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Hello all,

I've been working on a fractal style proof of the prime twin problem over at:
http://www.rankyouragent.com/primes/primes.htm

The fractal pattern of primes is remarkeably simple.  So simple I can define it in a few lines

Start with this binary pattern
100
Find the first zero and note it's 1-based position.  (here it's in the 2nd position).
Create a new binary pattern starting with 1 and (2*position of first zero) 0's
So we create 10000  (4 zeros because the first zero in the previous pattern was at position 2)

Merge the two patterns by running the old pattern the (length of the new pattern) times
and running the new pattern the (length of the old pattern times) and AND the two
100100100100100
010000100001000    AND
----------------------------------
110100100101100

REPEAT

That's it, that's all the primes are.  The first 0 in any such a pattern is guaranteed to be a prime, the remaining 0's are prime candidates and any 1's to the right of the first 0 are guaranteed to be composite.  (1's to the left of the first 0 are either prime or composite.)

So for our example of this pattern:
110100100101100

The first zero is at the 3rd position, so we know that 2*3+1 = 7 is prime.  All the 1's to the right of the first 0 are guaranteed to be composite, so 2*4+1 = 9 is composite, as is 7*2+1 = 15, and so on.

this is cool new stuff how to enumerate the primes, questions that appear in my mind are...

...why is the first prime you get with this method 7 ? does it start by 7 ?

...how do look the the decimal representation of these binary strings, any remarkable things?

... you enumerate all primes after another ?

... doesn't these binary strings grow very large very soon?

i am kinda happy that one of the most delicate problems in math has a fractal style, anyway, i
do not really get the fractal method here, let me try to describe what you are doing

base fractal property of self similarity is achieved by simply sequencing a simple pattern,
in a way it is like alway applying the same string to itself, at different scales ( the ones starting with 1 )
what you didn't mention was that you shift the newly generated string to the right ( is it so ? )
somehow it reminds me to a cantor set... very interesting
greets

>...why is the first prime you get with this method 7 ? does it start by 7 ?

No, the first entry is 5, 3 is the base case, then you get 5,7,11,13, etc etc

http://www.rankyouragent.com/primes/primes.htm

>...how do look the the decimal representation of these binary strings, any remarkable things?

You'd get some sort of irrational number.  That is a pattern of digits that never repeats.

>... you enumerate all primes after another ?

Yes

>... doesn't these binary strings grow very large very soon?

Very large, very fast, very soon, that's why they're good fodder for random generators

>i am kinda happy that one of the most delicate problems in math has a fractal style, anyway, i
>do not really get the fractal method here, let me try to describe what you are doing


>base fractal property of self similarity is achieved by simply sequencing a simple pattern,
>in a way it is like alway applying the same string to itself, at different scales ( the ones starting with 1 )
>what you didn't mention was that you shift the newly generated string to the right ( is it so ? )
>somehow it reminds me to a cantor set... very interesting

As opposed to self similarity, think of it as self complicating.  However every iteration has a similarity with a previous iteration.



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http://www.mersenne.org/prize.htm (http://www.mersenne.org/prize.htm)

You gotta go get yourself some cash!