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)
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)
Merenne numbers 2^{P} - 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.
Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1.
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."
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."
...except when P=2, where 2^{P} - 1 = 3.
Since all primes > 2 are of the form 2n+1,
2^{P}-1 {mod 6}
= 2^{2n+1}-1 {mod 6}
= 2(2^{2n})-1 {mod 6}
= 2(4^{n})-1 {mod 6}
= 2((3+1)^{n})-1 {mod 6}
= 2(3^{n} + k_{1}.3^{n-1} + k_{2}.3^{n-2} + ... + k_{n-1}.3 + 1) -1 {mod 6}, where k_{x} 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."
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)
. . . 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.
. . . 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.
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."