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Thread: Prime pairs.

  1. #21
    radical strawberry
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    Quote Originally Posted by Roy View Post
    ...except when P=2, where 2P - 1 = 3.

    Since all primes > 2 are of the form 2n+1,

    2P-1 {mod 6}
    = 22n+1-1 {mod 6}
    = 2(22n)-1 {mod 6}
    = 2(4n)-1 {mod 6}

    [and, because 2.4 = 2 mod 6]

    = 1 {mod 6}
    But the binomial expansion was cute.

  2. #22
    radical strawberry
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    Because the Euler phi function (counting the multiplicative group mod n) is multiplicative, and phi(p) = p-1 for all primes p ...

    phi(6) = phi(2).phi(3) = 1.2 = 2

    Hence, mod 6, all primes > 3 must fall into one of two equivalence classes.


    But no one more than six feet away from a crack pipe would call them paired primes.
    Last edited by lao tzu; 01-15-2018 at 01:28 PM.

  3. #23
    tWebber
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    Quote Originally Posted by lao tzu View Post
    Because the Euler phi function (counting the multiplicative group mod n) is multiplicative, and phi(p) = p-1 for all primes p ...

    phi(6) = phi(2).phi(3) = 1.2 = 2

    Hence, mod 6, all primes > 3 must fall into one of two equivalence classes.

    Nice addition to the conversation



    Jim
    Jorge's trueorigins paper: "...it is known that other volcanic features match what is usually associated with impact craters including ... shatter cones and crystal deformations"

    Planetary Science Institute: "Shatter cones are found in only two places on Earth, 1) in nuclear test sites and 2) meteorite impact structures. They are formed as a result of the high pressure, high velocity shock wave ...

    maximum pressures from 45 to 200 times greater than found in volcanic events (2->20 Gpa)

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