Re: Bug in Sun compiler WS6U2? - Crashes during compile phase with-fast.

From: Dave (nospam_at_nowhere.com)
Date: 03/24/05

  • Next message: Andrew Gabriel: "Re: A different zones question" 
    Date: Thu, 24 Mar 2005 00:31:15 +0000

    Logan Shaw wrote:
    > David Kirkby wrote:
    >
    >> Now if someone can find a fast way of factoring large prime numbers,
    >> that will be the end of ssh as it is currently known.
    >
    >
    > Now you're correctly quoting Bill Gates's famous incorrect statement
    > about cryptography.

    Believe it or not, I found on Mathworld

    http://mathworld.wolfram.com/PrimeNumber.html

    today that thing Gates said, found it funny and sent an email around at
    work to a few who I thought would find it funny too. Not realising I'd
    put an identical silly statement on a newsgroup the night before!!

    I'd like to say its an easy mistake to make (to excuse me), but I will
    not, as then it would excuse Bill Gates, who I rather dislike.

    Yes, I know you can't factor primes - by definition. What I meant of
    course is that if there was found a way of factorising large composite
    numbers, it would be the end of cryptography. I'm sure there are
    cryptographic techniques that don't use primes.

    > You can't factor large *prime* numbers, because
    > you can't factor *any* prime numbers. However, you can factor large
    > numbers that are the product of two primes, and if you did that, it'd
    > be a bad thing for cryptography as we know it.

    I'm sure one day someone will come up with a general formula for finding
    the nth prime, which would go a long way towards making factorisation of
    huge composite numbers. Mathematica takes about 45 seconds to find the
    100000000000th prime on my computer.

    In[8]:= Prime[100000000000] //Timing

    Out[8]= {44.51 Second, 2760727302517}

    But it can factor a composite number consisting of two similar sized
    primes virtually instantly.

    In[10]:= 2760727302559 * 2760727302517 // multiple two primes.

    Out[10]= 7621615238978741781241003 // get the result

    In[11]:= FactorInteger[7621615238978741781241003] // factor it

    Out[11]= {{2760727302517, 1}, {2760727302559, 1}} // The two prime factors.

  • Next message: Andrew Gabriel: "Re: A different zones question"

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