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Statistical patterns in primes - Journal of Omnifarious

May. 14th, 2009

06:18 pm - Statistical patterns in primes

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There is an interesting new result showing that the distribution of prime numbers obeys a modified version of Benford's Law. The result also shows that another sequence who's distribution is somehow fundamentally related to the distribution of primes, the 0s of the Reimann zeta function.

It is my feeling that results like this do not strongly affect the usefulness of prime number based cryptography algorithms like RSA. But this is just a guess on my part. Does anybody have a more definitive answer?

Current Mood: [mood icon] curious
Current Music: Cowboy Junkies - Seventeen Seconds

Comments:

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From:zanfur
Date:May 15th, 2009 01:31 am (UTC)
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This isn't a new result -- it's been known for decades. Of course they're logarithmically distributed! Think of the Eratosthenes sieve: every new prime found removes "potential" prime numbers farther along the sieve, giving to a logarithmically decreasing density of primes. We learned this in algebra class in my high school.
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From:zanfur
Date:May 15th, 2009 01:35 am (UTC)
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Ah, I misunderstood the article at first. Yeah, I agree, a weighted distribution of the first digit of a prime doesn't reduce the usefulness of primes in general (add another digit, if you care).

It would seem to me that this follows from the fact that they're logarithmically distributed, though. Logarithmically distributed means exponentially increasing (on average), which is exactly the class of number sequences that benford's law applies to.
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From:princessgeek
Date:May 15th, 2009 02:18 am (UTC)
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I don't know, but I'm feeling a little warm.
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