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Thread: Prime pairs.

  1. #11
    tWebber
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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.
    mod (6q-1,6) = mod (6q+5,6) = 5
    mod (6q+1,6) = mod (6q+7,6) = 1

    Jim
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    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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    Quote Originally Posted by 37818 View Post
    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.
    Roy already explained it. But perhaps I can reword the explanation a bit so it is perhaps easier to follow.

    The lines in question define a set of y values (for natural number x values) which might be prime. The reason they do that is that for numbers divided by 6, there are only 6 possible remainders, 0, 1, 2, 3, 4, 5

    For input values of q that are Natural numbers:

    The line 6q -1 = y (or for Whole numbers 6q+5) generates all Natural y values with reminder 5 when divided by 6,
    the line 6q +1 = y (or for Whole numbers 6q+7) generates all Natural y values with remainder 1 when divided by 6.

    Natural numbers with remainder 0, 2, and 4 are NOT prime because they are all divisible by 2 (because 6 itself is divisible by 2).

    Natural numbers with remainder 3 are NOT prime because they are divisible by 3 (because 6 is itself divisible by 3)

    Therefore only numbers divided by 6 that have a remainder of 1 or 5 are possible prime candidates, and thus ALL primes lie on one or the other line.

    It is not that complicated.


    But it is interesting. There are many, many more properties that can be associated with primes. It is a fascinating field of number theory.


    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)

  3. #13
    tWebber 37818's Avatar
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    Merenne numbers 2P - 1 [where P is to be a prime number] all lie only in the 6q + 1 sequence.
    . . . 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 Roy's Avatar
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    Quote Originally Posted by 37818 View Post
    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.
    6(6ab-a+b)-1 = 36ab-6a+6b-1 = (6a+1)(6b-1)
    6(6ab-a-b)+1 = 36ab-6a-6b+1 = (6a-1)(6b-1)
    6(6ab+a+b)+1 = 36+6a+6b+1 = (6a+1)(6b+1)

    Therefore they can only be prime if a=0 or b=0.
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    Lilpixieoferror: "Another day another Starlight fable. What actually causes high lead levels in water is lead pipes or lead solder, not industrial waste from any source. Well, so much for this Starlight fable... I wonder what tomorrow’s made up story will be in his ‘I HATE AMERICAN CHRISTIANS!!!’ quest."

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    tWebber Roy's Avatar
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    Quote Originally Posted by 37818 View Post
    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.
    That paper appears to be garbage. The author has effectively reinvented the sieve of Erastosthenes and applied it to a misunderstanding of the Riemann zeta function.

    I stopped skimming it after seeing the author claiming that it was "notable" that the series 6n+1 contains no numbers divisible by 2 or 3.
    Starlight: "In America a lot of tap-water is contaminated with lead or chemicals from fracking, because the right-wing crazies are anti-regulation."
    Lilpixieoferror: "Another day another Starlight fable. What actually causes high lead levels in water is lead pipes or lead solder, not industrial waste from any source. Well, so much for this Starlight fable... I wonder what tomorrow’s made up story will be in his ‘I HATE AMERICAN CHRISTIANS!!!’ quest."

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    tWebber Roy's Avatar
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    Quote Originally Posted by 37818 View Post
    Merenne numbers 2P - 1 [where P is to be a prime number] all lie only in the 6q + 1 sequence.
    ...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}
    = 2((3+1)n)-1 {mod 6}
    = 2(3n + k1.3n-1 + k2.3n-2 + ... + kn-1.3 + 1) -1 {mod 6}, where kx are the coefficients of the binomial expansion of n
    = 2(3.something + 3.something + ... + 3.something + 1) -1 {mod 6}
    = 6.something + 6.something + ... + 6.something + 2 -1 {mod 6}
    = 1 {mod 6}
    Last edited by Roy; 01-11-2018 at 01:30 PM.
    Starlight: "In America a lot of tap-water is contaminated with lead or chemicals from fracking, because the right-wing crazies are anti-regulation."
    Lilpixieoferror: "Another day another Starlight fable. What actually causes high lead levels in water is lead pipes or lead solder, not industrial waste from any source. Well, so much for this Starlight fable... I wonder what tomorrow’s made up story will be in his ‘I HATE AMERICAN CHRISTIANS!!!’ quest."

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    tWebber
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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}
    = 2((3+1)n)-1 {mod 6}
    = 2(3n + k1.3n-1 + k2.3n-2 + ... + kn-1.3 + 1) -1 {mod 6}, where kx are the coefficients of the binomial expansion of n
    = 2(3.something + 3.something + ... + 3.something + 1) -1 {mod 6}
    = 6.something + 6.something + ... + 6.something + 2 -1 {mod 6}
    = 1 {mod 6}
    very nice :)

    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)

  8. #18
    tWebber 37818's Avatar
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    Quote Originally Posted by oxmixmudd View Post
    very nice :)

    Jim
    Both 6q-1 and 6q+1 excluded 2 and 3. So it was to be understood since 22-1 = 3 is outside 6q+1 q beginning with 1.
    . . . 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.

  9. #19
    tWebber 37818's Avatar
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    Quote Originally Posted by Roy View Post
    6(6ab-a+b)-1 = 36ab-6a+6b-1 = (6a+1)(6b-1)
    6(6ab-a-b)+1 = 36ab-6a-6b+1 = (6a-1)(6b-1)
    6(6ab+a+b)+1 = 36+6a+6b+1 = (6a+1)(6b+1)

    Therefore they can only be prime if a=0 or b=0.
    If a=0 and b=0 then q=0.
    . . . 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.

  10. #20
    tWebber Roy's Avatar
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    Quote Originally Posted by 37818 View Post
    If a=0 and b=0 then q=0.
    True, but trivial and not really relevant.

    What's your point?
    Starlight: "In America a lot of tap-water is contaminated with lead or chemicals from fracking, because the right-wing crazies are anti-regulation."
    Lilpixieoferror: "Another day another Starlight fable. What actually causes high lead levels in water is lead pipes or lead solder, not industrial waste from any source. Well, so much for this Starlight fable... I wonder what tomorrow’s made up story will be in his ‘I HATE AMERICAN CHRISTIANS!!!’ quest."

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