Do Infinitely Many Prime Pairs Exist?

[Spin_Network]

My work in prime numbers has delivered me evidence that prime numbers are not connected to each other due to their prime nature, but due to the connections of the other numbers in prime number locations (which happen to be multiplications of prime numbers). I wrote extensively about this in Chapter 5 of In Search of a Cyclops http://www.pentapublishing.com/CyclopsBook5.html . Published as The Proof of Nothing in the year 2000.

When dividing all numbers in series of six it is possible to see that there are prime number positions and non-prime number positions. All prime numbers (except 2 and 3) appear in either the first position or in the fifth position. See http://www.pentapublishing.com/images/table1.gif
I made the choice to place 1 with the prime numbers even though that is not considered correct. The link between prime numbers is not a link between the prime numbers, but a link between the non-prime numbers. See http://www.pentapublishing.com/images/table2.gif
What are the red numbers in this table are non-prime numbers in first and fifth positions. These red numbers follow a pattern, like for instance those divisible by 7. See http://www.pentapublishing.com/images/table4.gif
As you can see in this table 7 'cuts' out numbers in turns in first and fifth positions according to a pattern of 4 plus 3 lines of six down.
All prime numbers 5 and up 'cut' away first and fifth position numbers from the prime number list according to a very strict and specific regimen. See http://www.pentapublishing.com/images/jump.gif which shows two numbers after each prime number (or multiplication of a prime number), portraying the lines of six jumped to take out numbers off the prime number list. All prime number multiplications follow these kinds of number specific jumps - and all these jumps are linked together. Therefore all prime numbers can then be calculated according to a subtraction method. It is not the link between them, but the link that eliminates the others from being prime numbers. From this information a new method can be created to quickly appoint the prime numbers for which I am in the (long) process of getting a patent (question so far is if that will happen).

Once you understand how non-prime numbers are formed, it becomes obvious (and a little bit boring) to see which numbers remain as the prime numbers. All prime numbers would appear in two packs if it wasn't for the multiplications of prime numbers taking numbers off that list of prime numbers. Have a look at http://www.pentapublishing.com/CyclopsBook5.html , a Chapter I wrote to deliver evidence that zero is intrinsic to the natural numbers (not a natural number itself according to number theorists - but which is a natural number according to set theorists).

Whatever you are trying to convey, in some sort of amazing discovery?

Take this:http://homepage.ntlworld.com/paul.valletta/PRIME GRIDS.htm

I discovered that the 'Ero-sieve' is not anatural representation of the numbers used, if one diagonalize's the cells into a certain progressive angle, then certain patterns arise.

I did not know at the time that this pattern is actually pertaining to:http://eureka.ya.com/angelgalicia30/Primesbehaviour.htm

which is quite an amazing site!

One can see that Prime numbers behave in a specific way?..if one uses the 'rectangle Sieve' for the first one hundered primes, there is NO concerning pattern that emerges. But if one Diagonalize's the sieve boxes, then one see's the Pattern is Emergent!

What is the significance?..it happens to be connected to Fractals and Prime Number distribution of real numbers, and my lack of Mathematical skills gave me a false sense of achievement ..the process was allready in existence, with maybe a slight of hand!

 

[shmoe]

I think it is something different. But please let me know if you have seen this all before. Prime number 5 creates a pattern of 1 + 4. Starting out at the six line that begins with 25 ONE line is moved down, while going from first to fifth location. Here, 35 is found. FOUR lines down moving back to first place, 55 is found. ONE line down moving to fifth location, 65 is found.

Same thing. In a basic Eratosthenes of size N you'll store your information in a string of N bits, where the nth bit is 1 if n is prime, 0 if it's composite. You start with a string of all 1's, 111111... First stage you remove 1: 011111... Next stage multiples of 2:0110101010... then multiples of 3:01101010001.. And so on.

Presieving by 2 and 3 is not only to save time but space. We need only consider numbers congruent to 1 or 5 mod 6, so this is the sequence we store. We need only about N/3 bits, the first bit represents 1, the next 5, the next 7, the next 11, then 13, and so on. Each pair of bits is one of your rows, so I'm going to separate them with commas. First stage we knock off 1: 01,11,11,11,11,11,... Next stage we knock off multiples of 5, this isn't as straightforward due to how our string is indexed, but we can easily see that we need to jump ahead 4 pairs and remove the first in the pair (this is 25) then we jump ahead one pair and remove the second (35) to get: 01,11,11,11,01,10,...And we continue jumping 4 pairs, 1 pair, 4 pairs, 1 pair crossing off as we go. Replace pair with line and this is what you're describing. I described in an earlier post how you'll know how many pairs (used your line terminology) to jump based on the k and the 1 or 5 in your primes representation as p=6k+1 or p=6k+5. Here k is just indexing the pair (or line) you're in (starting at 0) and 1 or 5 is whether you are 1st or 2nd in the pair.


A nice thing about Euclid's proof is that it's somewhat constructive and you can phrase in such a way to avoid the troublesome "infinite". If you take *any* finite list of primes then it not only guarantees there is a prime not on your list but also gives a multiple of this new prime, so you could find it with a little factoring. If you start with 3 and 5 it gives N=3*5+1=16, which though not prime has a the prime divisor 2, not on our list. We now take 2,3,5 and make N=2*3*5+1=31, another prime not on our list. So, when you've gotten to the point where you think you have all the primes, find the corresponding N and then what? What in your "reality" goes wrong? Did you just find a number with no prime factors? (do you think that's possible?)

 

[Fredrick]

Please, stop posting such nonsense, for the love of mathematics.

Thank you, guys, for very good answers, and good information.
I do not try to undermine math, math is fine as it is. I was just answering a question, and bumped into the limitations. You may think the limitations are inside of me (and you may be right), I think the limitation exist in math (in that it is abstract only, despite its many realistic applications). The thread divulged into a question about the infinite, which does not belong in this thread.
My famous last words:
I think the infinite in math is a mirror's mirror's image that is being given value. The infinite image truly exists — we need not argue about that — but is it still reflective of reality?
Thanks again.

 

[Gokul43201]

My famous last words:
I think the infinite in math is a mirror's mirror's image that is being given value. The infinite image truly exists — we need not argue about that — but is it still reflective of reality?

With that, let's call it a day here, wot ?