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Prime Numbers Not Random?

  1. Mar 31, 2003 #1
  2. jcsd
  3. Mar 31, 2003 #2
    The sequence of primes is entirely deterministic. There are even nth prime formulae; however, the formulae are of exponential complexity...or worse.

    Addendum: Oh, there's a link. The site explains how the sucession of primes is not so apparantly random after all.
     
    Last edited by a moderator: Mar 31, 2003
  4. Mar 31, 2003 #3

    Hurkyl

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    It gets better than that.

    There exist polynomials p(n) (n integer) that only take on prime or negative values. Even bettern there exist polynomials p(n) that can be every prime number and some negative values, but nothing else!

    There even exists a formula for the n-th prime number! (I've only heard this referenced though, I have never actually seen it)

    Hurkyl
     
  5. Mar 31, 2003 #4
    What if this is true, why are they still searching for big prime numbers with computers and stuff. Why don't they just plug 100,000,000,000,000,000,000,000,000,000,001 in for the n and get a massive prime number. I really have to doubt about this part.

    What are the functions you were refering to that take on all prime numbers and some negative numbers. Those sound kind of interesting.
     
  6. Mar 31, 2003 #5
    Exponential Complexity:

    If T(f; n) is the time it takes to calculate f(n), the T(f; n + 1) is approximately T(f; n) times some constant k > 1. Attempting to calulate the 100,000,000,000,000,000,000,000,000,000,001st prime would probably require more eons than there are Angstroms in a lightyear.
     
  7. Mar 31, 2003 #6
  8. Mar 31, 2003 #7
    Hurkyl
    Urban Legend?
     
  9. Mar 31, 2003 #8
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