## Tuesday, September 27, 2011

### The Complicated Fractal Nature Of Prime Numbers

Mandelbrot, the inventor of fractals, when he worked for IBM was presented with a problem involving interference in the transmission of information. Every so often parts of the transmitted information would seem to randomly drop off / scramble which, needless to say, caused problems with the transmitted informational message. The problem had to be fixed, but as the information drop off / scramble appeared to be random , everyone was flummoxed because of the lack of a recognizable pattern. Mandelbrot thought about it and started experimenting. One time he decided to take a straight line and divide it into 1/3rd . He discarded the middle 1/3rd and kept the other 2/3rd separated by a space ( ------ ------ ). He continued on and discovered that the pattern produced by this method matched the pattern of the informational message drop off / scramble. This discovery proved that the informational drop off / scramble wasn't random but followed a fractal pattern.

Prime Numbers also follow a fractal pattern. Prime Numbers are defined as numbers that can be only divided by themselves and one ( 1 ).

Prime Numbers follow a complicated fractal pattern. First of all, if you look at a list of prime numbers you will find that they always have the numbers 1, 3, 7, 9 in column zero or otherwise known as the far right column ( 11, 13, 17, 19 ). The second thing you will notice is that all numbers ending in ( 1, 3, 7, 9 ) aren't prime numbers ( 21, 33, 27, 39 ).

The second thing you will notice is that if the sum of the digits of any number ending ending in 1, 3, 7, 9 total a multiple of 3 ( divide by 1/3rd and discard the potential prime just like Mandelbrot discarded his string sections ), except for 3, ( for instance 6, 9, 12, etc. ) it isn't a prime number. If a number ending in 1, 3, 7, 9 in column zero ( far right column ) isn't a prime number it can usually be evenly divided by a number with 1, 3, 7, 9 in column zero ( far right column ).

Lastly, except for the one digit prime number 3 in the one digit prime number series ( 1, 2, 3, 5, 7 ) you will find if you continuously add the digits of a prime number ( for instance 97 = ( 9 + 7 = 16 ) ( 1 + 6 = 7 ) you will find the column zero or far right column one digit totals are ( 1, 2, 4, 5, 7, 8 ). All the rest of the columns are zero ( 01, 02, 04, 05, 07, 08 ).

In summary:

1. Prime numbers, if they are prime numbers, have the numbers 1, 3, 7, 9 in column 0 ( farthest right column ).

2. If the sum of the digits of any number ending in 1, 3, 7, 9, total a multiple of 3, except for 3, ( for instance total 6, 9, 12, etc. ) it isn’t a prime number. If a number ending in 1, 3, 7, 9 in column zero (0), isn’t a prime number it can usually be evenly divided by a number with 1, 3, 7, 9 in column (0).

3. Except for the one digit prime number 3 in the one digit prime number series ( 1, 2, 3, 5, 7 ) if you add the digits of a prime number ( for instance 97 = ( 9 + 7 = 16 ) ( 1 + 6 = 7 ) the column zero or far right column one digit totals are ( 1, 2, 4, 5, 7, 8 ).

## Thursday, September 22, 2011

### One Small Step For The Riemann Hypothesis

The Riemann Hypothesis says that all the non-trivial zeros ( 0 ) are on the line ( y = ½ ) and that this hypothesis has something to do with prime numbers. Another way of expressing it, is by saying that the magnitude of the oscillations of primes around their expected position is controlled by the real parts of the zeros of the zeta function. In particular, the error term in the prime number theorem is closely related to the position of the zeros.

In summary:

1. We have a line ( y = ½ ) .
2. We have some zeros that are real and we can use them since they touch / cross the line ( y = ½ )
3. The error term in the prime number theorem is related to the position of the zeros.

The Prime Number Theorem is concerned with the number of primes preceding a number. Due to the nature of mathematics when you multiply, it is probably better to have the number as a prime number for considerations of accuracy. In other words, if you can calculate the location of a prime number in the prime number series you automatically know how many prime numbers precede it.

We have the line ( y = ½ ) . Therefore let the first digit of the multiplier be ½ or .5. We have some zeros that are real and we can use them since they touch / cross the line ( y = ½ ) . Therefore let the middle digits be zeros ( 0 ). We now have the number .50. To finish our multiplier add the digit 9 to the end forming the number ( .5099999999 ).

The first prime numbers from 1 to 12 in order are 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31. If we multiply these numbers by ( .509999999 ) our answer is very close to their actual position ( 23 X .509999999 = 11.72999999 ). The actual position of prime number 23 is 10. There are 9 prime numbers preceding 23 ( 1, 2, 3, 5,7,11,13, 17, 19 ).

The prime numbers from 13 to 26 in order are ( 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 ). If you multiply these primes by ( .509999999 ) you will find that the prime number positions are hugely incorrect. You will see in the “ In summary “ list that I indicated under ( 3. ) that the error term in the prime number theorem is related to the position of the zeros. You can increase the number of zeros by either adding them between ½ and 9 (for instance .5000999999) or by raising ( .509999999 ) to the power of 2 ( .509999999 X.509999999 = ( .2600999 )). You will see from ( .2600999 ) that we have adjusted the error term in the prime number theorem by adjusting the zeros ( 0 ) from one to two. Multiply the prime numbers by ( .2600999 ) to obtain the prime number location.

If you do the multiplication, you will find that some of the prime number locations are still out. For instance, ( 37 X .2600999 = 9.623699981). The actual location is 13. For some inexplicable reason if you add Pi ( 3.141592654 ) to this number you get ( 12.76529263 ). This trick of either adding or subtracting Pi works in the majority of cases. In some cases adding or subtracting the natural number ( 2.718281828 ) also works.

Here’s how the system works for numbers in general.

1. Count the number of digits in a prime number. For instance 7919 has 4 digits. Subtract 1 from the number of digits ( 4 - 1 = 3 ) for 7919. Form another number equal to the number of digits in 7919 ( 4 ) by putting ( .5 ) in the far left column and 9 in the far right column. ( .5—9 ). Fill the middle with Riemann Hypothesis zeros ( 0 ) forming a four digit number ( .5009 ). Raise ( .5009 ) to the power of 3 ( which is the number of digits in 7919 ( 4 ) minus 1 ( 4 - 1 = 3 ). ( .5009 ) ^ 3 = .125676215. Multiply 7919 X .125676215 = 995.2299524. 7919 is the 1000th prime number. The calculation is short by approximately the value of Pi ( 3.141592654 ). Pi + 995.2299524 is 998.3715451 which is very close to 1000.
It can be seen from these calculations that the magnitude of the oscillations of the primes around their expected position is controlled by the zeros ( 0’s) in the multiplier. The error term is closely related to the position of the zeros in the number ( .509999999 ). The error term can be controlled by either adding zeros ( .500999999, .50009999 ) or by raising these numbers to a power ( multiply the numbers by themselves ) thereby increasing the zeros. A further adjustment can be made by adding or subtracting Pi ( 3.141592654 ) or the natural number “e” ( 2.718281828 ).thereby creating a range. The present method of proving the Riemann Hypothesis consists of calculating whether or not zeros cross or touch the line ( y = ½ ) . While I appreciate the effort, it seems to me that I have proved the Riemann Hypothesis because my zeros can be infinitely added between the digits ½ and 9 ( .5----9 ). It can be seen that the calculation of the position of a prime and the number of primes preceding that prime all depend on the Riemann Hypothesis' real zeros. Thus the Riemann Hypothesis has been proved by illustrating its’ real relationship to the position of the primes and the number of primes preceding it.

## Monday, September 19, 2011

### Theory Of Everything

Here's The Theory Of Everything in a nutshell without the mathematics. The classical world that you and I see every day consists of:

1. Time
2. Energy / Weight / Mass
3. Space

Einstein in his equation E = MC^2 said that energy and mass were equivalent. Weight is the pull of gravity on an object. That is why Newton's apple fell from the tree since the pull of the earth ( gravity ) is greater than the pull of the apple ( gravity ) on the earth. Mass is the same thing as weight without gravity pulling on you and I. As far as space is concerned, Einstein said that space doesn't exist unless something extends into it. If you look at something you are extending your sight ( observation ) into space. If you drive a car you are extending it into space ( distance ). If we didn't have space there wouldn't be velocity, acceleration or force ( Force = Mass X Acceleration ( into space) ). Time is a marker for something happening ( The apple fell from the tree at 2:00 a.m.. ). Time is also a measure of distance ( I traveled 30 kilometers / miles in 30 minutes ).

In the quantum world there is time but not space. Einstein spoke of spooky action at a distance which is true in the abstract but not existing physically. If space doesn't exist in the quantum world, you don't have any delays. The absence of space means you can have superposition because more than one thing can exist literally on / in the same spot. You can also have entanglement which means that if something happens in one location the something immediately happens / clones in the other location. This happens because the something doesn't have to travel through physical space. The speed of change is infinite ( timeless ), because the limitation on the speed of light only applies when it is moving through space and not time. Information also travels using the same principle. If we attempt to measure the quantum / spaceless world from our classical / space world, by using particles ( light / x-ray etc. ) we disturb the something we are measuring by adding quanta / energy ( particles ) to it. This energy addition changes the original quantum something so that we aren't measuring the original.

In summary quantum time world without classical space is:

1. Cloning
2. Superposition
3. Entanglement

In summary our classical world is:

1. Time
2. Space
3. Energy / Weight / Mass