subodhg · 2009-10-15 06:50 · Score: 0
  
  Sorry, but 2 and 5 are not Mersenne Primes.
  They are primes but not Mersenne Primes.
  Now if you had stated the numbers 2^n-1 were prime for
  n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257
  ... then you would be correct.
  Mersenne Primes are primes that are represented as 2^n - 1. You cannot represent 2 and 5 in that form.
31. Re:Actually the 47th by Yold · 2009-10-15 06:58 · Score: 1
  
  computing friggen large numbers isn't as easy as it appears. Consider the fact that your computer contains a discrete(limited) number of bits, and the processor can operate on about 64 bits at a time (depending on architecture). Try putting 2^100 into a scientific calculator, it will probably overflow (can't represent a number that large). 2^43,112,609 is a huge, huge, number.
32. Re:Actually the 47th by Brian+Gordon · 2009-10-15 07:02 · Score: 1
  
  If we simply focussed on running the existing primes through 2^n-1, we'd find every prine through a few billion didgits in a couple of years
  You have absolutely no idea what you're talking about.
33. Re:Actually the 47th by Brian+Gordon · 2009-10-15 07:05 · Score: 1
  
  It's still a mersenne number, which is his point. The parent AC up there first-replying to first-post also picked a bad non-prime number: eldavojohn's point.
34. Re:Actually the 47th by Anonymous Coward · 2009-10-15 07:10 · Score: 0
  
  Wow, does that mean we're close to discovering the largest prime?
  Not close, just closer.
35. Re:Actually the 47th by sexconker · 2009-10-15 07:14 · Score: 1
  
  2^(ab) - 1 is divisible by 2^a - 1 and 2^b - 1
  Prove it.
36. Re:Actually the 47th by bhsbulldozer · 2009-10-15 07:20 · Score: 1
  
  a implies b is not the same as b implies a. If both implications are true, then you imply a equivalence.. or sumthn.
37. Re:Actually the 47th by XSpud · 2009-10-15 07:26 · Score: 2, Informative
  
  If we simply focussed on running the existing primes through 2^n-1, we'd find every prine through a few billion didgits in a couple of years.
  Unfortunately it's not that simple. Not all primes are of the form 2^n-1, and numbers of that form are not necessarily prime.
  Currently there's no efficient algorithm for generating a list of primes in sequence and your estimate of a couple of years is way off (as in "many many lifetimes of the universe way off"). Even testing whether a number is prime is not efficient.
  The reason work is concentrated on Mersenne primes is that there there is a particularly fast test for primality for numbers of the form 2^n-1
38. Re:Actually the 47th by COMON$ · 2009-10-15 07:32 · Score: 1
  
  There are many many many applications for a large prime...stronger encryption being just one. Google is your friend.
  
  --
  CS: It is all sink or swim...oh and did I mention there are sharks in that water?
39. Re:Actually the 47th by skine · 2009-10-15 07:52 · Score: 1
  
  He said 2^n-1 can only be a prime if n is a prime. He didn't say the converse was true.
  Yes, but asking if the converse is true is the first natural step after you prove something.
  It can, however, be answered quickly by testing the first five primes, or by noting that there are a lot more than 47 primes between 2 and 43,112,609.
40. Re:Actually the 47th by SleazyRidr · 2009-10-15 07:53 · Score: 1
  
  I had a rather interesting time trying to prove that one... When I gave up on the purely mathematical route, some 'experimentation' showed me that this doesn't appear to be the case in situations where b is a multiplied by a prime. I'll probably be scratching on a bit pf paper about this for a while, but it would be nice to hear from someone who knew what they were talking about.
  
  --
  Is 1563649 a prime number?
41. Re:Actually the 47th by Abreu · 2009-10-15 08:00 · Score: 1
  
  It would have to be a very big abacus
  
  --
  No sig for the moment.
42. Re:Actually the 47th by skine · 2009-10-15 08:04 · Score: 1
  
  Wow, does that mean we're close to discovering the largest prime?
  Not close, just closer.
  No matter how many primes we find, there are the same amount left over. Such is infinity.
43. Re:Actually the 47th by sexconker · 2009-10-15 08:23 · Score: 1
  
  All you need to do is disprove it once.
  I tried a few examples and it worked.
  I couldn't see an obvious reason why it would be true, nor a way to go about proving it.
  It gets 5 minutes of my active attention (they're already up), but it will bug me for years until I get a proof/disproof.
44. Re:Actually the 47th by Anonymous Coward · 2009-10-15 08:40 · Score: 0
  
  You? I doubt it.
45. Re:Actually the 47th by selven · 2009-10-15 08:55 · Score: 1
  
  Yep, there' only one more left - just multiply all the ones we have and subtract 1. Err... and multiply all the ones we have and add 1. Crap, now there's more prime numbers to multiply.
46. Re:Actually the 47th by Hognoxious · 2009-10-15 09:05 · Score: 1
  
  Or a number of medium ones in a Beowulf cluster.
  
  --
  Confucius say, "Find worm in apple - bad. Find half a worm - worse."
47. Re:Actually the 47th by lgw · 2009-10-15 09:43 · Score: 1
  
  2^(ab) - 1 is divisible by 2^a - 1 and 2^b - 1
  Prove it.
  Let x = 2^a. It suffices to prove that (x - 1) divides (x^b - 1).
  (x^b - 1)/(x - 1) = x^(b-1) + x^(b-2) + ... + x + 1
  Quite Easily Done.
  
  --
  Socialism: a lie told by totalitarians and believed by fools.
48. Re:Actually the 47th by Red+Flayer · 2009-10-15 10:05 · Score: 1
  
  No matter how many primes we find, there are the same amount left over. Such is infinity.
  We cannot say there are the same amount left over... we can only say that there are an infinite number of primes left to be found. Not all infinities are equal.
  
  --
  "Trolls they were, but filled with the evil will of their master: a fell race..." -- J.R.R. Tolkien on Olog-hai
49. Re:Actually the 47th by PTBarnum · 2009-10-15 10:22 · Score: 1
  
  I find it easiest to visualize using binary notation:
  2^ab = 1000 .... 000 (ab zeroes)
  2^ab - 1 = 111 ... 111 (ab ones)
  divide those into a groups of b ones
  The least significant group of b ones = 2^b - 1. Each group to the left of that is shifted by b bits, so it is 2^b times the previous group.
  Hence, 2^ab - 1 = 2^(a-1)b * (2^b - 1) + 2^(a-2)b * (2^b - 1) + ... + 2^2b * (2^b - 1) + 2^b * (2^b -1) + (2^b - 1)
  Clearly, that is divisible by 2^b - 1
  Example:
  2^12 - 1 = 1000000000000 - 1 = 111111111111 = (1111)(1111)(1111) = 16*16*15 + 16*15 + 15 = 15 * (16*16 + 16 + 1) = 15*273
50. Re:Actually the 47th by onemorechip · 2009-10-15 10:27 · Score: 1
  
  Ah, well, I realized after posting that I'd left out the detail that there is one prime number that is divisible by 3. So 3 and 7 are the only consecutive Mersenne numbers that are prime.
  
  --
  But, I wanted socialized health insurance!
51. Re:Actually the 47th by sustik · 2009-10-15 10:30 · Score: 1
  
  Furthermore: (2^n - 1, 2^m - 1) = (2^(n,m) - 1), where (n,m) is the greatest common divisor of n and m. (Maybe in your high school they used the more verbose gcd(n, m).)
  The above has a quite elementary, and beautiful proof. (Substitute n = ab, m = a:
  (2^ab -1, 2^a -1) = 2^a - 1, so the above is a more general theorem.)
  Even further: (F_n, F_m) = F_(n,m), where F_1 = 1, F_2 = 1, F_{k+2} = F_{k+1} + F_k, the Fibonacci sequence. Then muse about M_1 = 1, M_{k+1} = 2*M_k + 1 defining the sequence 2^k - 1, and try to further generalize...
  (If you need a proof just ask, I will check back tomorrow.)
52. Re:Actually the 47th by onemorechip · 2009-10-15 10:32 · Score: 1
  
  But all countably infinite sets have the same cardinality: aleph-null. So skine was right.
  
  --
  But, I wanted socialized health insurance!
53. Re:Actually the 47th by severoon · 2009-10-15 10:41 · Score: 2, Informative
  Is it strange to anyone else that this number can be written as 2 to the 43,112,609 minus 1, and 43,112,609 is itself...
  
  prime
  furthermore, a Germain prime
  the hypotenuse of a pythagorean triple (with 13003809 & 41104720)
  the sum of two squares (3880 & 5297)
  This number itself has a lot of notable properties, besides generating another prime when plugged into the ol' 2-to-the-n-plus-1 thing...
  --
  but have you considered the following argument: shut up.
54. Re:Actually the 47th by sexconker · 2009-10-15 12:22 · Score: 1
  
  And now my day is complete.
  Step 1: Yup. Makes sense.
  Step 2: Yup. Just multiply both sides by (x-1), for anyone who still cant see it / hates polynomial division.
  And thus the world is safe again.
55. Re:Actually the 47th by Paradise+Pete · 2009-10-15 12:31 · Score: 1
  
  Doesn't that make the 48th Mersenne prime 2 to the power of 43,112,610 minus 1? Can I have my $100,000 now please?
  Yes, of course. There is a small processing fee that has to be covered. Please send immediately so that these funds can be released to you.
56. Re:Actually the 47th by lewiscr · 2009-10-15 12:43 · Score: 2, Funny
  
  Finally! A thread where "7 of 9" and "procreation" aren't offtopic!
57. Re:Actually the 47th by lewiscr · 2009-10-15 12:47 · Score: 1
  
  You might have just stumbled onto a new suitability test. The search is currently looking for new numbers, it doesn't care if you skip some of them on the way.
58. Re:Actually the 47th by skine · 2009-10-15 14:23 · Score: 1
  
  Let me respond by making a joke:
  "Aleph-naught bottles of beer on the wall, Aleph-naught bottles of beer; you take one down, pass it around; Aleph-naught bottles of beer on the wall.
  Aleph-naught bottles of beer on the wall..."
59. Re:Actually the 47th by Anonymous Coward · 2009-10-15 15:02 · Score: 0
  
  Hmmmm.
  Will knowing these numbers help me procreate before I die?
  I don't know about the three or the seven, but the two certainly will... after all, it takes two to tango.
  The three may still be applicable. At least, it's within the realm of possibility. The seven is probably best left alone unless you're the kind of person who hangs around coke parties.
60. Re:Actually the 47th by coolsnowmen · 2009-10-15 16:43 · Score: 1
  
  Oh, I got confused with which was a p, and which was M_p
61. Re:Actually the 47th by Anonymous Coward · 2009-10-15 19:58 · Score: 0
  
  Quite often though, when 2^n-1 is prime for the same n, 2^n+1 is also prime, but not always.
  You are either a troll, or ignorant enough to say this happens quite often without even finding more than one example.
  2^n-1 can only be prime if n is prime, and 2^n+1 can only be prime if n is a power of 2 (or 0).
  Therefore 2^n-1 and 2^n+1 are prime for the same n precisely ONCE, when n=2. I fail to see how anyone could call that "quite often".
62. Re:Actually the 47th by Anonymous Coward · 2009-10-15 20:24 · Score: 0
  
  No, it can be proven that there is no largest prime! There are infinitely many...
63. Re:Actually the 47th by Anonymous Coward · 2009-10-15 21:07 · Score: 0
  
  Epic FAIL...
64. Re:Actually the 47th by Sandbags · 2009-10-16 02:49 · Score: 1
  
  every "mersenne" prime, I should have clarified. Might not mean "every" prime.
  We're already at 12M didgits, and yes I understand the processing power required to process numbers on that scale. However, the last 9 in a row primes found have all been mersenne, and we've increased the didgit count 3 fold over those 9. Between here and 1B didgits, maybe there's 10-15 more primes? (based on historical slide in primes per number of didgits as it increases, which is no way is a simple plotable line, just an estimation that it declines as it goes). We're finding about 3 more a year using less efficint techniques. Granted the power it takes to find each larger one grows, but we should be able to clean out all the mersenne primes inside 5 years tops.
  The idea is, we know all the primes to use as "n" in the equasion, so finding each new one, including the ones that can be excluded through simpler mathematic formula, should not be difficult. (just time consuming).
  Fact is, would that buy us any new intelligence? Would plotting 15 or 20 more points on a graph that has over 50M prime numbers on it already give us any new insight? no. That's why I feel this is pointless.
  
  --
  There is no contest in life for which the unprepared have the advantage.
65. Re:Actually the 47th by onemorechip · 2009-10-16 03:56 · Score: 1
  
  Whoosh, but you posted anonymously so I guess you'll never know.
  
  --
  But, I wanted socialized health insurance!
66. Re:Actually the 47th by Brian+Gordon · 2009-10-16 04:26 · Score: 1
  
  Verifying whether a 12 million digit number is prime is staggeringly difficult
  At this point these "sets new record!" stories are significant because researchers aren't just brute-forcing it, they're using all sorts of clever tricks to push so far ahead of current processing capability. It's a serious area of mathematical research.
67. Re:Actually the 47th by daveime · 2009-10-16 06:45 · Score: 1
  
  Easy.
  Any number 2^N-1 represented in binary is of the form 1111...1111, i.e it is composed of N '1' bits.
  When N is composite (N=ab), it can easily be seen that ab '1' bits can be broken down into "a groups of length b", or alternatively "b groups of length a", thus it is always composite.
  Only when N is prime can the resulting number *possibly* be prime.
so? by Anonymous Coward · 2009-10-15 03:47 · Score: 0

What can you do with big primes? Why the fascination?
I've heard the "Oh, it's useful in crypto" answer, but never WHY it's useful in crypto.
1. Re:so? by Tubal-Cain · 2009-10-15 03:53 · Score: 1
  
  Since you're AC, I'll just send you here.
2. Re:so? by FlyingBishop · 2009-10-15 03:56 · Score: 0, Flamebait
  
  What can you do with plutonium? I mean, I've heard, oh it's useful in nuclear bombs, but never WHY it's useful in nuclear bombs.
  You haven't heard why because you're not a fucking cryptoanalyst.
  Now, if you really want a primer on primes and cryptography http://en.wikipedia.org/wiki/RSA is a good place to start. But anyone with a CS degree at least should understand the basics of why big primes make good private keys
3. Re:so? by kalirion · 2009-10-15 04:00 · Score: 5, Funny
  
  Great,everyone starts using the new largest known prime number in their private key! That's like SUPER secure!
4. Re:so? by Yold · 2009-10-15 04:10 · Score: 1
  
  (wikipedia)
  Several public-key cryptography algorithms, such as RSA or the Diffie-Hellman key exchange are based on large prime numbers (for example with 512 bits). They rely on the fact that it is thought to be much easier (i.e., more efficient) to perform the multiplication of two (large) numbers x and y than to calculate x and y (assumed coprime) if only the product xy is known.
  Many mathematical research subjects are not firmly grounded in real-world applications.
5. Re:so? by Jeian · 2009-10-15 04:11 · Score: 1
  
  I have a basic understanding of the principle, but I'm still not seeing the practical application of constantly finding larger and larger prime numbers. Sure, a million-digit prime number is cool if math is your thing, but as best I can tell it's not useful in a practical sense. (Maybe it has some academic value that I'm not aware of, entirely possible.)
  I can run PGP and have it generate primes for me within a few seconds that are sufficient for decent encryption, and they don't need to be a gazillion digits long.
  I could be way off on this, but that's just how it seems to me.
6. Re:so? by maxfresh · 2009-10-15 04:14 · Score: 3, Informative
  
  Yes, in fact, it is very secure.
  
  The fact that the (very large) prime modulus is not secret, but rather public, is part of the design of many PK encryption systems, and therein lies their beauty, simplicity, and charm. If you are interested in learning more about it, here's a description of one very widely used system: http://en.wikipedia.org/wiki/Diffie-Hellman_key_exchange
7. Re:so? by FlyingBishop · 2009-10-15 04:29 · Score: 1
  
  Today, yes. It remains to be seen if, in 15 years time, we will be able to trivially decrypt your decent encryption. Finding good ways of generating larger primes is very important until Moore's law is proven dead.
  Mersennes are useful for this as someone noted above.
8. Re:so? by gnick · 2009-10-15 04:30 · Score: 2, Interesting
  
  I can run PGP and have it generate primes for me within a few seconds that are sufficient for decent encryption, and they don't need to be a gazillion digits long.
  I agree with you entirely. The debate, however, is in the definitions of "sufficient" and "decent". For most needs, you need far fewer than a gazillion digits. For national security type stuff, a gazillion digits may be appropriate. For a math/crypto nerd, even a bazillion gazillion digits will never be enough.
  
  --
  He's getting rather old, but he's a good mouse.
9. Re:so? by 91degrees · 2009-10-15 04:34 · Score: 2, Interesting
  
  But anyone with a CS degree at least should understand the basics of why big primes make good private keys
  
  Indeed. Although it should be noted that Mersenne primes are sort of useless for this. If you know one of the factors is a Mersenne Prime then there are only 47 candidates.
10. Re:so? by Anonymous Coward · 2009-10-15 04:57 · Score: 0
  
  What use is a newborn child?
11. Re:so? by cez · 2009-10-15 04:58 · Score: 1
  
  duh... to win $100,000 of course!
  
  --
  Walk with Music;
12. Re:so? by Anonymous Coward · 2009-10-15 05:12 · Score: 0
  
  doorstop?
13. Re:so? by JoshuaZ · 2009-10-15 05:15 · Score: 3, Interesting
  
  Strictly speaking, large primes are useful but not specific large primes. Indeed, this Mersenne prime is much too large to be useful for practical cryptography.
  The main reason that primes are useful for cryptography is that there are functions associated with primes where the functions are easy to calculate but have inverses that are very difficult to calculate unless one has extra information. The classic example of this is the discrete log problem. Essentially, if one is doing modular arithmetic with a given prime (that is arithmetic where you only look at the remainders when divided by that prime. This is essentially like a clock with p numbers on it. On a normal clock is arithmetic mod 12) then it turns out that for any prime p, there is a number k such that k^1, k^2, k^3... k^(p-1) taken mod pruns through all the possible remainders 1,2,3... p-1 (obviously not in order). Such a k is called a primitive root (or a generator) Now, it is very easy given a k and an n to calculate k^n (mod p). However, given the equation k^x=m (mod p) it is very hard to find the right value of x without doing a lot of work (essentially, you have to more or less list out k^1,k^2,k^3... until you get to m). The difficulty in this process is used in a number of public key crypto systems and other systems. For example, the Diffie-Hellman algorithm which was the first modern crypto algorithm discovered uses the difficulty of this process to make it so that two people can without ever having talked to each other before have a conversation and at the end of it have a secret code that no one else can figure out without impractical levels of computation. This is true even if one has access to all the communication that goes on between the two parties. The RSA algorithm which is more practical than DH for a variety of reasons also works off of a similar procedure.
  The above is assuming that the discrete log is actually a difficult problem which everyone believes but is not proven. Proving this would imply that P != NP which is one of the Clay Millennium Problems (so million dollar prize and all that fun stuff). Mersenne primes are very interesting but not for any crypto related reason.
14. Re:so? by Jonmash · 2009-10-15 05:36 · Score: 1
  
  Awesome...
  
  --
  --- Jon
15. Re:so? by Jeian · 2009-10-15 05:36 · Score: 1
  
  I thought about that, but then the question arises: if in 15 years, we have the processing power to easily crack whatever I encrypted today... then in 15 years shouldn't we also have enough processing power to easily generate these primes Of This Magnitude?
16. Re:so? by kalirion · 2009-10-15 05:48 · Score: 2, Interesting
  
  I was going by this description of RSA. Quote:
  In real life situations the primes selected would be much larger, however in our example it would be relatively trivial to factor n, 3233, obtained from the freely available public key back to the primes p and q. Given e, also from the public key, we could then compute d and so acquire the private key.
  I didn't go through all the math myself, but if this description is true, then knowing one of the primes makes factoring n becomes unnecessary, allowing us to "compute d and so acquire the private key."
  So at least the RSA encryption is easily broken if you have a good guess as to one of the primes used.
17. Re:so? by onemorechip · 2009-10-15 05:54 · Score: 1
  
  If you're Bill Gates, you can try to factor them.
  
  --
  But, I wanted socialized health insurance!
18. Re:so? by FlyingBishop · 2009-10-15 06:14 · Score: 2, Informative
  
  Sure, but when you consider how often primes must be generated in this sort of algorithm, optimizations are very useful. (That's why most algorithms actually in use use parabolas in place of primes, generating random primes is too computationally intensive.) But research is always worthwhile to see if new approaches can be found (and often the research leads us down paths that most people would say "What can you do with that? Why the fascination with..."
  If we knew it wouldn't be called research, it would be called engineering.
19. Re:so? by ChiRaven · 2009-10-15 06:24 · Score: 1
  
  Using a Mersenne prime for your private key is kinda like hiding the key to your house under the welcome mat. WAY too hard for any average dumb burglar to figure out.
20. Re:so? by Anonymous Coward · 2009-10-15 11:09 · Score: 0
  
  If you know one of the primes you just divide the product to get the other one. Easily done, even with 43 million bits.
  A 43 million bit public key might be a tip as to what prime someone used.
  I really hope the GP was kidding when he said it was "very secure". Yes the PRODUCT of the two primes is public, the primes themselves have to stay private.
21. Re:so? by maxfresh · 2009-10-15 11:44 · Score: 2, Informative
  
  No, I wasn't kidding at all when I said "very secure". I really mean it. It's just that Kalirion (and you AC), and I are thinking of, and referring to, two very different systems of PK encryption, which have very different properties, and would be affected very differently by the choice of prime numbers.
  
  In the case of Diffie-Hellman, only *one* prime number is used, and it is not a secret at all. It is transmitted in the clear, over an insecure channel, to the other party, in order to be used to establish the mutually shared secret key. This is by design, and in no way weakens the security of the encryption system. Please, don't take my word for it, just read the link in my first post.
  
  In contrast, in the RSA system, which you and Kalirion are both referring to, *two* prime numbers are used, and these two primes must both be kept secret. Obviously, in this case, choosing one of the two secret primes from among the "famous" prime numbers, would certainly weaken the overall security of the encryption, by reducing the search space for a brute-force attack. However, given the huge set of primes from wich the other one could be chosen, I don't know whether choosing just one "famous" prime number for your secret pair would make the resulting secret key easy, or even computationally feasible to find, given our current state of technology.
22. Re:so? by kalirion · 2009-10-16 02:23 · Score: 1
  
  In contrast, in the RSA system, which you and Kalirion are both referring to, *two* prime numbers are used, and these two primes must both be kept secret. Obviously, in this case, choosing one of the two secret primes from among the "famous" prime numbers, would certainly weaken the overall security of the encryption, by reducing the search space for a brute-force attack. However, given the huge set of primes from wich the other one could be chosen, I don't know whether choosing just one "famous" prime number for your secret pair would make the resulting secret key easy, or even computationally feasible to find, given our current state of technology.
  With the RSA system, knowing one prime number lets you find the other one by a single division operation, since the product of the two primes is public. But yes, the Diffie-Hellman encryption would stay secure since the prime is known already.
23. Re:so? by jonaskoelker · 2009-10-16 04:46 · Score: 1
  
  For example, the Diffie-Hellman algorithm which was the first modern crypto algorithm discovered uses the difficulty of this process to make it so that two people can without ever having talked to each other before have a conversation and at the end of it have a secret code that no one else can figure out without impractical levels of computation.
  Note that this only works if all the evil people listening in don't modify anything that Alice and Bob. If they do, Alice knows that she's communicating in private with someone, not that she's communicating in private with Bob.
  Here's how it works: the eavesdropper in the middle, Eve, pretends to be Alice as far as Bob can tell, and pretends to be Bob as far as Alice can tell. Alice and Eve can then communicate in private, as can Bob and Eve, so Eve can just pass along all the messages unmodified and listen in, or can insert, remove or alter messages.
24. Re:so? by maxfresh · 2009-10-16 06:52 · Score: 1
  
  Yes, I know that with RSA, if your adversary knows even one of your secret primes for certain, then she can compute your other secret prime, and therefore your secret key, in an instant, leaving you with no security at all. That's why I mentioned that they must both be kept secret.
  
  The RSA situation that I was wondering about, and I'm still not sure about, is one where you have chosen just one famous prime for your secret pair, but your adversary doesn't know it for certain. In that case, I would expect the adversary to try famous primes first, when attempting to factor your key. But still they must test the primality of the other possible secret factor, that they derived by a single division. I wonder, would they find it truly feasible to do, or merely less difficult, because of your choice of one famous prime?
25. Re:so? by JoshuaZ · 2009-10-16 08:09 · Score: 1
  
  Yes, man-in-the-middle attacks still work. There are a number of other attacks that work also. This wasn't an attempt at explaining every single little detail of cryptography but rather answering the question which was asked- why we care about large primes for crypto purposes.
26. Re:so? by kalirion · 2009-10-16 09:46 · Score: 1
  
  If dividing the product by one famous prime comes out to an easy integer but it takes a long time to test whether that integer is a prime, then you could just assume that it's a prime and see if you can derive the valid private key from that :)
Re:waste of money by Anonymous Coward · 2009-10-15 03:49 · Score: 0

Cloud Computing?
Sounds cool, but... by GMonkeyLouie · 2009-10-15 03:49 · Score: 2, Insightful

Call me a n00b, but I'm unsure there are any ways to use this newfound information about prime numbers.
Next time good ol' (2^43,112,609 - 1) comes up in conversation, I'll make sure to impress everyone with my new knowledge, but other than that, I feel no smarter for having read this article.
1. Re:Sounds cool, but... by ArhcAngel · 2009-10-15 04:00 · Score: 5, Funny
  
  n00b
  
  --
  "A person is smart. People are dumb, panicky dangerous animals and you know it." - K
2. Re:Sounds cool, but... by geekmux · 2009-10-15 04:06 · Score: 2, Funny
  
  Call me a n00b, but I'm unsure there are any ways to use this newfound information about prime numbers.
  Next time good ol' (2^43,112,609 - 1) comes up in conversation, I'll make sure to impress everyone with my new knowledge, but other than that, I feel no smarter for having read this article.
  You think you feel bad? Talk to the guy who just signed that $100,000 check for this...
3. Re:Sounds cool, but... by Anonymous Coward · 2009-10-15 04:30 · Score: 1, Informative
  
  http://primes.utm.edu/notes/faq/why.html
  "Why?" we are often asked, "why would anyone want to find a prime that big?"" I often now answer with "did you ever collect anything?"" or "did you ever try to win a competition?"" Much of the answer for why we collect large primes is the same as why we might collect other rare items. Below I will present a more complete answer divided into several parts.
  Tradition!
  For the by-products of the quest
  People collect rare and beautiful items
  For the glory!
  To test the hardware
  To learn more about their distribution
  For the money?
  This does not exhaust the list of reasons, for example some might be motivated by primary research or a need for publication. Many others just hate to see a good machine wasting cycles (sitting idle or running an inane screen saver).
  Perhaps these arguments will not convince you. If not, just recall that the eye may not see what the ear hears, but that does not reduce the value of sound. There are always melodies beyond our grasp. (*)
  1. Tradition!
  Euclid may have been the first to define primality in his Elements approximately 300 BC. His goal was to characterize the even perfect numbers (numbers like 6 and 28 which are equal to the sum of their aliquot divisors: 6 = 1+2+3, 28=1+2+4+7+14). He realized that the even perfect numbers (no odd perfect numbers are known) are all closely related to the primes of the form 2p-1 for some prime p (now called Mersennes). So the quest for these jewels began near 300 BC.
  Large primes (especially of this form) were then studied (in chronological order) by Cataldi, Descartes, Fermat, Mersenne, Frenicle, Leibniz, Euler, Landry, Lucas, Catalan, Sylvester, Cunningham, Pepin, Putnam and Lehmer (to name a few). How can we resist joining such an illustrious group?
  Much of elementary number theory was developed while deciding how to handle large numbers, how to characterize their factors and discover those which are prime. (Look, for example, at the concepts required to develop simple proofs such as [1] or [2].) In short, the tradition of seeking large primes (especially the Mersennes) has been long and fruitful It is a tradition well worth continuing.
  2. For the by-products of the quest
  Being the first to put a man on the moon had great political value for the United States of America, but what was perhaps of the most lasting value to the society was the by-products of the race. By-products such as the new technologies and materials that were developed for the race that are now common everyday items, and the improvements to education's infrastructure that led many man and women into productive lives as scientists and engineers.
  The same is true for the quest for record primes. In the tradition section above I listed some of the giants who were in the search (such as Euclid, Euler and Fermat). They left in their wake some of the greatest theorems of elementary number theory (such as Fermat''s little theorem and quadratic reciprocity).
  More recently, the search has demanded new and faster ways of multiplying large integers. In 1968 Strassen discovered how to multiply quickly using Fast Fourier Transforms. He and Schönhage refined and published the method in 1971. GIMPS now uses an improved version of their algorithm developed by the long time Mersenne searcher Richard Crandall [see CF94].
  The Mersenne search is also used by school teachers to involve their students in mathematical research, and perhaps to excite them into careers in science or engineering. And these are just a few of the by-products of the search.
  3. People collect rare and beautiful items
  Mersenne primes, which are usually the largest known primes, are both rare and beautiful. Since Euclid initiated the search for and study of Mersennes approximately 300 BC, very few have been found. Less than fifty in all of human history--that is rare!
  But they are also beautiful. Mathematics, like all fields of study, has a definite notion of beauty. What qual
4. Re:Sounds cool, but... by Nerdposeur · 2009-10-15 04:45 · Score: 2, Interesting
  
  Talk to the guy who just signed that $100,000 check for this...
  ...who works for EFF.
  So what's their interest in this? Is it cryptography related?
5. Re:Sounds cool, but... by Anonymous Coward · 2009-10-15 04:57 · Score: 0
  
  and the improvements to education's infrastructure that led many man and women into productive lives as scientists and engineers
  Hahaha if the educational system was so improved then why are there so many dumbasses everywhere? That part about women being productive scientists and engineers was pretty funny too! Yeah, 1% of them can do it but only because they have masculine traits, the rest of the women just aren't interested and all the PC "inclusiveness" in the world won't make them want to do this kind of work and you know it.
6. Re:Sounds cool, but... by Duradin · 2009-10-15 05:07 · Score: 1
  
  Call me a n00b, but I'm unsure there are any ways to use this newfound information about prime numbers. Next time good ol' (2^43,112,609 - 1) comes up in conversation, I'll make sure to impress everyone with my new knowledge, but other than that, I feel no smarter for having read this article.
  So as long as you know that water is wet, the sky is blue, and the Sun goes around the Earth you are content?
7. Re:Sounds cool, but... by Anonymous Coward · 2009-10-15 05:11 · Score: 4, Informative
  
  Think about how easy it is for a computer to multiply together (2^43112609 - 1) and (2^13466917 - 1).
  Then think about how long it would take a computer to identify the factors of the resulting number, given that it is composed of two primes with twelve and four million digits, respectively.
  Cryptography is all about simple math operations that can be performed one way, but cannot be easily and quickly reversed without knowing a secret (in my example, one of the original primes).
8. Re:Sounds cool, but... by Anonymous Coward · 2009-10-15 05:25 · Score: 0
  
  memorize 43112609 now and if you happen to travel back more than 30 but less than 50 years, people who have access to millions of dollars in computer equipment just might believe your story.
9. Re:Sounds cool, but... by Anonymous Coward · 2009-10-15 06:13 · Score: 0
  
  Isn't knowledge for knowledge's sake good enough? As prime numbers have a concrete and useful application in various forms of cryptography, I don't see why you are acting apathetic about this.
10. Re:Sounds cool, but... by Quothz · 2009-10-15 06:29 · Score: 1
  
  So what's their interest in this?
  That's what I was wondering, so I peeked. Initially when I saw this article, I was a bit disturbed, since people don't donate to the EFF for this purpose--that's what contributions to research organizations and universities are for. However, it turns out the money comes from a private individual specifically for this purpose; the EFF merely administers the award. It's free publicity for 'em in a good cause, a Good Thing by my reckoning.
11. Re:Sounds cool, but... by Ant+P. · 2009-10-15 07:10 · Score: 1
  
  I bet sshing in with that RSA key would take a while
12. Re:Sounds cool, but... by karmarep · 2009-10-15 07:15 · Score: 1
  
  I was at first kind of miffed that the EFF gave them 100k for this. I'm glad it wasn't from the general fund and instead came from a private individual. I donate to the EFF to help protect digital rights, not figure out prime numbers.
13. Re:Sounds cool, but... by Anonymous Coward · 2009-10-15 08:03 · Score: 0
  
  I agree; this is dubious piece of research. After all, of what value (if any) is this discovery of a new inconceivably large prime compared to the previous discovery of a large prime...
  (I'm sure there was some reasonably clever software programming behind the search algorithum).
14. Re:Sounds cool, but... by Anonymous Coward · 2009-10-15 08:14 · Score: 0
  
  Even if there is no application at the moment (I'm not sure if there is either), there could be applications discovered in the future.
  For example, there were areas in the study of number theory that were once thought to be purely abstract with no real application. Those studies have been incorporated into cryptography and internet security.
15. Re:Sounds cool, but... by the_one(2) · 2009-10-15 08:19 · Score: 1
  
  It's not easy for a computer to multiply those two numbers! You would have to perform 2^56582998 multiplications (on a 64-bit processor) and as many additions... That would take pretty much literally forever.
16. Re:Sounds cool, but... by selven · 2009-10-15 08:58 · Score: 1
  
  It's a separate donation fund managed by the EFF. They're not stealing from our brave soldiers fighting the RIAA and the government.
17. Re:Sounds cool, but... by selven · 2009-10-15 08:59 · Score: 1
  
  Um... the primes in question are just a long list of ones.
18. Re:Sounds cool, but... by Katmando911 · 2009-10-15 10:29 · Score: 1
  
  Computing the factors would be a pretty brute force way to do it. It'd be much faster to assume the factors you are looking for are prime and test the number to see if the known primes are factors. I guess that would add value to know a Mersenne prime that isn't known to the public.
19. Re:Sounds cool, but... by Anonymous Coward · 2009-10-16 03:11 · Score: 0
  
  Well, cryptographic security only improves linearly with the number of binary digits of the primes if it isn't easy to just guess these primes.
  Though I don't think using Mersenne primes is a good way to set up a cryptographic key. If you see a public key with 56+ million bits, guessing that the two primes are just the ones you provided is easy. It's not as if there's many other pairs of primes known that, multiplied, result in a 56 million bit number.
  Ok, the calculations still require time, but about the same on encoding and decoding ends...
20. Re:Sounds cool, but... by GargamelSpaceman · 2009-10-16 03:11 · Score: 1
  
  Yeah, why the heck is the EFF paying out prizes for this? It was a 'Cooperative Computing Award'.
  From their site:
  
  EFF hopes to spur the technology of cooperative networking and encourage Internet users worldwide to join together in solving scientific problems involving massive computation. EFF is uniquely situated to sponsor these awards, since part of its mission is to encourage the harmonious integration of Internet innovations into the whole of society.
  
  Why not encourage people to cooperate solving a useful problem? I mean if you've got half a million dollars to spend on this useless crap, then I certainly won't be donating any of my money to the EFF, despite my agreeing with their larger purpose. Damn waste.
  
  --
  ...
21. Re:Sounds cool, but... by Anonymous Coward · 2009-10-17 10:21 · Score: 0
  
  I read your post and thought WTF are you on about, no they aren't, then I realised you were refering to the binary representation of the number that the computer would use internally.
Man, oh, man... by bennomatic · 2009-10-15 03:50 · Score: 4, Funny

The biggest prime number I know is 8675309. I'll have to tell Jenny about this new one.

--
The CB App. What's your 20?
1. Re:Man, oh, man... by Anonymous Coward · 2009-10-15 03:58 · Score: 0
  
  Don't call her; you'll get this guy instead.
2. Re:Man, oh, man... by Anonymous Coward · 2009-10-15 04:18 · Score: 1, Funny
  
  the prime number 641 should be high enough for everybody
3. Re:Man, oh, man... by .sig · 2009-10-15 04:25 · Score: 0, Redundant
  
  I'd rather have 655357, as anything more than 655360 (640K) is just too much.
  
  --
  -Space for rent
4. Re:Man, oh, man... by sconeu · 2009-10-15 04:30 · Score: 1
  
  Damn you Tommy Tutone!
  
  --
  General Relativity: Space-time tells matter where to go; Matter tells space-time what shape to be.
5. Re:Man, oh, man... by dkleinsc · 2009-10-15 04:52 · Score: 1
  
  What about 2 ^ 2079460347? You know, the odds that you can get rescued while floating in outer space by a passing Heart of Gold.
  
  --
  I am officially gone from /. Long live http://www.soylentnews.com/
6. Re:Man, oh, man... by bennomatic · 2009-10-15 05:03 · Score: 1
  
  That's clearly not a prime number! The "2 ^" gives it away!
  
  --
  The CB App. What's your 20?
7. Re:Man, oh, man... by mcgrew · 2009-10-15 05:27 · Score: 1
  
  But the best prime "number" (encoded of course) is 5t34k.
  
  --
  Free Martian Whores!
8. Re:Man, oh, man... by Anonymous Coward · 2009-10-15 05:30 · Score: 0
  
  Jenny, I got your number, I need to make you prime.
9. Re:Man, oh, man... by Anonymous Coward · 2009-10-15 13:26 · Score: 0
  
  My prime goes to 11.
woo by nomadic · 2009-10-15 03:54 · Score: 0, Troll

Glad to hear they're putting all those donations to use. There's no telling the impact on civil liberties that having access to a really large prime number will have...
1. Re:woo by geekmux · 2009-10-15 04:03 · Score: 2, Insightful
  
  Glad to hear they're putting all those donations to use. There's no telling the impact on civil liberties that having access to a really large prime number will have...
  Er, yeah no shit...I'm all for supporting the EFF(seriously, I am), but when I have to whip out my "what-the-fuck-good-is-THAT-for?!?" card, I tend to re-think my tax write-offs, especially to the tune of $100K...
2. Re:woo by characterZer0 · 2009-10-15 04:04 · Score: 1
  
  Encryption.
  
  --
  Go green: turn off your refrigerator.
3. Re:woo by Computer_kid · 2009-10-15 04:07 · Score: 2, Informative
  
  One of EFFs goals is personal privacy. Encryption is based on prime numbers, the larger the prime, the more secure it is. Having an insanely large prime would take nearly forever to crack the encrypted message. http://www.cpaadvisor.us/sub/8_encryption.htm
4. Re:woo by Nibbler999 · 2009-10-15 04:13 · Score: 5, Informative
  
  The money does not come from regular donations.
  http://www.eff.org/awards/coop
  
  (Prize money comes from a special donation provided by an individual EFF supporter, earmarked specifically for this project. Prize money does NOT come from EFF membership dues, corporate or foundation grants, or other general EFF funds.)
5. Re:woo by geekoid · 2009-10-15 04:17 · Score: 3, Insightful
  
  They just got advertising in every math/scientific magazine on the planet.
  Mostly read my professionals that make decent money.
  Sounds like a well spent 100K to me.
  
  --
  The Kruger Dunning explains most post on /. http://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect
6. Re:woo by nomadic · 2009-10-15 04:26 · Score: 1
  
  Ok, that's better.
7. Re:woo by Anonymous Coward · 2009-10-15 04:54 · Score: 0
  
  Thanks, I was a bit miffed at this use of funds too.
8. Re:woo by XSpud · 2009-10-15 07:41 · Score: 1
  
  One of EFFs goals is personal privacy. Encryption is based on prime numbers, the larger the prime, the more secure it is. Having an insanely large prime would take nearly forever to crack the encrypted message.
  I'm not convinced using one of the 48 known Mersenne primes as the basis for a new encryption algorithm is going to be particularly secure!
I'm way late to this thread by Anonymous Coward · 2009-10-15 03:56 · Score: 2, Funny

(2^43,112,609 - 1)th post!
nice! by Anonymous Coward · 2009-10-15 03:57 · Score: 0

A prime example of what can be done when....gah *dodges tomatoes*
What?!? Somebody else found this number? by Anonymous Coward · 2009-10-15 04:09 · Score: 0

Now I'll gave to change my PIN number again. Just as well... I was getting a little tired typing it in every time anyway!
Obligatory by Anonymous Coward · 2009-10-15 04:12 · Score: 0

2 ^ 43112609 - 1? That's the same combination I have on my luggage!
I haven't tested this thoroughly, but... by The+Altruist · 2009-10-15 04:13 · Score: 1

Take any base 10 number that ends with 4 or 6. Square it. Add 1. So far, in my limited testing experience, it has worked.
1. Re:I haven't tested this thoroughly, but... by mctk · 2009-10-15 04:18 · Score: 2, Interesting
  
  34^2+1 = 17*89
  
  --
  Paul Grosfield - the quicker picker upper.
2. Re:I haven't tested this thoroughly, but... by Anonymous Coward · 2009-10-15 04:24 · Score: 0
  
  I have read many crazy ways people find primes. I must admit, the one you suggested is the craziest i have come across.
3. Re:I haven't tested this thoroughly, but... by Canazza · 2009-10-15 04:27 · Score: 2, Informative
  
  (6*6) -1 = 35
  
  --
  It pays to be obvious, especially if you have a reputation for being subtle.
4. Re:I haven't tested this thoroughly, but... by Canazza · 2009-10-15 04:29 · Score: 1
  
  bugger, - instead of +, I fail at maths
  
  --
  It pays to be obvious, especially if you have a reputation for being subtle.
5. Re:I haven't tested this thoroughly, but... by Anonymous Coward · 2009-10-15 04:31 · Score: 0
  
  Why go to all that trouble when you can just take all known primes, multiply them by each other, then add 1? Repeat as necessary until you achieve the desired size BFPN (Big Fricking Prime Number).
6. Re:I haven't tested this thoroughly, but... by Anonymous Coward · 2009-10-15 04:53 · Score: 2, Informative
  
  Nope.
  17*89 = 1513
  34^2+1 = 1157
  You are 50% correct, however, as you probably meant to type 13*89, which would work.
7. Re:I haven't tested this thoroughly, but... by SoVeryTired · 2009-10-15 04:53 · Score: 1
  
  Euclid used that technique to show that there are an infinite number of primes, but it's not guaranteed to generate primes.
  For example (2x3x5x7x11x13)+1 = 59x509
  
  --
  Slashdot: news for Apple. Stuff that Apple.
8. Re:I haven't tested this thoroughly, but... by Anonymous Coward · 2009-10-15 05:25 · Score: 0
  
  Or, simpler, 3x5 + 1 = 16 = 2x2x2x2...
9. Re:I haven't tested this thoroughly, but... by Anonymous Coward · 2009-10-15 05:27 · Score: 0
  
  Correct. This proof just states that either your number is a prime or it is divisible by a prime larger than the largest prime in your multiplication (here both 59>13 and 509>13.)
10. Re:I haven't tested this thoroughly, but... by Anonymous Coward · 2009-10-15 06:08 · Score: 0
  
  try 44, and divide result by 13.
11. Re:I haven't tested this thoroughly, but... by onemorechip · 2009-10-15 06:12 · Score: 1
  
  Then we just need to find *that* number...and it's reassuring that the problem is bounded.
  (/facetious mode)
  But the other hole in GGP's proposal is that the sequence "all known primes" has lots of gaps in it.
  
  --
  But, I wanted socialized health insurance!
12. Re:I haven't tested this thoroughly, but... by harry666t · 2009-10-15 11:43 · Score: 1
  
  Just test it out already!
  $ python
  >>> from commands import getouput as sh
  >>> # i'm too lazy to write my own prime test function:
  >>> def is_prime(n): return not bool(sh("factor %d" % n).split()[2:])
  >>> # check a few integers to make sure it works:
  >>> zip(xrange(10), map(is_prime, xrange(10)))
  >>> maybe_primes = [(((i*10)+4)**2)+1 for i in xrange(20)]
  >>> zip(maybe_primes, map(is_prime, maybe_primes))
  That's what we have computers for.
Mersenne Primes Link by KiwiCanuck · 2009-10-15 04:17 · Score: 2, Informative

http://primes.utm.edu/mersenne/
A Question by rshol · 2009-10-15 04:18 · Score: 1

What is it about Mersenne Primes that makes finding a new one worth $100k? Is there an intrinsic value to the number or is it just one of those things that are so hard to do, like running a world's record hundred meters, that the effort and talent to do it merits a rewarded?
1. Re:A Question by mikael · 2009-10-15 04:30 · Score: 1
  
  The more digits that prime numbers have, the further apart adjacent primes are. If you imagine the value of a prime number represents the distance along a coastline in terms of centimeters, then you would only need a few billion to cover the entire length of a continent, and adjacent prime numbers would be separated by a few hundred metres.
  These Mersenne prime numbers are hundreds of digits long, so as a distance that would be measured in light years, nor metres or kilometres. There just isn't the computational power to check every single possible location, so they use Mersenne prime numbers are a way of taking a short cut to known locations where a prime number might be located.
  
  --
  Vintage computer adverts: http://www.vintageadbrowser.com/computers-and-software-ads
2. Re:A Question by Locke2005 · 2009-10-15 04:39 · Score: 1
  
  What is it about going to the Moon that makes it worth spending $20 billion? Advances in pure mathematics aren't done for immediate benefit, they are done on the off chance that the new "discovery" might be useful some day, like non-Euclidean geometry. In this case, it was more of an incentive to develop the algorithms and computing power necessary to deal effectively with the problem space. Hopefully this provided insights into how other large, intractable problems may be solved.
  
  --
  I've abandoned my search for truth; now I'm just looking for some useful delusions.
3. Re:A Question by KevinKnSC · 2009-10-15 05:07 · Score: 1
  
  The more digits that prime numbers have, the further apart adjacent primes are.
  That's not actually true. As numbers get larger you'll get longer composite runs, but you'll still find prime constellations between some of those runs. If what you say was true, the twin prime conjecture would be closed with a "Myth: BUSTED!" sticker on it, instead of open with overwhelming evidence in its favor.
4. Re:A Question by Hadlock · 2009-10-15 05:11 · Score: 2, Interesting
  
  I think $100,000 is roughly how much, in electricity costs, it costs to run the many, many computers for 5-10 years needed to grind out this particular number. Plus maintenance and taxes. You could pretty much say this research was done "at cost".
  
  --
  moox. for a new generation.
5. Re:A Question by Ambiguous+Puzuma · 2009-10-15 07:10 · Score: 1
  
  I think what he meant is that on average adjacent primes get further apart (see prime number theorem).
6. Re:A Question by Anonymous Coward · 2009-10-15 18:41 · Score: 0
  
  What is it about going to the Moon that makes it worth spending $20 billion?
  As far as I can tell, absolutely nothing.
7. Re:A Question by Locke2005 · 2009-10-16 02:36 · Score: 1
  
  Those chips in the computer your using to post facetious comments are a spinoff of NASA technology. As is your satellite television feed.
  
  --
  I've abandoned my search for truth; now I'm just looking for some useful delusions.
Whoever added the "founditontheground" tag... by magsol · 2009-10-15 04:22 · Score: 2, Insightful

...is a freaking genius. I can't stop laughing. I tip my hat to you, good sir/ma'am.

--
"I'd just like to emphasise that taking a million years isn't a metaphor here..." -Rich Bradshaw
A new autobot discovered? by Anonymous Coward · 2009-10-15 04:29 · Score: 0

We'll definitely need Mersenne Prime when Optimus finally dies for real in the 3rd Transformers movie.
1. Re:A new autobot discovered? by .sig · 2009-10-15 04:36 · Score: 1
  
  You mean the 4th one? Optimus did die for real in the first movie (animated, back in the mid-80's), and was replaced by Rodimus Prime at the end of the movie. I'll admit I haven't seen most of the cartoons since then, so I'm not really sure where Mersenne came from.
  
  --
  -Space for rent
Wait a minute... by 01100111 · 2009-10-15 04:29 · Score: 1

... and this new founded information is coming from an organization going by the name of GIMPS?
What a wasted opportunity by y5 · 2009-10-15 04:32 · Score: 5, Funny

They could have made the reward $100,003 instead...
1. Re:What a wasted opportunity by bitt3n · 2009-10-15 04:54 · Score: 5, Funny
  
  They could have made the reward $100,003 instead...
  yeah, brilliant idea. next day's headline would be "Five Mathematicians Slain in Argument Over Division of Prize Money"
  
  --
  how many pairs of boxer shorts should you own?
2. Re:What a wasted opportunity by 31415926535897 · 2009-10-15 05:45 · Score: 1
  
  They could have made the reward $100,003 instead...
  yeah, brilliant idea. next day's headline would be "Five Mathematicians Slain in Argument Over Division of Prize Money"
  Why? It's not like the prize is in Yen.
3. Re:What a wasted opportunity by Anonymous Coward · 2009-10-15 05:46 · Score: 0
  
  They could have made the reward $100,003 instead...
  yeah, brilliant idea. next day's headline would be "Five Mathematicians Slain in Argument Over Division of Prize Money"
  it's called cents... as in each Mathematician get $20000.60
4. Re:What a wasted opportunity by Anonymous Coward · 2009-10-15 05:58 · Score: 0
  
  There were 6 mathematicians, 5 were killed.
5. Re:What a wasted opportunity by Carbaholic · 2009-10-15 06:10 · Score: 1
  
  You just need a prime number they can split evenly between five people
6. Re:What a wasted opportunity by Anonymous Coward · 2009-10-15 06:57 · Score: 0
  
  So much death...
  and it could have been avoided with 10 quarters and 5 dimes.
7. Re:What a wasted opportunity by Anonymous Coward · 2009-10-15 07:33 · Score: 0
  
  They could have made the reward $100,003 instead...
  yeah, brilliant idea. next day's headline would be "Five Mathematicians Slain in Argument Over Division of Prize Money"
  Your joke doesn't make any cents.
8. Re:What a wasted opportunity by Anonymous Coward · 2009-10-15 08:24 · Score: 0
  
  Why's that? It seems to be evenly divisible by both 5 and 6.
9. Re:What a wasted opportunity by Anonymous Coward · 2009-10-15 09:46 · Score: 0
  
  20 000.6
they're useful for security researchers by circletimessquare · 2009-10-15 04:35 · Score: 1

http://www.jcu.edu/math/vignettes/mersenne.htm

Why So Much Interest in Primes?
You might wonder whether the search for large primes is of any value. Apart from the adventurous spirit of exploration, there actually are uses for large prime numbers. One of the most important applications is to the field of cryptography -- the encoding and decoding of messages. National security often relies on having a secure method of encoding and deciphering messages; yet the existence of high-speed computers have rendered all but the most sophisticated coding schemes insecure. One commonly used method of message coding is the RSA scheme, named for its creators, Ron Rivest, Adi Shamir, and Len Adleman. The RSA scheme relies on the fact that it is easy to multiply two prime numbers, yet hard to factor their product -- especially if the prime numbers are large. Consequently, knowledge of large prime numbers can lead to coding schemes that are difficult to break.

--
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
dude by circletimessquare · 2009-10-15 04:42 · Score: 1

mersenne prime discoveries have a direct, practical use in cryptography. cryptography is very important for secure communication on teh intarwebs. secure communication outside the prying eyes of intrusive governments is very important for the eff and its goals

--
intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
I'm pissed! by UnknowingFool · 2009-10-15 04:45 · Score: 3, Funny

Now that everyone knows this number, I have to change my luggage combination again. Thanks for nothing EFF!

--
Well, there's spam egg sausage and spam, that's not got much spam in it.
1. Re:I'm pissed! by Hurricane78 · 2009-10-15 20:31 · Score: 1
  
  May I recommend: One... two... three... four... ...FIVE!?
  
  --
  Any sufficiently advanced intelligence is indistinguishable from stupidity.
45th in order of discovery by Noren · 2009-10-15 04:45 · Score: 3, Informative

The article is correct by order of discovery- it was the 45th Mersenne prime to be discovered (on August 23, 2008.) Two smaller Mersenne primes were discovered later, on September 6, 2008 and April 12, 2009, which are also included in the Wikipedia table.
1. Re:45th in order of discovery by coolsnowmen · 2009-10-15 06:16 · Score: 1
  
  How did they miss 2?
2. Re:45th in order of discovery by MistrX · 2009-10-15 20:53 · Score: 1
  
  Why would they need it?
  I mean, I understand the use of prime numbers but to search for such high numbers do not exibit any kind of use. I think the potential calculating time, computerpower and electricity could also be spent on helping finding cures for diseases. Finding such prime numbers are in my eyes just a waste of time and energy.
3. Re:45th in order of discovery by Man+Eating+Duck · 2009-10-15 21:02 · Score: 1
  
  How did they miss 2?
  
  It's a distributed effort like Folding@Home, and it's not testet strictly sequentially. You can choose roughly the size of the candidates you want to test, the largest ones will take weeks or months on regular hardware. They do try to fill in the bottom gaps between tested numbers, but before they have tested every number 2^n-1 below a certain value of n they can't be sure they haven't missed any Mersenne primes in that range. I believe they also tests every n twice to make sure one isn't missed due to bugs or faulty hardware.
  
  --
  Are you a grammar Nazi? I'm trying to improve my English; please correct my errors! :)
4. Re:45th in order of discovery by coolsnowmen · 2009-10-16 05:19 · Score: 1
  
  Wow, nothing to do with my question,
  Also From the, 'everything adds up argument,' why are you wasted time, computerpower, and electricity browsing and commenting on /. if you feel so strongly?
  But I'll take a stab, since you did. What if large prime numbers help create more secure crypto. If the governmental research on prime numbers ever outpaces public by an order of magnitude, then primenumber based crypto can be more easily broken and evil govn't can better spy on citizen who want to freely communicate.
  Additionally, the optimal weighting of computer power to solving out prioritized problems isn't 100% on the top priority until it is solved. Because computational ability can be broken up into the millions of computers we have, we can similarly break down out priority list and spend X_1% computing power on Y_1% pririty, and X_2% computing power on Y_2% priority ad finitum.
So what is it? by AP31R0N · 2009-10-15 05:02 · Score: 1

What is the awesome number? The summary makes a big deal about this number but doesn't include it! WtF?

--
Utilizing the synergization of benchmark e-solutions to pre-workaround action items!
1. Re:So what is it? by patrickthbold · 2009-10-15 05:16 · Score: 1
  
  "2 to the power of 43,112,609, minus 1" or if it helps 2^43112609-1
2. Re:So what is it? by LordEd · 2009-10-15 05:28 · Score: 2, Informative
  
  There is a link in TFA to the number. It gives an abbreviated version first, but links to the full number as well:
  http://prime.isthe.com/chongo/tech/math/prime/m42643801/prime-c.html
3. Re:So what is it? by wastedlife · 2009-10-15 05:34 · Score: 1
  
  I hope you were going for funny here, although I am curious as to how much RAM firefox would eat trying to display a page displaying a 12 million digit long string.
  
  --
  Said, "It's just like dice but it's got more sides And it tells me who lives and who dies"
4. Re:So what is it? by wastedlife · 2009-10-15 05:43 · Score: 1
  
  http://prime.isthe.com/no.index/chongo/merdigit/long-m42643801/prime-c.html
  Before: 140 MB used
  Several minutes and 1 maxed CPU core later: Jumping between 250 MB and 300 MB used before I gave up and closed the tab.
  
  --
  Said, "It's just like dice but it's got more sides And it tells me who lives and who dies"
5. Re:So what is it? by AP31R0N · 2009-10-15 07:12 · Score: 1
  
  i was.
  Yeah, that would be h00t. Lemme see what happens to IE....
  170MB. Wow.
  
  --
  Utilizing the synergization of benchmark e-solutions to pre-workaround action items!
Sooooo Last Year by Buffaloaf · 2009-10-15 05:22 · Score: 1

I don't know why they are running a story about something that happened August 2008!
http://science.slashdot.org/story/08/09/13/1940218/45th-and-46th-Mersenne-Primes-Confirmed
And since then we've found 2 more hence the 47th prime.
http://science.slashdot.org/story/09/06/13/2218226/47th-Mersenne-Prime-Confirmed
1. Re:Sooooo Last Year by muhgcee · 2009-10-15 06:02 · Score: 1
  
  As far as I know, it takes a while for the number to be verified as correct.
2. Re:Sooooo Last Year by Samah · 2009-10-15 16:32 · Score: 1
  
  I don't know why they are running a story about something that happened August 2008!
  I dunno, that's pretty close to breaking news for Slashdot.
  
  --
  Homonyms are fun!
  You're driving your car, but they're riding their bikes there.
Amazing coincidence by noidentity · 2009-10-15 05:28 · Score: 1

The number, known as a Mersenne prime, is the 45th known Mersenne prime, written shorthand as 2 to the power of 43,112,609, minus 1
That's amazing. I've got the same combination on my luggage!
Various useful details by JoshuaZ · 2009-10-15 05:34 · Score: 3, Interesting

The project GIMPS that is mentioned in the title uses a distributed computing system to search for Mersenne primes. They use a modified form of the Lucas-Lehmer test http://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test where they use a Fast Fourier Transform to be able to do the large multiplications efficiently.
We care about Mersenne primes because they correspond to even perfect numbers. If one has a Mersenne prime 2^p -1 then (2^p-1)(2^(p-1)) is an even perfect number. This was proven by the ancient Greeks. Euler then proved much later that every even perfect number is of this form. The oldest two unsolved problems in mathematics are whether there are infinitely many even perfect numbers and whether there are any odd perfect numbers. Thus, every time we discover a new Mersenne prime we get a new even perfect number. And if we can ever get enough insight to resolve whether or not there are infinitely many Mersenne primes then we can resolve one of the oldest unsolved problems in all of mathematics.
1. Re:Various useful details by Ibag · 2009-10-15 10:06 · Score: 1
  
  The problem is, finding new Mersenne primes doesn't actually give us any insight into whether there are an infinite number of them. Yes, the problem of finding perfect numbers (or rather, determining whether there are an infinite number of them, or whether there are any odd ones) has been a tantalizing problem since antiquity (as are most problems that are as easy to understand but as hard to prove), but individual examples like this aren't particularly important . Indeed, they are curiosities. And at the size and sparsity of the known Mersenne primes make it very unlikely that anybody will be able to find in them a usable pattern.
  Don't get me wrong, many great discoveries have come from people studying curiosities, and I'm more than happy to let people continue searching for bigger and bigger Mersenne primes (or would be if there wasn't a real environmental impact associated to the energy cost from all those computer cycles devoted to the project), but I really don't want to confuse the importance of questions involving Mersenne primes with the triviality of determining that yet another Mersenne number is actually prime.
2. Re:Various useful details by JoshuaZ · 2009-10-15 10:29 · Score: 1
  
  That's a valid point. However, in general having more numeric data can lead to patterns and new insights which we can then try to prove. For example, tables of primes were compiled in the 19th century extending well beyond anything anyone practically needed. However, the data lead people to notice a number of patterns including the Prime Number Theorem http://en.wikipedia.org/wiki/Prime_number_theorem. For example, this new Mersenne prime undermines slightly the general belief that if 2^p -1 is prime then p-1 should have many small prime factors. (In this case, p-1=2^5 * 7 * 11 * 17497 ).
  The argument about energy use is also a red herring. Since GIMPS is a distributed computing most of the energy would be wasted normally anyways on extra clock cycles. Sure, more energy will be used but not that much.
3. Re:Various useful details by Anonymous Coward · 2009-10-16 03:29 · Score: 0
  
  Modern CPUs use far less power on idle than on heavy load. Say, 20 Watts instead of 100, or 5 instead of 35. This DOES add up quite a bit.
I'm glad it's voluntary by onemorechip · 2009-10-15 05:38 · Score: 1

From TFA:

A 12 million digit prime number, the largest such number ever discovered, has landed a voluntary math research group a $100,000 prize from the Electronic Frontier Foundation (EFF).

I'd hate to learn that EFF is using slave labor.

--
But, I wanted socialized health insurance!
Prove it by Anonymous Coward · 2009-10-15 05:43 · Score: 0

Oh yeah, prove it.
Oh, wait, never mind.
Mersenne number by Anonymous Coward · 2009-10-15 05:45 · Score: 1, Insightful

A Mersenne number is a positive integer that is one less than a power of two, the group stated.
Yeah, well, you know, that's just, like, their opinion, man.
outrageous name by Anonymous Coward · 2009-10-15 05:47 · Score: 0

Discovered by "the computing project called the Great Internet Mersenne Prime Search (GIMPS)".
I am surprised that nobody yet has protested against such an outrageous name. It happens any time with GIMP...
Thank goodness it's voluntary by handy_vandal · 2009-10-15 05:47 · Score: 4, Funny

A 12-million-digit prime number, the largest such number ever discovered, has landed a voluntary math research group a $100,000 prize from the Electronic Frontier Foundation (EFF).

"Voluntary" math research group? Is there any other kind?
I'm trying to imagine an "involuntary" math research group, and all I'm getting is scenes from dystopian science fiction ... or possibly a scene from the life of Léon Theremin.

--
-kgj
1. Re:Thank goodness it's voluntary by JoshuaZ · 2009-10-15 05:55 · Score: 1
  
  In this case I presume that voluntary is referring to the fact that people do this as a hobby. The Great Internet Mersenne Prime Search is run by volunteers, not people doing research as academics or such.
2. Re:Thank goodness it's voluntary by Anonymous Coward · 2009-10-15 06:38 · Score: 0
  
  Yes, the PAID kind.
3. Re:Thank goodness it's voluntary by Anonymous Coward · 2009-10-15 15:35 · Score: 0
  
  I'm trying to imagine an "involuntary" math research group,
  
  I believe there's one in every major high school on the continent (with a few exceptions, of course).
WHO CARES??? by Anonymous Coward · 2009-10-15 05:58 · Score: 0

Honestly, what practical application does a 12 million digit number server.
1. Re:WHO CARES??? by Anonymous Coward · 2009-10-15 06:11 · Score: 1, Insightful
  
  What practical application does discovering gaseous planets that are >100 million light years away? It doesn't need a practical application to be interesting. Welcome to humanity, dipshit.
Slashdot Mods: Grow Up by Rary · 2009-10-15 06:07 · Score: 1

Your point is valid, and you're not the only one who thought of it. Others have pointed out that this didn't come from regular donations, but I just wanted to weigh in and say that the moderation you've received (currently "Score: 0, Troll") is ridiculous. Yours was a valid comment, and a useful contribution to this discussion.

--
"You cannot simultaneously prevent and prepare for war." -- Albert Einstein
Fails the first time: by Anonymous Coward · 2009-10-15 06:09 · Score: 0

4*4-1=15=2*5
Ima Karma Whore by handy_vandal · 2009-10-15 06:56 · Score: 1

Well, yeah, I kinda overlooked that (hoping for +1 Funny, karma-whore that I am).

--
-kgj
My irony must be rusty by handy_vandal · 2009-10-15 07:58 · Score: 1

Well, sure. I was shooting for droll irony -- must've aimed low.

--
-kgj
1. Re:My irony must be rusty by JoshuaZ · 2009-10-15 09:45 · Score: 1
  
  Apparently I don't have a functioning irony meter. It seems however that the people with mod points do.
where is my money by deodiaus2 · 2009-10-15 08:38 · Score: 0, Redundant

I claim knowing a higher prime!! 2^(2^43,112,609 - 1) - 1 or 2^(2^(2^43,112,609 - 1) - 1) - 1 better yet 2^(2^(2^(2^43,112,609 - 1) - 1) - 1) - 1 .. recursively .. Where do I get my money!!
1. Re:where is my money by Anonymous Coward · 2009-10-15 11:21 · Score: 0
  
  Okay. Now show us that these numbers are prime.
You mean... by Schnoogs · 2009-10-15 09:22 · Score: 0

I could have been paid when I discovered this number last year?
The difference is the sponsor. . . by JSBiff · 2009-10-15 09:23 · Score: 1

I'm going to have to do a little research on this issue, to find out why the *EFF* funded this prize. As an EFF donor, I donate money to them so that they can use it to advance the causes of liberty and privacy. I'm a little puzzled at how them spending $100k of (I presume) *donor money* is advancing the cause of liberty or privacy? Here I thought my money was going to precedent-setting lawsuits and criminal trials, and to lobby congress and educate the press about technology and liberty/privacy issues?
I suppose *maybe* this is somehow tied into the last part (government/public education about the issues) sort of "crypto awareness", since most cryptography is based on large prime numbers, but I'm a bit skeptical at them moment that my donations are being used wisely.
My prime by Anonymous Coward · 2009-10-15 10:35 · Score: 0

is bigger than your prime!
uni-brows by Anonymous Coward · 2009-10-15 15:42 · Score: 0

That's a big group uf uni-brows who will never get laid.
Sorry, but I think you are wrong. by RichiH · 2009-10-15 20:34 · Score: 1

The Mersenne primes are useless for this task, though. They are so long and so far in between that you can guess which of them are involved by just looking at the length of any given key. Which would be _way_ too long to handle, anyway. And they could just use ECC instead.
So no, I am not sure that is the reason. In fact, I am sure that can't be the reason.
That being said, if anyone has any ideas, please share them :)
Useless by Anonymous Coward · 2009-10-15 21:57 · Score: 0

Absolutely useless research.
Re:45th in order of discovery or just RTFWikipedia by dezent · 2009-10-16 02:05 · Score: 1

If you read the wikipedia article.. "It is not known whether any undiscovered Mersenne primes exist between the 39th (M13,466,917) and the 47th (M43,112,609) on this chart; the ranking is therefore provisional. Primes have also not been discovered in increasing order. For example, the 29th Mersenne prime was discovered after the 30th and the 31st. Similarly, the current record holder was followed by 2 smaller Mersenne primes, first 2 weeks later and then 8 months later."
Not the prime choice but the choice *process* by jonaskoelker · 2009-10-16 04:39 · Score: 1

and would be affected very differently by the choice of prime numbers.
I think they're more affected by the rules for the process by which the primes are chosen... rather than the particular choice of primes.
Let p be the number from the summary. If your rule is "choose a random element of {p}", it's fine for D-H and ElGamal, bad for RSA. If it's "choose a random element of {primes less than or equal to p}" and you just happen to (randomly!) choose p, it's not a problem for RSA any more. It's not that p has any particular numeric properties that makes it weak (it might, but with RSA, these days I hear it's more important to choose large numbers rather than specific kinds of numbers).
Well, except that your adversary might try a dictionary attack against your secret primes.
It's the same with weak passwords: no particular password is weak, were it not for a lot of other people being more likely to choose it rather than "%xF8o0_a". And to all the people who choose bad passwords: choose some hunter2-ing better passwords! ;-)