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Re: [PrimeNumbers] Miller-Rabin question...

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  • David Cleaver
    ... Thank you for the reassurance that I wasn t doing all of this wrong. I ve found where I got my mis -information. It was at mathworld:
    Message 1 of 3 , Jan 24, 2006
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      eliasen@... wrote:
      >
      > David Cleaver wrote:
      > > Hello everyone,
      > >
      > > We've all heard of the results that for all numbers up to
      > > z=341550071728321, we can prove primality by running 8 MR tests
      > using
      > > the first 8 consecutive prime bases (cpb's), right? And we've also
      > > heard that 9 gives no improvement, right? Well, I've run into
      > something
      > > curious. I recently wrote my own program to run MR on the first k
      > cpb's
      > > and found that z is "prime" by 8 cpb's, but it is not "prime" by 9
      > > cpb's. (ie, we do get an improvement with 9 cpb's.)
      > >
      > > Am I mis-understanding something somehwere?
      >
      > Probably. I don't know how you're counting primes, or where you
      > got the
      > above information, but it doesn't seem right.

      Thank you for the reassurance that I wasn't doing all of this wrong.
      I've found where I got my "mis"-information. It was at mathworld:
      http://mathworld.wolfram.com/Rabin-MillerStrongPseudoprimeTest.html
      On that page it said "the first 8 primes (using 9 gives no improvement)"
      and I took that for granted.

      Sorry for the confusion everyone. BTW, does anyone know how to contact
      Eric W. to let him know of this small typo on his web page?

      -David C.

      > Testing against bases
      > 2,3,5,7,11,13,17 is sufficient to prove primality for all numbers <
      > 341550071728321. Testing against base 19 gives no additional
      > improvements.
      >
      > --
      > Alan Eliasen | "You cannot reason a person out of a
      > eliasen@... | position he did not reason himself
      > http://futureboy.homeip.net/ | into in the first place."
      > | --Jonathan Swift
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