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prime observation/question

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  • leavemsg1
    maybe... let Z = 2^(2^(p+1))+1 ; p is prime Z is prime iff [Z (mod (2^p+1))] == 2^q ; for some q for p = 2, 3,..., next??? eg. p=2, 2^8+1 mod 5 == 2^1 and...
    Message 1 of 2 , Jul 7, 2007
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      maybe... let Z = 2^(2^(p+1))+1 ; p is prime

      Z is prime iff [Z (mod (2^p+1))] == 2^q ; for some q

      for p = 2, 3,..., next???

      eg. p=2, 2^8+1 mod 5 == 2^1 and...
      p=3, 2^16+1 mod 9 == 2^3 and...

      I searched up to p=389 using 'Try GMP!' interpreter and the result for
      all the primes thus far were a residue of 17... not 2^5 as expected.

      If it were to jump up to 2^5,... I think that the Z as stated in the
      first statement would be prime.

      Are p=2,3,... the only generators for a prime Z ????

      Thanks in advance for any commentary.
    • Bill Bouris
      ... maybe if q can only be odd???, then a statement that all Fermat primes greater than F4 are composite may arise??? just tinkering with the idea!
      Message 2 of 2 , Jul 8, 2007
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        --- In primenumbers@yahoogroups.com, "leavemsg1"
        > wrote:
        >
        > maybe... let Z = 2^(2^(p+1))+1 ; p is prime
        >
        > Z is prime iff [Z (mod (2^p+1))] == 2^q ; for some q

        maybe if q can only be odd???, then a statement that
        all Fermat primes greater than F4 are composite may
        arise??? just tinkering with the idea! comments???

        >
        > for p = 2, 3,..., next???
        >
        > eg. p=2, 2^8+1 mod 5 == 2^1 and...
        > p=3, 2^16+1 mod 9 == 2^3 and...
        >
        > I searched up to p=389 using 'Try GMP!' interpreter
        > and the result for all the primes thus far were a
        > residue of 17... not 2^5 as expected.
        >
        > If it were to jump up to 2^5,... I think that the
        Z as stated in
        the
        > first statement would be prime.
        >
        > Are p=2,3,... the only generators for a prime Z ????
        >
        > Thanks in advance for any commentary.
        >
        I ran it up a little further to p=509 and I'm still
        not able to produce a residue other than 17 for any
        prime up to 509




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