- Jul 20 9:21 AM--- On Sun, 7/20/14, amel dalluge <youngpoohter@...> wrote:

> From: amel dalluge <youngpoohter@...>

> Subject: (reply to) Re: [PrimeNumbers] Pairs of Odd Numbers and Prime Number Consequences

> To: "w_sindelar@..." <w_sindelar@...>

> Date: Sunday, July 20, 2014, 9:17 AM

> the trouble

> i am finding that all prime numder solvers have is that any

> tangible solution has to be four seperate equations (not

> one).

> the reason being that there is four

> seperate unique waves created that repeat at a growth of ten

> to each wave (see my post to the group and, note, it got

> messed up during the emailing [the waves aren't perfect]).

> the trick is to determine the

> initial starting point of each wave, coordinate the next

> point which will be, starting at one, a growth of plus two

> (1,3,5,7,9,11,13...) times the value of the initial point of

> the wave, repeat for next point (one times the value of the

> initial point would be the start, and than, three times the

> value of the initial point would be the second point in the

> wave and, five times the value of the initial point would be

> the third point in the wave, so on and so forth).

> also note, the waves' wave will also

> repeat at a growth of ten times the value of the initial

> point plus the value of the prior point.

> as i said above,what i am finding is

> prime solvers are using one equation instead of four as

> required for a tangible solution as i above laid out above

> (just not in symbols but in layman's terms)[ that's the

> solution to all prime numbers, yes above].

> --------------------------------------------

> On Sun, 7/20/14, 'w_sindelar@...'

> w_sindelar@...

> [primenumbers] <primenumbers-noreply@yahoogroups.com>

> wrote:

>

> Subject: [PrimeNumbers] Pairs of Odd Numbers and Prime

> Number Consequences

> To: primenumbers@yahoogroups.com

> Date: Sunday, July 20, 2014, 7:11 AM

>

>

>

> One, For all pairs of odd positive primes A<B with the

> same difference D and A>3, the number N of even

> integers

> between A and B that are divisible by a twin prime middle

> number remains the same, and equals D/3, if D mod 3 equals

> 0, or equals (D-1)/3, if D mod 3 equals 1, or equals

> (D+1)/3, if D mod 3 equals 2.

>

> I found statement one to be true for many (A, B) prime

> pairs.

>

> I also found the following generalized statement two to be

> true for many non-prime odd integers.

>

> Two, For all pairs of odd positive integers A<B, that

> satisfy these 4 requirements:

>

> a), Their greatest common divisor equals 1.

>

> b), They are not divisible by 3.

>

> c), They are not prime

>

> d), They have the same difference D.

>

> the number N of even integers between A and B that are

> divisible by a twin prime middle number remains the same,

> and equals D/3, if D mod 3 equals 0, or equals (D-1)/3, if

> D

> mod 3 equals 1, or equals (D+1)/3, if D mod 3 equals 2.

>

> Statement one example: Pick D=22. The first occurrence of

> a

> pair of primes with a difference D=22 is A=7 and B=29. The

> number N of even integers between A and B that are

> divisible

> by a twin prime middle number is N=7 by actual count.

> Since

> (D mod 3) equals 1, (D-1)/3=7 which agrees with the actual

> count N. Take the consecutive primes A=1129 and B=1151.

> D=22. Again N equals 7, and remains constant for all pairs

> of odd primes with the same difference D=22.

>

> Statement two example: Again pick D=22. The first

> occurrence

> of a pair of odd integers with a difference of 22 that

> satisfies the 4 requirements is A=133 and B=155. Again

> N==7.

> prompting the following statement three.

>

> For convenience, let’s call any pair of distinct odd

> primes a “P”, and any pair of distinct odd positive

> integers that satisfies the 4 requirements a “Z”.

>

> Three, if a P and a Z have the same difference D, then the

> number Np of even integers in P that are divisible by a

> twin

> prime middle number always equals the number Nz of even

> integers in Z that are divisible by a twin prime middle

> number.

>

> Is all of the above obvious and well known? Anyone care

> try

> these exercises and check me on this? Thanks folks.

>

> Bill Sindelar

>

>

>

>

>

> .

>

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