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Thread: Prime pairs.

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    tWebber 37818's Avatar
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    Prime pairs.

    All positive prime numbers, with the exception of 2 and 3 can be found to lie on two parallel lines. 6x + 5 = y1 and 6x + 7 = y2.

    Now not every number on those two lines are prime. But all the prime numbers, except 2 and 3 in the sequence x=0 , x=1, etc.

    Where x=0, y1=5, y2=7
    x=1, y1=11, y2=13
    x=2, y1=17, y2=19
    etc.
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  2. Amen mikewhitney amen'd this post.
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    tWebber Roy's Avatar
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    Quote Originally Posted by 37818 View Post
    All positive prime numbers, with the exception of 2 and 3 can be found to lie on two parallel lines. 6x + 5 = y1 and 6x + 7 = y2.
    ... because all numbers which are equivalent to 0/2/4 {mod 6} are divisible by 2, and all numbers which are equivalent to 3 {mod 6} are divisible by three, so all prime numbers except 2 and 3 must be 1 or 5 {mod 6}.
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    tWebber
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    Quote Originally Posted by 37818 View Post
    All positive prime numbers, with the exception of 2 and 3 can be found to lie on two parallel lines. 6x + 5 = y1 and 6x + 7 = y2.

    Now not every number on those two lines are prime. But all the prime numbers, except 2 and 3 in the sequence x=0 , x=1, etc.

    Where x=0, y1=5, y2=7
    x=1, y1=11, y2=13
    x=2, y1=17, y2=19
    etc.
    A reasonably well known and provable result. Though normally expressed as 6q +- 1.

    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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    tWebber
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    Quote Originally Posted by Roy View Post
    ... because all numbers which are equivalent to 0/2/4 {mod 6} are divisible by 2, and all numbers which are equivalent to 3 {mod 6} are divisible by three, so all prime numbers except 2 and 3 must be 1 or 5 {mod 6}.
    missed this reply - sorry. About the same summary I was going to give :)

    The statement might look a bit mysterious to those not familiar with primes, but it's not really much different than saying all primes after 2 are odd.

    Jmi
    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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    tWebber 37818's Avatar
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    Quote Originally Posted by oxmixmudd View Post
    A reasonably well known and provable result. Though normally expressed as 6q +- 1.

    Jim
    Quote Originally Posted by oxmixmudd View Post
    missed this reply - sorry. About the same summary I was going to give :)

    The statement might look a bit mysterious to those not familiar with primes, but it's not really much different than saying all primes after 2 are odd.

    Jmi
    Well, 6q - 1 and 6q +1 series are will known. So the two sets of numbers. 5 series incremented by 6 and the 7 series incremented by 6.
    . . . the Gospel of Christ, for it is [the] power of God to salvation to every [one] believing, . . . -- Romans 1:16.

    . . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3, 4.

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    tWebber 37818's Avatar
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    Quote Originally Posted by Roy View Post
    ... because all numbers which are equivalent to 0/2/4 {mod 6} are divisible by 2, and all numbers which are equivalent to 3 {mod 6} are divisible by three, so all prime numbers except 2 and 3 must be 1 or 5 {mod 6}.
    Yep.
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    . . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3, 4.

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    tWebber
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    Quote Originally Posted by 37818 View Post
    Well, 6q - 1 and 6q +1 series are will known. So the two sets of numbers. 5 series incremented by 6 and the 7 series incremented by 6.
    They are the same: -1 ==5 mod 6, 7 ==1 mod 6

    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)

  9. Amen Leonhard amen'd this post.
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    tWebber 37818's Avatar
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    Quote Originally Posted by oxmixmudd View Post
    They are the same: -1 ==5 mod 6, 7 ==1 mod 6

    Jim
    The mod (6q-1,6) = 5 and mod (6q+1, 6) = 1. So how is that the same?

    Now 6q - 1 series if q = 6ab-a+b those numbers are never prime.
    With 6q + 1 series if q = 6ab-a-b or q = 6ab+a+b those numbers are never prime.
    a and b of course being whole numbers.
    . . . the Gospel of Christ, for it is [the] power of God to salvation to every [one] believing, . . . -- Romans 1:16.

    . . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3, 4.

    Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1.

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    tWebber shunyadragon's Avatar
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    Quote Originally Posted by 37818 View Post
    The mod (6q-1,6) = 5 and mod (6q+1, 6) = 1. So how is that the same?

    Now 6q - 1 series if q = 6ab-a+b those numbers are never prime.
    With 6q + 1 series if q = 6ab-a-b or q = 6ab+a+b those numbers are never prime.
    a and b of course being whole numbers.
    OK math basic lesson. What's the big deal?
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    tWebber 37818's Avatar
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    Quote Originally Posted by shunyadragon View Post
    OK math basic lesson. What's the big deal?
    Ok. Find a site that explains all primes greater than 3 are found in only in the two number sets. 6q -1 set and 6q + 1 set.
    Never mind, _here_ is a link to a paper written on this.
    . . . the Gospel of Christ, for it is [the] power of God to salvation to every [one] believing, . . . -- Romans 1:16.

    . . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3, 4.

    Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1.

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