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Re: example of T3 Sequence

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  • leavemsg1
    ... yes!, if n is even... ... don t know about that complicated mess, but if m IS odd, say 15... then T15 = T8 * T7 - 3 mod N it s that simple!; the author
    Message 1 of 3 , Feb 15, 2008
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      --- In primenumbers@yahoogroups.com, "Christ van Willegen"
      <cvwillegen@...> wrote:
      >
      > Bill,
      >
      > just to clarify something for myself..
      >
      > For even n:
      > T(n) = T(n/2)^2 - 2 (MOD 47)
      yes!, if n is even...

      > T(n + 1) = T(n/2) * T((n+2)/2) - 3 (MOD 47)
      don't know about that complicated mess,

      but if m IS odd, say 15... then T15 = T8 * T7 - 3 mod N
      it's that simple!; the author described it easily...

      here's my newest modification... but it's a bit more profound than
      the original article; it combines the T3 sequence w/ sqrt N

      it'll work with any number; take N = 207…

      find sqrt N = 14.3 {roughly};

      then compute terms T14, T12, T7, T6, T4, T3, T2, and T0 = 2, T1 = 3;

      so…

      T2 = T1^2-2 mod 207 = 7,
      T3 = T1*T2-3 mod 207 = 18,
      T4 = T2^2-2 mod 207 = 47,
      T6 = T3^2-2 mod 207 = 115,
      T7 = T4*T3-3 mod 207 = 15,
      T12 = T6^2-2 mod 207 = 182,
      & T14 = T7^2-2 mod 207 = 16;

      Since 182 + 16 < 207, then 207 is composite;
      if the sum were > 207, then it would've been prime;
      this technique combines SQRT and the T3 sequence.
      Try it! or wait 'til you understand the T3 sequence alone.

      >
      > I was figuring out where the -2 and -3 came from. Is this it?
      >
      > On Wed, Feb 13, 2008 at 3:57 PM, Bill Bouris <leavemsg1@...> wrote:
      > > > take the number 47, for example...
      > > > the program calculates the terms, ...
      > > >
      > > > T47
      > > > T24,T23
      > > > T12,T11
      > > > T6,T5
      > > > T3,T2
      > > > T1,and T0
      > > >
      > > > so...
      > > > every term is taken MOD 47,
      > > > to keep them small...
      > > >
      > > > T0 = 2 mod 47
      > > > T1 = 3 mod 47
      > > > T2 is T1^2 -2 mod 47
      > > > T3 is T1*T2 -3 ...
      > > > T5 is T2*T3 -3 ... etc
      > > > T6 is T3^2 -2
      > > > T11 is T5*T6 -3
      > > > T12 is T6^2 -2
      > > > T23 is T11*T12 -3
      > > > T24 is T12^2 -2
      > > > and T47 is T23*T24 -3
      > > >
      > > > if the result is T47 = 3, then 47 is prime!
      > > > neat, huh?
      >
      > I can't comment on this, though...
      >
      > Christ van Willegen
      > --
      > 09 F9 11 02 9D 74 E3 5B D8 41 56 C5 63 56 88 C0
      >
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