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 ).
Showing posts with label Prime Numbers. Show all posts
Showing posts with label Prime Numbers. Show all posts
Tuesday, September 27, 2011
Sunday, October 17, 2010
Riemann Hypothesis Resolved Using Prime Numbers
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. It is known that there are infinitely many zeros on the line 1/2 + it as t ranges over the real numbers. A prime number is any number that is evenly divided by itself and 1. Therefore, a prime number is a specialized real number which exists on the x axis. It is also known that any prime number can create a real number that isn’t a prime. A real number is a number that is sequentially placed on the x - axis and therefore has a specific location that can be calculated through subtraction. A prime number, however, cannot be specifically located on the x - axis because the distance between the prime numbers aren’t consistent. Riemann extended his equation into complex numbers which oscillate on a vertical plane at right angles to the x - axis or in other words across the line ( y = ½ ). The non-trivial zeros do not become real until the oscillating complex zero crosses ( y = ½ ) and becomes real. The complex zero is really on an imaginary string before it lies along the line ( y = ½ ). At this point the real zero can be used to calculate the location of the prime number on the x - axis. It is also known that there are an infinite number of prime numbers and by extension an infinite number of real numbers because prime numbers can be used to construct real numbers. So far the calculated zeros lie on the critical line, but the prime’s location strays because the calculation process behaves just like a 50:50 coin toss. The 50:50 distribution law says that coins will divide themselves proportionately over the long term, but on the specific terms they generally will not distribute themselves evenly. There are always exceptions. The most important thing that Riemann said was 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 and the error term in the prime number theorem is closely related to the position of the zeros.
Here are some facts about prime numbers.
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. A prime number is defined as being only evenly divisible by itself and one ( 1 ).
Here’s the proof:
A prime number is defined as any number that can be only divided evenly by itself and one. Furthermore a prime number, if it is a prime number, only has the digits, 1, 3, 7, 9 in column 0 which is the farthest right column. I have also discovered that if the sum of the digits of any number ending in 1, 3, 7, 9 total a multiple of 3, except for prime number 3 ( for example total 6, 9, 12, etc. ) then it isn’t a prime number. The single digit prime numbers are 1, 2, 3, 5, 7, if we ignore the convention of no longer considering 1 as a prime number. A real number which includes prime numbers are located somewhere on the x - axis. If we multiply each single digit prime number ( 1, 2, 3, 5, 7 ) by ½ we get 1 at approximately ½, 2 at approximately 1, 3 at approximately 1.5, 5 at approximately 2.5 and 7 at approximately 3.5. 1 is actually at 1, 2 at 2, 3 at 3, 5 at 4 and 7 at 5. 97 is a prime and if we multiply 97 by ½, we get 48.5. The prime 97 isn’t anywhere close to being the 48th prime. The Riemann Hypothesis says 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. Our initial calculation indicated that the prime number 97 was oscillating around position 48.5 on the x axis which isn’t correct. The Riemann Hypothesis says 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. What to do???? We know that the prime number 97 lies on the x axis as it is a specialized real number. The Riemann Hypothesis says 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. Therefore we make up a multiplier. The first digit is ½ or .5. The second digit is one of the Riemann Hypothesis zeros so we now have ( .50 ) . ( .50 ) X 97 is no better off than multiplying 97 X ( .5 ). We know that the prime numbers have 1, 3, 7, or 9 in column 0. Therefore arbitrarily add the 9 digit to ( .50 ) forming ( .509 ). If we multiply prime 97 X ( .509 ) the answer is worse. If, however, we take ( .509 ^ 2 ) we get ( .259081 ) and 97 X ( .259081 ) = 25.130857. Prime number 97 is in actuality the 26th prime. The Riemann Hypothesis says 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. Using the Riemann Hypothesis zeros between .5 and 9 ( .5----9 ) and raising it to a power we can oscillate the prime 97 around its’ position. Thus the error can be controlled by adjusting the Riemann Hypothesis zeros.
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 which equals 995.2299524. 7919 is the 1000th prime. The answer is out by approximately 5. Adjust error accordingly using Riemann Hypothesis zeros.
As a matter of interest, if we are looking for the largest prime number in existence, the simplest way of doing it is to add digits to the left of any number ending in 1, 3, 7, 9 in column zero ( 0 ). Find the total of all the digits added together and divide by 3. If the result is an integer with no remainder, it is not a prime number. This truth can be verified by seeing if the number is only evenly divisible by itself and 1. It is also interesting that any number ending in 1, 3, 7, 9, if it isn’t a prime, is usually divisible by some number ending in 1, 3, 7, 9 in column 0.
If all the zeros used for calculating the position of primes on strings are real, then the primes themselves are real. Primes can be combined to create real numbers as well as fractions, so all the zeros for those numbers are real. Therefore the Riemann Hypothesis is true.
Actual Location Primes Multiplier 2 To Power 2 Power 2 Calculated Location
1 1 0.509999999 1 0.509999999 0.509999999
2 2 0.509999999 1 0.509999999 1.019999999
3 3 0.509999999 1 0.509999999 1.529999998
4 5 0.509999999 1 0.509999999 2.549999997
5 7 0.509999999 1 0.509999999 3.569999996
6 11 0.509999999 1 0.509999999 5.609999994
7 13 0.509999999 1 0.509999999 6.629999993
8 17 0.509999999 1 0.509999999 8.669999991
9 19 0.509999999 1 0.509999999 9.68999999
10 23 0.509999999 1 0.509999999 11.72999999
11 29 0.509999999 1 0.509999999 14.78999997
12 31 0.509999999 1 0.509999999 15.80999998
13 37 0.509999999 2 0.260099999 9.623699981
14 41 0.509999999 2 0.260099999 10.66409998
15 43 0.509999999 2 0.260099999 11.18429998
16 47 0.509999999 2 0.260099999 12.22469998
17 53 0.509999999 2 0.260099999 13.78529997
18 59 0.509999999 2 0.260099999 15.34589997
19 61 0.509999999 2 0.260099999 15.86609997
20 67 0.509999999 2 0.260099999 17.42669997
21 71 0.509999999 2 0.260099999 18.46709996
22 73 0.509999999 2 0.260099999 18.98729996
23 79 0.509999999 2 0.260099999 20.54789996
24 83 0.509999999 2 0.260099999 21.58829996
25 89 0.509999999 2 0.260099999 23.14889995
26 97 0.509999999 2 0.260099999 25.22969995
The position of the primes was calculated by multiplying the primes ( 1 to 31 ) by ( .509999999 ^ 1). From ( 37 to 97 ) the primes were multiplied by ( .509999999 ^ 2 ) to keep the calculated distance close to the actual distance.
Actual Location Primes String 1 String 2 Multiplier 2 To Power 2 Power 2 Calculated Location
27 101 2 2 0.509999999 2 0.2601 26.27009995
28 103 4 4 0.509999999 2 0.2601 26.79029995
29 107 8 8 0.509999999 2 0.2601 27.83069994
30 109 10 1 0.509999999 2 0.2601 28.35089994
31 113 5 5 0.509999999 2 0.2601 29.39129994
32 127 10 1 0.509999999 2 0.2601 33.03269993
33 131 5 5 0.509999999 2 0.2601 34.07309993
34 137 11 2 0.509999999 2 0.2601 35.63369993
35 139 13 4 0.509999999 2 0.2601 36.15389993
36 149 14 5 0.509999999 2 0.2601 38.75489992
37 151 7 7 0.509999999 2 0.2601 39.27509992
38 157 13 4 0.509999999 2 0.2601 40.83569992
39 163 10 1 0.509999999 2 0.2601 42.39629992
40 167 14 5 0.509999999 2 0.2601 43.43669991
41 173 11 2 0.509999999 2 0.2601 44.99729991
42 179 17 8 0.509999999 2 0.2601 46.55789991
43 181 10 1 0.509999999 2 0.2601 47.07809991
44 191 11 2 0.500999999 2 0.251001 47.9411909
45 193 13 4 0.500999999 2 0.251001 48.4431929
46 197 17 8 0.500999999 2 0.251001 49.4471969
47 199 19 1 0.500999999 2 0.251001 49.9491989
The position of the primes was calculated by multiplying the primes ( 101 to 181 ) by (.5099999999^2) From (191 to 199 ) the primes were multiplied by ( .5009999999 ^ 2 ) to keep the calculated distance close to the actual distance.
The most important thing that Riemann said was 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 and the error term in the prime number theorem is closely related to the position of the zeros. If you multiplied the primes from ( 191 to 199 ) by ( .509999999^2 ) the answer would be further from their real locations and hence the error would be greater.
It is also interesting that by either adding or subtracting Pi or ( e^1 ) depending on what is required you can get the Riemann Zero calculation closer to the actual location of the primes.
Actual Location Calculated Location Add / Subtract Total
1 0.509999999 0 0.509999999
2 1.019999999 0 1.019999999
3 1.529999998 0 1.529999998
4 2.549999997 0 2.549999997
5 3.569999996 0 3.569999996
6 5.609999994 0 5.609999994
7 6.629999993 0 6.629999993
8 8.669999991 0 8.669999991
9 9.68999999 0 9.68999999
10 11.72999999 0 11.72999999
11 14.78999997 -3.141592654 11.64840732
12 15.80999998 -3.141592654 12.66840733
13 9.623699981 3.141592654 12.76529263
14 10.66409998 3.141592654 13.80569263
15 11.18429998 3.141592654 14.32589263
16 12.22469998 3.141592654 15.36629263
17 13.78529997 3.141592654 16.92689263
18 15.34589997 3.141592654 18.48749262
19 15.86609997 3.141592654 19.00769262
20 17.42669997 3.141592654 20.56829262
21 18.46709996 3.141592654 21.60869262
22 18.98729996 3.141592654 22.12889262
23 20.54789996 3.141592654 23.68949261
24 21.58829996 3.141592654 24.72989261
25 23.14889995 0 23.14889995
26 25.22969995 0 25.22969995
27 26.27009995 0 26.27009995
28 26.79029995 0 26.79029995
29 27.83069994 0 27.83069994
30 28.35089994 0 28.35089994
31 29.39129994 0 29.39129994
32 33.03269993 0 33.03269993
33 34.07309993 0 34.07309993
34 35.63369993 0 35.63369993
35 36.15389993 0 36.15389993
36 38.75489992 -2.718281828 36.03661809
37 39.27509992 -2.718281828 36.55681809
38 40.83569992 -2.718281828 38.11741809
39 42.39629992 -3.141592654 39.25470726
40 43.43669991 -3.141592654 40.29510726
41 44.99729991 -3.141592654 41.85570726
42 46.55789991 -3.141592654 43.41630725
43 47.07809991 -3.141592654 43.93650725
44 47.9411909 -3.141592654 44.79959825
45 48.4431929 -3.141592654 45.30160025
46 49.4471969 -3.141592654 46.30560425
47 49.9491989 -2.718281828 47.23091707
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 since ( .509999999 ) and (.599999990) both hold the same digits but the zero ( 0 ) position has been shifted thus putting the position of the primes further out of alignment. 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.
Here are some facts about prime numbers.
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. A prime number is defined as being only evenly divisible by itself and one ( 1 ).
Here’s the proof:
A prime number is defined as any number that can be only divided evenly by itself and one. Furthermore a prime number, if it is a prime number, only has the digits, 1, 3, 7, 9 in column 0 which is the farthest right column. I have also discovered that if the sum of the digits of any number ending in 1, 3, 7, 9 total a multiple of 3, except for prime number 3 ( for example total 6, 9, 12, etc. ) then it isn’t a prime number. The single digit prime numbers are 1, 2, 3, 5, 7, if we ignore the convention of no longer considering 1 as a prime number. A real number which includes prime numbers are located somewhere on the x - axis. If we multiply each single digit prime number ( 1, 2, 3, 5, 7 ) by ½ we get 1 at approximately ½, 2 at approximately 1, 3 at approximately 1.5, 5 at approximately 2.5 and 7 at approximately 3.5. 1 is actually at 1, 2 at 2, 3 at 3, 5 at 4 and 7 at 5. 97 is a prime and if we multiply 97 by ½, we get 48.5. The prime 97 isn’t anywhere close to being the 48th prime. The Riemann Hypothesis says 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. Our initial calculation indicated that the prime number 97 was oscillating around position 48.5 on the x axis which isn’t correct. The Riemann Hypothesis says 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. What to do???? We know that the prime number 97 lies on the x axis as it is a specialized real number. The Riemann Hypothesis says 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. Therefore we make up a multiplier. The first digit is ½ or .5. The second digit is one of the Riemann Hypothesis zeros so we now have ( .50 ) . ( .50 ) X 97 is no better off than multiplying 97 X ( .5 ). We know that the prime numbers have 1, 3, 7, or 9 in column 0. Therefore arbitrarily add the 9 digit to ( .50 ) forming ( .509 ). If we multiply prime 97 X ( .509 ) the answer is worse. If, however, we take ( .509 ^ 2 ) we get ( .259081 ) and 97 X ( .259081 ) = 25.130857. Prime number 97 is in actuality the 26th prime. The Riemann Hypothesis says 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. Using the Riemann Hypothesis zeros between .5 and 9 ( .5----9 ) and raising it to a power we can oscillate the prime 97 around its’ position. Thus the error can be controlled by adjusting the Riemann Hypothesis zeros.
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 which equals 995.2299524. 7919 is the 1000th prime. The answer is out by approximately 5. Adjust error accordingly using Riemann Hypothesis zeros.
As a matter of interest, if we are looking for the largest prime number in existence, the simplest way of doing it is to add digits to the left of any number ending in 1, 3, 7, 9 in column zero ( 0 ). Find the total of all the digits added together and divide by 3. If the result is an integer with no remainder, it is not a prime number. This truth can be verified by seeing if the number is only evenly divisible by itself and 1. It is also interesting that any number ending in 1, 3, 7, 9, if it isn’t a prime, is usually divisible by some number ending in 1, 3, 7, 9 in column 0.
If all the zeros used for calculating the position of primes on strings are real, then the primes themselves are real. Primes can be combined to create real numbers as well as fractions, so all the zeros for those numbers are real. Therefore the Riemann Hypothesis is true.
Actual Location Primes Multiplier 2 To Power 2 Power 2 Calculated Location
1 1 0.509999999 1 0.509999999 0.509999999
2 2 0.509999999 1 0.509999999 1.019999999
3 3 0.509999999 1 0.509999999 1.529999998
4 5 0.509999999 1 0.509999999 2.549999997
5 7 0.509999999 1 0.509999999 3.569999996
6 11 0.509999999 1 0.509999999 5.609999994
7 13 0.509999999 1 0.509999999 6.629999993
8 17 0.509999999 1 0.509999999 8.669999991
9 19 0.509999999 1 0.509999999 9.68999999
10 23 0.509999999 1 0.509999999 11.72999999
11 29 0.509999999 1 0.509999999 14.78999997
12 31 0.509999999 1 0.509999999 15.80999998
13 37 0.509999999 2 0.260099999 9.623699981
14 41 0.509999999 2 0.260099999 10.66409998
15 43 0.509999999 2 0.260099999 11.18429998
16 47 0.509999999 2 0.260099999 12.22469998
17 53 0.509999999 2 0.260099999 13.78529997
18 59 0.509999999 2 0.260099999 15.34589997
19 61 0.509999999 2 0.260099999 15.86609997
20 67 0.509999999 2 0.260099999 17.42669997
21 71 0.509999999 2 0.260099999 18.46709996
22 73 0.509999999 2 0.260099999 18.98729996
23 79 0.509999999 2 0.260099999 20.54789996
24 83 0.509999999 2 0.260099999 21.58829996
25 89 0.509999999 2 0.260099999 23.14889995
26 97 0.509999999 2 0.260099999 25.22969995
The position of the primes was calculated by multiplying the primes ( 1 to 31 ) by ( .509999999 ^ 1). From ( 37 to 97 ) the primes were multiplied by ( .509999999 ^ 2 ) to keep the calculated distance close to the actual distance.
Actual Location Primes String 1 String 2 Multiplier 2 To Power 2 Power 2 Calculated Location
27 101 2 2 0.509999999 2 0.2601 26.27009995
28 103 4 4 0.509999999 2 0.2601 26.79029995
29 107 8 8 0.509999999 2 0.2601 27.83069994
30 109 10 1 0.509999999 2 0.2601 28.35089994
31 113 5 5 0.509999999 2 0.2601 29.39129994
32 127 10 1 0.509999999 2 0.2601 33.03269993
33 131 5 5 0.509999999 2 0.2601 34.07309993
34 137 11 2 0.509999999 2 0.2601 35.63369993
35 139 13 4 0.509999999 2 0.2601 36.15389993
36 149 14 5 0.509999999 2 0.2601 38.75489992
37 151 7 7 0.509999999 2 0.2601 39.27509992
38 157 13 4 0.509999999 2 0.2601 40.83569992
39 163 10 1 0.509999999 2 0.2601 42.39629992
40 167 14 5 0.509999999 2 0.2601 43.43669991
41 173 11 2 0.509999999 2 0.2601 44.99729991
42 179 17 8 0.509999999 2 0.2601 46.55789991
43 181 10 1 0.509999999 2 0.2601 47.07809991
44 191 11 2 0.500999999 2 0.251001 47.9411909
45 193 13 4 0.500999999 2 0.251001 48.4431929
46 197 17 8 0.500999999 2 0.251001 49.4471969
47 199 19 1 0.500999999 2 0.251001 49.9491989
The position of the primes was calculated by multiplying the primes ( 101 to 181 ) by (.5099999999^2) From (191 to 199 ) the primes were multiplied by ( .5009999999 ^ 2 ) to keep the calculated distance close to the actual distance.
The most important thing that Riemann said was 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 and the error term in the prime number theorem is closely related to the position of the zeros. If you multiplied the primes from ( 191 to 199 ) by ( .509999999^2 ) the answer would be further from their real locations and hence the error would be greater.
It is also interesting that by either adding or subtracting Pi or ( e^1 ) depending on what is required you can get the Riemann Zero calculation closer to the actual location of the primes.
Actual Location Calculated Location Add / Subtract Total
1 0.509999999 0 0.509999999
2 1.019999999 0 1.019999999
3 1.529999998 0 1.529999998
4 2.549999997 0 2.549999997
5 3.569999996 0 3.569999996
6 5.609999994 0 5.609999994
7 6.629999993 0 6.629999993
8 8.669999991 0 8.669999991
9 9.68999999 0 9.68999999
10 11.72999999 0 11.72999999
11 14.78999997 -3.141592654 11.64840732
12 15.80999998 -3.141592654 12.66840733
13 9.623699981 3.141592654 12.76529263
14 10.66409998 3.141592654 13.80569263
15 11.18429998 3.141592654 14.32589263
16 12.22469998 3.141592654 15.36629263
17 13.78529997 3.141592654 16.92689263
18 15.34589997 3.141592654 18.48749262
19 15.86609997 3.141592654 19.00769262
20 17.42669997 3.141592654 20.56829262
21 18.46709996 3.141592654 21.60869262
22 18.98729996 3.141592654 22.12889262
23 20.54789996 3.141592654 23.68949261
24 21.58829996 3.141592654 24.72989261
25 23.14889995 0 23.14889995
26 25.22969995 0 25.22969995
27 26.27009995 0 26.27009995
28 26.79029995 0 26.79029995
29 27.83069994 0 27.83069994
30 28.35089994 0 28.35089994
31 29.39129994 0 29.39129994
32 33.03269993 0 33.03269993
33 34.07309993 0 34.07309993
34 35.63369993 0 35.63369993
35 36.15389993 0 36.15389993
36 38.75489992 -2.718281828 36.03661809
37 39.27509992 -2.718281828 36.55681809
38 40.83569992 -2.718281828 38.11741809
39 42.39629992 -3.141592654 39.25470726
40 43.43669991 -3.141592654 40.29510726
41 44.99729991 -3.141592654 41.85570726
42 46.55789991 -3.141592654 43.41630725
43 47.07809991 -3.141592654 43.93650725
44 47.9411909 -3.141592654 44.79959825
45 48.4431929 -3.141592654 45.30160025
46 49.4471969 -3.141592654 46.30560425
47 49.9491989 -2.718281828 47.23091707
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 since ( .509999999 ) and (.599999990) both hold the same digits but the zero ( 0 ) position has been shifted thus putting the position of the primes further out of alignment. 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.
Wednesday, January 07, 2009
Largest Prime Number
If you want to wile away an afternoon, try finding the largest prime number. For those that may have forgotten, a prime number is a number that is only evenly divisible by itself and 1. This definition eliminates all the even numbers that are evenly divisible by 2, leaving the odd numbers. The usual method of finding a prime number is to multiply 2 umpteen dozen times by itself and then subtracting 1 from that number, thereby creating an odd number (( 2 X 2 = 4), ( 4 - 1 = 3 )). You then take that odd number ( 3 ) and see if you can find a previous whole number up to 3, ( 1, 2, ) which will divide into it evenly leaving no remainder. There is a faster method. Numbers are written into a series of columns. Number 13 has 3 in column 0 and 1 in column 1. You will soon realize that any larger number can be easily created by adding another column For instance 3, 13, 213 etc.. It can also be seen that the total number of numbers is infinite because you just keep putting a number from 0 to 9 inclusive in the column to the left of a filled column.
Here are some rules:
A prime number, if it is a prime number , ends in 1, 3 , 7, 9 in column 0 ( far right column ). For instance 11, 13, 17, 19 are all prime numbers.
Any number whose digits, except for number 3, adds to 3 or an even multiple of 3 isn’t a prime number. For instance 39 isn’t a prime number because its’ digits ( 3 and 9 ) total 12 ( 3 + 9 = 12 ). ( 12/ 3 = 4 ).
A number, not a prime number, ending in 1, 3, 7, 9 in column 0 ( far right column ) is only evenly divisible by a number ending in 1, 3, 7, 9 in column 0 ( far right column ). For instance 39 is evenly divisible by 3 and 13 ( 3 X 13 = 39 ).
Here are some rules:
A prime number, if it is a prime number , ends in 1, 3 , 7, 9 in column 0 ( far right column ). For instance 11, 13, 17, 19 are all prime numbers.
Any number whose digits, except for number 3, adds to 3 or an even multiple of 3 isn’t a prime number. For instance 39 isn’t a prime number because its’ digits ( 3 and 9 ) total 12 ( 3 + 9 = 12 ). ( 12/ 3 = 4 ).
A number, not a prime number, ending in 1, 3, 7, 9 in column 0 ( far right column ) is only evenly divisible by a number ending in 1, 3, 7, 9 in column 0 ( far right column ). For instance 39 is evenly divisible by 3 and 13 ( 3 X 13 = 39 ).
Saturday, November 22, 2008
Primes & The Riemann Hypothesis
Here’s how Primes and The Riemann Hypothesis are connected. If you write down all the primes from 1 to 97 you will find there are 26 of them. All numbers are basically a connected string so you can use String Mathematics on them. Riemann said that all the zeros of his zeta function lay on the line ( y = ½ ). It turns out that the fraction ½ in the equation ( y = ½ ) can be used to estimate the location of any prime in a prime list. The single digit string primes are ( 1, 2, 3, 5, 7 ). If you multiply the single digit primes ( 1, 2, 3, 5, 7 ) by ½ you get the approximate location of these primes in a list of primes. The two digit string primes start at 11 and go to 97. Here it gets trickier because not all numbers ending in 1, 3, 7, 9 in column zero ( the far right column ) are primes. Two digit string primes have two digits. In estimating the location of two digit primes sometimes you multiply the two digit prime by ½ and sometimes by ( ½ X ½ ). If you use string mathematics to solve the Riemann Hypothesis the limit of the sum is (0.258363501). If you multiply the limit of the sum ((0.258363501) X 97) you get 25 in round numbers and 97 is the 26th prime. The square root of the limit of the sum (0.258363501) is ( .508 ) to three digits. If you use ( .508 ) in your calculations of the location of the primes ( 1 to 97 ) you will find your answer is generally closer to the real position in the list. ( 7919 ) is the 1000th prime. Using string mathematics you will see the number of string digits in ( 7919 ) is 4. In this particular case you multiply (½) 3 times to get an answer close to 1000 ( 7919 X .5 X .5 X .5 = 989.875 ). Multiplying ( .508 ) 3 X gives ( 1038 ) but using String Mathematics add a zero between 5 and 8 giving ( .5008 ). ( 7919 X (.5008 X .5008 X .5008 ) = 994.63 ) which is about 5 short of 1000 which is more accurate than multiplying ( 7919 X .5 X .5 X .5 ) = 989.875) The calculation of the location of any prime probably involves the adjustment of zeros (0) in (.508) and then deciding how many times you should multiply the revised figure ( for example (.5008 ) before multiplying it with the suspected prime number ending in 1, 3, 7, 9.
The general approach is possibly the following:
(.508 ) multiplied twice for primes 2 to 3 digits in width since there is an overlap in 3 digit prime numbers.
(.5008 ) multiplied three times for primes 3 to 4 digits in width ( see 7919 example ) since there is an overlap in 4 digit prime numbers.
( .50008 ) multiplied 4 times for primes 4 - 5 digits in width since there is an overlap in 5 digit prime numbers.
( .5 ) multiplied a number of times equal to one ( 1 ) less than the number of digits will give you a rough position ( ex. 7919 has 4 digits, so multiply ( .5 ) 3 times since ( 4 - 1 = 3 ).
Here’s the explanation:
The location of the real part of the not obvious or unseen zeros ( 0 ) is exactly ½ in the equation ( y = ½ ), since the number of primes in this region are denser, so the formula gives a relatively precise location. As the primes spread out, multiplying with ( .5 ) and the not obvious zeros ( .50000 etc. ) becomes increasingly inaccurate, so the obvious zeros ( 0 ) have to be added between (.5 ) and ( .008 ) to form numbers that are less close to ½. ( .508, .5008, .50008, etc. ). If the primes did not spread themselves in comparison to the other numbers you wouldn’t have to spread the obvious zeros ( 0 ) between (.5) and (.008). The not obvious zeros ( 0 ) lie on the vertical complex plane because they aren’t required for the real calculation. Therefore it can be said that the positive zeros ( 0 ) lie on the complex plane on one side of the real line ( y = ½ ) and the negative zeros ( - 0 ) lie on the other side of ( y = ½ ) on the complex plane vertical to ( y = ½ )
Using String Mathematics, the Riemann Hypothesis can be resolved like this:
The universe consists of particles / objects, strings and frames. Each object or particle has a string attached to it which we may call a tail, trail, or highway as well as anything else. Most strings do not have a location unless you state a formula such as ( y = 2 ) or ( y = ½ ). A string is a total of the object’s digits. For instance 97 has a string total of ( 9 + 7 = 16 ) or ( 9 + 7 = 16, 1 + 6 = 7 ). Therefore, as an example, 97 has two strings which are 16 and 7. The formula ( y = 2 ) has a string value of 2 and a particle / object value of 2. Here’s the solution to Riemann’s Hypothesis using string mathematics. Riemann said that all the zeros of his zeta function lie on the line ( y = ½ ) as the result of summing. In the formula ( y = 2 ), the string holds an infinity of numbers providing their sum doesn’t exceed 2. These numbers can be created by adding zeros to a number ( 101, 1001, etc. ). The string can also hold the number 2 and 11 since ( 1 + 1 = 2 ).
Here’s a condensed version of the Riemann Hypothesis proof based on string mathematics and the conversion of ( y = 2 ) to ( y = ½ ) :
1. Write down the number 2 which represents both the string length of number 2 and number 2 itself.
2. Write down the number 11 since ( 1 + 1 = 2 ) and the string length of number 2 is still intact.
3. Put a series of zeros between the two 1’s creating numbers 101, 1001, 10001, ----- 100000001. ( the string length of number 2 is still intact ).
4. Write the fractions ½, 1/11, 1/101, 1/1001, 1/1001, ------ 1/100000001.
5. Raise each fraction to the power of 2 ( this is the value of the string / tail and not the number 2 ).
6. Sum the fractions to the power of string / tail value 2.
7. Depending on the power of your calculator / spreadsheet / perseverance, the limit or convergence will be around (0.258363501).
So what??? When you were doing your calculation involving the zeros between the "1" digits ( 101, 1001, etc. ) you were actually using the string / tail values in the string which was attached to the mathematical value of 2 which was on the line ( y = 2 ). When you wrote the fractions, you were converting the line ( y = 2 ) to the line ( y = ½ ). The summation of the fractions ( ½, 1/11, 1/ 101, etc. ) produced the limit of (0.258363501). The zeros never left the string / tail when the line was converted and therefore the Riemann Hypothesis is proved using string mathematics. The same principle applies to any other equation converted to its’ reciprocal. The zeros can be placed anywhere to make a number in the string .
The general approach is possibly the following:
(.508 ) multiplied twice for primes 2 to 3 digits in width since there is an overlap in 3 digit prime numbers.
(.5008 ) multiplied three times for primes 3 to 4 digits in width ( see 7919 example ) since there is an overlap in 4 digit prime numbers.
( .50008 ) multiplied 4 times for primes 4 - 5 digits in width since there is an overlap in 5 digit prime numbers.
( .5 ) multiplied a number of times equal to one ( 1 ) less than the number of digits will give you a rough position ( ex. 7919 has 4 digits, so multiply ( .5 ) 3 times since ( 4 - 1 = 3 ).
Here’s the explanation:
The location of the real part of the not obvious or unseen zeros ( 0 ) is exactly ½ in the equation ( y = ½ ), since the number of primes in this region are denser, so the formula gives a relatively precise location. As the primes spread out, multiplying with ( .5 ) and the not obvious zeros ( .50000 etc. ) becomes increasingly inaccurate, so the obvious zeros ( 0 ) have to be added between (.5 ) and ( .008 ) to form numbers that are less close to ½. ( .508, .5008, .50008, etc. ). If the primes did not spread themselves in comparison to the other numbers you wouldn’t have to spread the obvious zeros ( 0 ) between (.5) and (.008). The not obvious zeros ( 0 ) lie on the vertical complex plane because they aren’t required for the real calculation. Therefore it can be said that the positive zeros ( 0 ) lie on the complex plane on one side of the real line ( y = ½ ) and the negative zeros ( - 0 ) lie on the other side of ( y = ½ ) on the complex plane vertical to ( y = ½ )
Using String Mathematics, the Riemann Hypothesis can be resolved like this:
The universe consists of particles / objects, strings and frames. Each object or particle has a string attached to it which we may call a tail, trail, or highway as well as anything else. Most strings do not have a location unless you state a formula such as ( y = 2 ) or ( y = ½ ). A string is a total of the object’s digits. For instance 97 has a string total of ( 9 + 7 = 16 ) or ( 9 + 7 = 16, 1 + 6 = 7 ). Therefore, as an example, 97 has two strings which are 16 and 7. The formula ( y = 2 ) has a string value of 2 and a particle / object value of 2. Here’s the solution to Riemann’s Hypothesis using string mathematics. Riemann said that all the zeros of his zeta function lie on the line ( y = ½ ) as the result of summing. In the formula ( y = 2 ), the string holds an infinity of numbers providing their sum doesn’t exceed 2. These numbers can be created by adding zeros to a number ( 101, 1001, etc. ). The string can also hold the number 2 and 11 since ( 1 + 1 = 2 ).
Here’s a condensed version of the Riemann Hypothesis proof based on string mathematics and the conversion of ( y = 2 ) to ( y = ½ ) :
1. Write down the number 2 which represents both the string length of number 2 and number 2 itself.
2. Write down the number 11 since ( 1 + 1 = 2 ) and the string length of number 2 is still intact.
3. Put a series of zeros between the two 1’s creating numbers 101, 1001, 10001, ----- 100000001. ( the string length of number 2 is still intact ).
4. Write the fractions ½, 1/11, 1/101, 1/1001, 1/1001, ------ 1/100000001.
5. Raise each fraction to the power of 2 ( this is the value of the string / tail and not the number 2 ).
6. Sum the fractions to the power of string / tail value 2.
7. Depending on the power of your calculator / spreadsheet / perseverance, the limit or convergence will be around (0.258363501).
So what??? When you were doing your calculation involving the zeros between the "1" digits ( 101, 1001, etc. ) you were actually using the string / tail values in the string which was attached to the mathematical value of 2 which was on the line ( y = 2 ). When you wrote the fractions, you were converting the line ( y = 2 ) to the line ( y = ½ ). The summation of the fractions ( ½, 1/11, 1/ 101, etc. ) produced the limit of (0.258363501). The zeros never left the string / tail when the line was converted and therefore the Riemann Hypothesis is proved using string mathematics. The same principle applies to any other equation converted to its’ reciprocal. The zeros can be placed anywhere to make a number in the string .
Tuesday, November 11, 2008
Prime Secrets
1. Primes are defined as any number that can only be divided evenly by itself and 1.
2. Primes end in 1, 3, 7, 9 in column "0" ( far right column ).
3. Not all numbers ending in 1, 3, 7, 9 are prime numbers.
4. Numbers that aren’t prime numbers but end in 1, 3, 7, 9 are evenly divisible by some number ending in 1, 3, 7, 9 in column "0" ( far right column ).
5. Except for the prime number 3, any number ending in 1, 3, 7, 9, say (39), when their digits are totaled ( 3 + 9 = 12 ) are not a prime if the total of their digits can be evenly divided by 3 ( 3 + 9 = 12) ( 12 / 3 = 4 ) ( 39 / 13 = 3 ).
6. The number of primes preceding a prime number can be approximated by first taking a prime number, say (7919), and counting all its’ digits. Prime number ( 7919 ) has 4 digits ( 7,9,1,9 = 4 digits ). The other method is to count all of the prime’s digits and subtract (1). Prime number ( 7919 ) has 4 digits and subtracting ( 1 ) leaves 3 digits. Prime number ( 7919 ) has 4 digits ( 7, 9, 1, 9 = 4 digits ), and subtracting (1) leaves ( 4 - 1 = 3 ) digits. Next take the total number of its’ digits or the total number of its’ digits minus 1 and multiple the prime ((7919) X (½ ^ 4) = 494.94) or ((7919) X (½ ^ 3) = 989.88). Since it’s unlikely that 7919 only has approximately 494 primes behind it, the likelier answer is around 989. Add 2, 4, 6, 8, 10 to 989 to get a closer approximate number. In this case add 10. ( 989.88 + 10 = 999.88 ). 7919 is the 1000th prime according to the tables. The approximation requires some obvious juggling but if you apply points 1 to 5 to the approximation you will come close to a probable answer.
2. Primes end in 1, 3, 7, 9 in column "0" ( far right column ).
3. Not all numbers ending in 1, 3, 7, 9 are prime numbers.
4. Numbers that aren’t prime numbers but end in 1, 3, 7, 9 are evenly divisible by some number ending in 1, 3, 7, 9 in column "0" ( far right column ).
5. Except for the prime number 3, any number ending in 1, 3, 7, 9, say (39), when their digits are totaled ( 3 + 9 = 12 ) are not a prime if the total of their digits can be evenly divided by 3 ( 3 + 9 = 12) ( 12 / 3 = 4 ) ( 39 / 13 = 3 ).
6. The number of primes preceding a prime number can be approximated by first taking a prime number, say (7919), and counting all its’ digits. Prime number ( 7919 ) has 4 digits ( 7,9,1,9 = 4 digits ). The other method is to count all of the prime’s digits and subtract (1). Prime number ( 7919 ) has 4 digits and subtracting ( 1 ) leaves 3 digits. Prime number ( 7919 ) has 4 digits ( 7, 9, 1, 9 = 4 digits ), and subtracting (1) leaves ( 4 - 1 = 3 ) digits. Next take the total number of its’ digits or the total number of its’ digits minus 1 and multiple the prime ((7919) X (½ ^ 4) = 494.94) or ((7919) X (½ ^ 3) = 989.88). Since it’s unlikely that 7919 only has approximately 494 primes behind it, the likelier answer is around 989. Add 2, 4, 6, 8, 10 to 989 to get a closer approximate number. In this case add 10. ( 989.88 + 10 = 999.88 ). 7919 is the 1000th prime according to the tables. The approximation requires some obvious juggling but if you apply points 1 to 5 to the approximation you will come close to a probable answer.
Friday, December 14, 2007
How Many Primes Precede------???
One of the things that drive mathematicians crazy is trying to figure out how many prime numbers precede a number. For example if you look up a table of Prime Numbers you will find Prime Number 7919 is the 1000th Prime Number. A prime number is defined as any number that can only be divided evenly by itself and 1. This means that if you suspect a number is a prime then you have to divide it by all the numbers that precede it to see if any number divides into it evenly. The current way of finding the number of Primes preceding any number is by taking the number (7919 for instance) and dividing it by its’ LN or the Log of the Natural Number. The LN or Log of the Natural Number (7919) is (8.977020214). For those of you that don’t have a clue what I’m talking about LN or the Log of the Natural Number (2.718281828) is the number of times that the Natural Number (2.718281828) has to be multiplied by itself to create (7919) which is our present example. Naturally, (2.718281828), doesn’t always multiply by itself evenly to create the number which you want so hence the fraction ( 977020214). I have discovered another way which appears to be consistently closer to the number of primes up to any chosen random number. If you take a look at a list of prime numbers you will discover that, excluding the single digit primes, 1, 2, 3, 5, 7, the far right column of primes end in 1, 3, 7 or 9 once you get to primes of more than one digit. As an example, the following two digit numbers (11, 13, 17, 19) are all primes. Unfortunately, you will soon realize that all numbers ending in 1, 3, 7, 9 aren’t prime numbers. For instance, 21, 33, 27, 39 aren’t prime numbers because each one is divisible evenly by 3. Crazy as it may seem, there is a neat way to get it almost right. I don’t know why it works this way but it seems to be related to chance. You know if you flip a coin it will come up on average over time and many flips as 50% heads or 50% tails. The same principle seems to apply to prime numbers on average. For instance 7919 has 4 digits ( 7, 9, 1, 9 ). Therefore you multiply 7919 by ½ or .5, 3 X. ( 7919 X .5 = 3959.5, 3959.5 X .5 =1979.75, 1979.75 X .5 = 989.875 ) is almost 990 or 10 short of 1000. The secret of how many times to multiply by ½ or .5 is to count the number of digits ( 4 are in 7919 (7, 9, 1, 9 ) and subtract 1 from the total ( 4 - 1 = 3 ). To add to the fun, prime numbers aren’t evenly spaced so for more accuracy choose any arbitrary number ending in 1, 3, 7, 9 in the end column as that arbitrary number may itself be a prime number!!!
If you want to be even more accurate follow these rules for choosing the original number ( 7919 for example )
Prime Numbers have the numerals 1, 3, 7, 9 in their farthest right column which eliminates a lot of numbers that you might think are primes. So choose a number ending in 1, 3, 7, 9.
Not all numbers having 1, 3, 7, 9 in their farthest right column are Prime Numbers, but these numbers can be divided evenly by numbers ending in 1, 3, 7, 9 in the far right column ( 21, 33, 27, 39 ). Try dividing your number by numbers ending in 1, 3, 7, 9 to see if your number is a Prime.
Except for Prime Number 3, the sum of the digits of Prime Numbers never total 3 or multiples of 3. ( 21, 33, 27, 39 ). Add the digits in your chosen number to see of those numbers are divisible by 3. For instance the digits of 69 ( 6 + 9 = 15 ) are divisible evenly by 3 ( 15 / 3 = 5 ). Therefore you know it isn’t a Prime Number.
If you are still curious 7919 / LN (7919) or 7919 / 8.977020214 comes to 882.1412686 or 882 in round figures. 882 is 118 primes short of 1000 which is the number of primes before and including 7919 which is also a prime. My method 7919 X .5 X .5 X.5 = 989.875 or in round figures 990 which is 10 short of the true number of 1,000 or 9 short if you want to think of 999 primes before 7919 which is also a Prime.
If you want to be even more accurate follow these rules for choosing the original number ( 7919 for example )
Prime Numbers have the numerals 1, 3, 7, 9 in their farthest right column which eliminates a lot of numbers that you might think are primes. So choose a number ending in 1, 3, 7, 9.
Not all numbers having 1, 3, 7, 9 in their farthest right column are Prime Numbers, but these numbers can be divided evenly by numbers ending in 1, 3, 7, 9 in the far right column ( 21, 33, 27, 39 ). Try dividing your number by numbers ending in 1, 3, 7, 9 to see if your number is a Prime.
Except for Prime Number 3, the sum of the digits of Prime Numbers never total 3 or multiples of 3. ( 21, 33, 27, 39 ). Add the digits in your chosen number to see of those numbers are divisible by 3. For instance the digits of 69 ( 6 + 9 = 15 ) are divisible evenly by 3 ( 15 / 3 = 5 ). Therefore you know it isn’t a Prime Number.
If you are still curious 7919 / LN (7919) or 7919 / 8.977020214 comes to 882.1412686 or 882 in round figures. 882 is 118 primes short of 1000 which is the number of primes before and including 7919 which is also a prime. My method 7919 X .5 X .5 X.5 = 989.875 or in round figures 990 which is 10 short of the true number of 1,000 or 9 short if you want to think of 999 primes before 7919 which is also a Prime.
Friday, December 07, 2007
Weird Spread
One of the things that drive people nuts that enjoy puzzles are Primes. Primes are any number that can be divided evenly by only itself and 1. If you ever look at a Table Of Primes, you will see they seem to have a pattern but there isn’t any readily recognizable rhyme or reason to it. Logically, you would think that the spaces that would separate Primes would be even or at the most not far off even. Here’s what I mean. The simplest Primes are the single digits 1, 2, 3, 5, 7. Looks relatively simple to me, but the larger the numbers, the more the Primes’ locations seem to be completely disorganized. Since Primes are defined as numbers divisible by themselves and 1 you can eliminate some numbers immediately. Two (2) divides evenly into any number that has 0, 2, 4, 6, 8 in the far right column ( 10, 12, 24, 36, 48, for example ). Five (5) is the only other number that divides evenly into any number that has 5 or 0 in the far right column (125, 155, 175 ), ( 120, 150, 180). The remaining prime numbers are 1, 3, 7. They may or may not divide evenly into any number that has a 1, 3, 7 in the far right column. The only other number not discussed is 9 which isn’t a prime number because it’s divisible by 3 ( 9 / 3 = 3 ) Weird as it is, you will find that the numbers 1, 3, 7, and 9 are in the farthest right column of Prime Numbers. For example, ( 11, 13, 17, 19 ) are all Prime Numbers. If you divide any number ending in 1, 3, 7, 9 in the far right column into any number ending in ( 1, 3, 7, 9 ) in the far right column sometimes it divides evenly which means that particular number that ends in ( 1, 3, 7, 9 ) isn’t a Prime Number, For example, ( 21, 33, 27, 39 ) are all divisible by 3. You will see that the Prime Number locations would now start to spread out because not all numbers ending in ( 1, 3, 7, 9 ) in the far right column are only divisible by themselves and 1. The final randomizer is due to the fact that, except for single digit prime number 3, the total of the digits forming a Prime number ending in 1, 3, 7, 9, will never total 3 or a multiple of 3. For instance 69 is not a Prime because its’ digits 6 and 9 total 15 which is divisible evenly by 3. ( 69, 6 + 9 = 15, 15 / 3 = 5 ).
So, in summary, randomizing occurs because:
Prime Numbers have 1, 3, 7, 9 in their farthest right column leaving spaces of 1, 2, multiples of 2 or even odd or even powers of 2 between Prime Numbers.
Not all numbers having 1, 3, 7, 9 in their farthest right column are Prime Numbers ( 21, 33, 27, 39 ).
Except for Prime Number 3, the sum of the digits of Prime Numbers never total 3 or multiples of 3. ( 21, 33, 27, 39 )
So, in summary, randomizing occurs because:
Prime Numbers have 1, 3, 7, 9 in their farthest right column leaving spaces of 1, 2, multiples of 2 or even odd or even powers of 2 between Prime Numbers.
Not all numbers having 1, 3, 7, 9 in their farthest right column are Prime Numbers ( 21, 33, 27, 39 ).
Except for Prime Number 3, the sum of the digits of Prime Numbers never total 3 or multiples of 3. ( 21, 33, 27, 39 )
Sunday, November 18, 2007
Oh, Incidentally, Primes In Patterns!!!
1. A Prime Number is defined as any number that can only be divided evenly by itself and 1. One digit Primes are 1, 2, 3, 5, 7 since they can only be divided evenly by 1 and themselves. .
2. A Prime Number, if it is a Prime Number, has 1, 3, 7, 9 in its’ far right column. (11, 13, 17, 19) are all Primes since they can only be divided by 1 and themselves..
3. Except for single digit prime number 3 ( see 1.), if you add the digits forming a prime number ending in 1, 3, 7, 9, a prime number’s digits will never total 3 or be a multiple of 3. For instance 69 is not a Prime because its’ digits 6 and 9 total 15 which is divisible evenly by 3. ( 69, 6 + 9 = 15, 15 / 3 = 5 ).
More Confusion:
1. Not all numbers having 1, 3, 7, 9 in their far right column are Prime Numbers. ( 21, 33, 27, 39 ) are all divisible by 3 (My lazy example). The rule is divisible by any old number except 1, since 1 never changes the number it’s dividing. The total of their digits ( 3, 6, 9 12 ) are all divisible by 3 ( see 3, last section ).
2.A number which ends in 1, 3, 7, 9 and isn’t a prime, is divisible by a number ending in 1, 3, 7, or 9 in its’ first column ( 469, 469 / 7 = 67, 7909, 7909 / 11 = 719 ).
2. A Prime Number, if it is a Prime Number, has 1, 3, 7, 9 in its’ far right column. (11, 13, 17, 19) are all Primes since they can only be divided by 1 and themselves..
3. Except for single digit prime number 3 ( see 1.), if you add the digits forming a prime number ending in 1, 3, 7, 9, a prime number’s digits will never total 3 or be a multiple of 3. For instance 69 is not a Prime because its’ digits 6 and 9 total 15 which is divisible evenly by 3. ( 69, 6 + 9 = 15, 15 / 3 = 5 ).
More Confusion:
1. Not all numbers having 1, 3, 7, 9 in their far right column are Prime Numbers. ( 21, 33, 27, 39 ) are all divisible by 3 (My lazy example). The rule is divisible by any old number except 1, since 1 never changes the number it’s dividing. The total of their digits ( 3, 6, 9 12 ) are all divisible by 3 ( see 3, last section ).
2.A number which ends in 1, 3, 7, 9 and isn’t a prime, is divisible by a number ending in 1, 3, 7, or 9 in its’ first column ( 469, 469 / 7 = 67, 7909, 7909 / 11 = 719 ).
Saturday, October 13, 2007
Well Jar My Preserves!!!
The Count was right in Sesame Street when he said " This Universe is being brought to you by the number 3!!!". Here are 3 things that are all you need to know about numbers including Primes. For you excitable types, that have been driven dippy about Primes read 2 first!!!
1. Numbers ending in 2, 4, 6, 8 in the far right column ( 22, 34, 56, 48, etc. ) are all divisible by 2.
2. Numbers ending in 1, 3, 7, 9 in the far right column ( 11, 21,13, 33, 17, 27, 19, 49 ) may or may not be divisible by numbers ending in 1, 3, 7, 9. If they are not divisible by numbers ending in 1, 3, 7, 9 in the far right column they are Prime Numbers, which are only divisible by themselves and 1.
3. Numbers ending in 0 and 5 in the far right column ( 30, 40, 35, 45, etc. ) are always divisible by 5.
1. Numbers ending in 2, 4, 6, 8 in the far right column ( 22, 34, 56, 48, etc. ) are all divisible by 2.
2. Numbers ending in 1, 3, 7, 9 in the far right column ( 11, 21,13, 33, 17, 27, 19, 49 ) may or may not be divisible by numbers ending in 1, 3, 7, 9. If they are not divisible by numbers ending in 1, 3, 7, 9 in the far right column they are Prime Numbers, which are only divisible by themselves and 1.
3. Numbers ending in 0 and 5 in the far right column ( 30, 40, 35, 45, etc. ) are always divisible by 5.
Thursday, September 13, 2007
Weird Numbers
The world is full of weird things like numbers. A prime number is any number that can only be divided by itself and 1. The single digit prime numbers are 1, 2, 3, 5, 7 as they can only be divided by themselves and 1. 1 will divide evenly into any number odd or even. 2 will only divide into even numbers such as 0, 2, 4, 6, 8 in the first column (10, 12, 14, 16, 18). 5 will divide evenly into any number ending in 0 or 5 in the first column like 40 or 25. 3 will not always divide evenly into any number from 1 to 9 in the first column.. For instance 3 will divide evenly into 33 but not 43. 7 will not always divide evenly into any number that has numbers from 1 to 9 in the first column. 7 will divide evenly into 7 but not 47. There are 5 one column prime numbers. ( 1, 2, 3, 5, 7 ). If you go to two column prime numbers ( 11, 13, 17, 19 ) you will see that 1, 3, and 7 are all prime numbers in the first column but 9 ( 3 X 3 ) isn’t a prime number. You will soon discover that this pattern follows in the first column for all prime numbers. In other words if a number is a prime it will end in 1, 3, 7 or 9 in the first column. The rub, of course, is not all numbers ending in 1, 3, 7 or 9 are prime numbers. 21, 33, 27, 39 aren’t prime numbers.
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