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Math Help - Prime testing with base 2 test.

  1. #1
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    Prime testing with base 2 test.

    I have a question in my book as follow:

    Use the base 2 test on 511 and 509

    (base 2 test is n does not satisfy 2^n\equiv2mod(n) then it is composite)

    For the first part I think I am good:

    Noting that 2^9=512\equiv1mod(511) so

    2^{511}=({2^{9}})^{56}*2^7\equiv2^7mod(511)

    and 2^7 is not \equiv2mod(511)

    However for the second part I get a bit confused:

    2^9=512\equiv3mod(509) so

    2^{509}=({2^{9}})^{56}*2^5\equiv(3^{56}*2^5) But I am a bot confused as to where to go next.

    Thanks for any help

    (oh and anybody knows the Latex symbol for not equivalent that would be great)
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by hmmmm View Post
    (oh and anybody knows the Latex symbol for not equivalent that would be great)
    \not \equiv = \not \equiv

    -Dan
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