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Another Breakthrough in Prime Number Theory

Posted by timothy on from the brother-go-find-your-brother dept.

Battal Boy writes "From aimath.org: Dan Goldston and his Turkish colleague Yalcin Cem Yildirim have smashed all previous records on the size of small gaps between prime numbers. This work is a major step toward the centuries-old problem of showing that there are infinitely many 'twin primes': prime numbers which differ by 2, such as 11 and 13, 17 and 19, 29 and 31,...I am especially proud of this achievement as Yalcin is a close friend of mine from way back! You may also want to check out the Mercury News Article and Dan Goldston's home page where you can see a photo of Dan's back being slowly but surely broken by two of his children ..." Finding patterns in primes seems to be all the rage.

7 of 241 comments (clear)

  1. Good work by wyvern5 · · Score: 4, Interesting

    This is certainly a signficant advance in mathematics... prime numbers are one of the most enigmatic, yet useful aspects of number theory. What I'm really curious to see is whether or not this will help the efforts to find a more efficient algorithm for factoring a number into its prime factors. (A multiple of two very large primes is an integral part of RSA encryption, as well as other schemes.)

    --
    -- Apple: Where Microsoft wants to go today.
  2. other patterns in prime numbers by TerraFrost · · Score: 3, Interesting
    you can read about other patterns in prime numbers from mathworld... here:

    here

  3. Re:Interesting? by jointm1k · · Score: 5, Interesting

    I don't think this will help cracking RSA in anyway. I even believe this will even strengthen the RSA encryption. RSA is based upon the fact that it is very difficult (as in there is no trivial way) to factor a composit number into two primes. And these new theories won't help factorization. Ofcourse, if there is indeed a usufull pattern, it may help to find the primes---that are required for factorization---faster, but the person who uses the RSA-technique can do this too. This will allow the this person to find even bigger primes faster then usuall, so even if the cracker can find possible usufull primes faster, he has to try a whole lot more to facter the composite number. And since trying out a factor to see if the is part of the composite takes much longer time, I only see benefits for the RSA encryption scheme.

    --
    You know it makes sense, a little reminder from jointm1k.
  4. Buffon's Needle by Flamesplash · · Score: 3, Interesting

    Indeed, take Buffon's Needle Problem for instance. whoda thunk it.

    --
    "Not knowing when the dawn will come, I open every door." - Emily Dickinson
  5. Boring? by Battal+Boy · · Score: 5, Interesting

    You want boring? Then go and take a look at the PDF papers on this site.

    Are they boring? Yes, exruciatingly and mind numbingly so...
    Did they help us win the Second World War? err...yes

    --

    A cynic is what an idealist calls a realist...
  6. Prime Number Advances by Effugas · · Score: 3, Interesting

    Mathematicians described the advance -- announced at a conference in Germany -- as the most important breakthrough in the field in decades.

    Personally, I think the technique for provably determining the primality of an arbitrary number in polynomial time -- "PRIMES is in P" -- was a more unexpected result. It's always seemed like the probability of a twin prime occuring on the number continuum was a limit approaching but never quite reaching 0 -- an artifact of the number of previous primes already "exposed" approaching, but never reaching infinity. But actually sitting down and proving this -- excellent! Very cool.

    --Dan

  7. Re:Interesting? by ghjm · · Score: 4, Interesting

    Not so fast with the assumption that people protecting information can just automatically make use of new techniques. The idea with encryption is that you transmit your information over an insecure channel. This means that the bad guys already have copies of your information, encrypted using the techniques you used. If new techniques become available, you can't go back and use them on your old data, because it's already been transmitted. Therefore, in an arms race where cryptography and cryptanalysis proceed at equal rates, all the information you already own becomes increasingly vulnerable.

    People (or agencies) holding a portfolio of critically sensitive information that has already been transmitted (and therefore probably intercepted in encrypted form) have a vital and sustaining interest in research into prime numbers. In many case their interest is in having such research stopped. It will be interesting to see what happens to super-smart but real-world-naive math Ph.D candidates if and when high efficiency factoring techniques become the subject of dissertations....

    -Graham