A Brief Proof of the Riemann Hypothesis, Giving Infinite Results. Item Total Pages

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1 A Brief Proof of the Riemann Hypothesis, Giving Infinite Results Item 42 We will also show a positive proof of Fermat s Last Theorem, also related to the construction of the universe. 9 Total Pages 1

2 A Brief Proof of the Riemann Hypothesis, Giving Infinite Results There is a function that applies to all prime numbers starting with 11, that helps to solve the Riemann Hypothesis. Finding patterns of prime numbers, as all prime numbers reduced to a single integer by addition will become one of these 6 integers 1, 2, 4, 5, 7, or 8 from 1/7 through 6/7. We will use the real Pi, 201/64, as a decimal , to construct an infinite continued fraction, related to all of our countable numbers in rotation 1, 2, 3 that includes primes. The smallest part of 201/64 is 1/64, so that 64 becomes our denominator and our countable numbers in rotation 1, 2, 3 and so on, will be our numerators. Our numerators are also counted as whole numbers reduced to single integers by addition giving us all odd numbers and primes in rotation. When our prime numbers make the transformation to single integers by addition, they leave us with an infinite set of zeros of the Zeta function. Our results for our numerators, 1 through 9 will be the same as our numerators. Example 2(prime) = 2/64 = = 11 = 2, the same result. For our first reducible prime we have 11 = 2, for our matching result from our infinite fraction of 11/64, we also have 11/64 = = 29 = 11 = 2. Our next prime is 13, so that 13 reduced to a single integer by addition gives us 13 = 4, then from our infinite fraction we have 13/64 = = 13 = 4. For our prime 17, 17 = 8, then for our decimal 17/64 = = 26 = 8. The same integers. Also, our prime 19 = 10 = 1. For our decimal result, 19/64 = = 37 = 10 = 1. The same integers. Our end results will always have two corresponding results, for both primes and decimals, as well as our countable numbers. When we reach whole numbers, they are also counted in our results, for Pi we have 201 = 3, then 201/64 = = 21 = 3. When we complete each set in rotation we will obtain infinite repeating sets of 1 through 9, for our whole number application. All even number numerators can reduce to their lowest terms like our single integer 2, that would give us 2/64 = 1/32, while the decimal remains the same. If we change the numerator, we would lose the relativity of numbers, destroying our proof. So then, for the Riemann Hypothesis, we don t reduce even numbers to their lowest term, we use the first even number divided by 64. I have proven that the present day calculation for Pi is invalid, and along with that proof that the real Pi is 201/64, as a decimal

3 In the proof from Wikipedia that Pi is irrational they state that any continued fraction that is infinite is irrational. We can see from this work, that the statement that they made is invalid. They present 6 proofs that Pi is irrational. One proof was that Pi squared is irrational, how do you square a never ending, never repeating decimal? However, you can square the real Pi. If you go through their 6 proofs and use the real Pi in each case where they show Pi, you will prove their 6 proofs invalid. The continued fraction that I show gives us infinite sets of numerators over denominators, that is related to our infinite count of numbers 1, 2, 3 and so on that also includes primes for as long as you want to do so. Now, we will give a short list of our continued fraction. A. B. C. D. 1/ = 19 = 10 = 1 2/ = 11 = 2 2 3/ = 30 = 3 3 4/ = 13 = 4 5/ = 23 = 5 5 6/ = 24 = 6 7/ = 25 = 7 7 8/ = 8 9/ = 18 = 9 10/ = 19 = 10 = 1 11/ = 29 = 11 = 2 11= 2 12/ = 21 = 3 13/ = 13 = 4 13 = 4 14/ = 23 = 5 15/ = 24 = 6 16/64.25 = 7 17/ = 26 = 8 17 = 8 18/ = 18 = 9 19/ = 37 = 10 = 1 19 = 10 = 1 20/ = 11 = 2 = 2 A. is part of our continued fractions. B. is our decimals from our continued fractions. 3

4 C. is our decimals reduced to a single integer by addition. D. is a list of our primes from C. reduced to a single integer by addition. If we carry our decimal point over to our result of C. we would have 4.5 for each total set of 9 decimals. Our numerators of A. are also counted as whole numbers 1, 2, 3 that gives us all odd numbers and primes in rotation, an infinite process that also gives us C. When we reduce our numerators of A. that are prime, they will match our end results of our primes of D., so that we will have infinite corresponding results of prime numbers reduced to a single integer by addition, related to our end result of our infinite continued decimals reduced to single integers by addition (B., C., and D.) that are the same giving us infinite patterns of integers related to prime numbers. Our end result is that we have infinite repeating sets of integers 1 through 9 of (C.), so that we can know that our results are infinite. Also, when we reduce our numerators of A. to a single integer by addition, we will have two infinite repeating sets of 1 through 9 in A. and C. There are 3 ways that we can construct the zeros of the zero function. However here, we deleted the zeros of the Zeta function. We can produce them, and also delete them. P Versus NP Our complete set, for as long as we want to go is NP. Our first set of 1 through 9 is P. Although P is a part of NP, it is not equal to NP, as P is finite. What to Look for in the Riemann Hypothesis and Zeta Function Shown Next We will show twin primes that have application to our dual constructed universe, as well as producing the zeros of the Riemann Zeta Function, from the even numbers between our twin primes. Each even number between our dual primes will be evenly dividable by both 3 and 6, an infinite process for every set of twin primes. When we will reduce our twin prime sets in rotation to single integers by addition we will make the transformation from set (1) to set (2) where columns (A) and (C) will give us infinite time integers, from 1/7 through 6/7, infinite time integers of 1, 2, 4, 5, 7, and 8, that total 27, 3 cubed, related to the 27 faces of our Poincare One Geometry, as well as the lowest state for inflated bosons, (27 GeV) where they produced protons and neutrons for the mass structure of our universe. 4

5 Column (A) of set (2) will contain 2, 5, and 8. Then column (C) will contain 1, 4, and 7, column (B) will give us 3, 6, and 9 accounting for all of our Quantum integers. 3, 6, and 9 when multiplied gives us 162, the 162 outcomes of our probability models B, C, D, E, and F. That gives us the geometry and mass structure of our universe constructed in transit, by our 2 different directions of time. The Riemann Hypothesis and Zeta Function Twin Primes Set (1) A B C Pattern of the Primes Set (2) A B C Quantum Math (Q.M) - reducing numbers to single integers by addition. Results of Set (1) shown in Set (2) with Q.M. = 9 = 18 = 9 = 18 = 9,, = 45 = 9 PRIMES TOTAL: 17 = 8 (time integers) = 27 The only 3 outcomes for A & C of Set (2) A C INTEGERS TOTAL: 27 = 9 PRIMES TOTAL: 14 = 5 5

6 Two Infinite Sets For Set (1) the columns of A and C are primes 2 numbers apart. Column B is the numbers between the 2 primes. If we add any line of numbers together for Set (1) then apply Q.M. (reducing to a single integer by addition) our results will be 9. Then, if we add the individual integers of the lines for A, B, C, and apply Q.M. the result will also be 9. Thus, giving two corresponding results. Dual numbers have application to our dual constructed universe 14, 17, 18, 27, and 45, see M-Theory Parts 1, 2, and 3. 3 and 6 of set (2) represent 5 dimensions and 5 forces and 9 represents the velocity for the construction of the universe related to the even numbers of column B, set (1) that makes the transformation to 3, 6, and 9 of column B, set (2). Set 2 is quternions (sets of 3) horizontal. Vertical applications are octonions, both have infinite applications, just like our twin primes. For The Columns of Set (2) The columns of Set (2) are the results of where we applied Q.M. to the numbers of Set (1). All prime numbers reduced to a single integer, by addition become one of 6 time integers 1, 2, 4, 5, 7, and 8 related to 1/7 and 6/7, negative and positive time. A and C columns are from the prime columns of Set (1), where the Q.M. results for each line for the primes for Set (2) gives one of only 3 results 1 4, 5 7, or 8 1. As = 6, then = 12 = 3, and = 9, gives us the integers of Set (2) Column B 3, 6, and 9. Each even number in B will be evenly dividable by both 3 and 6 of Set (2) Column B, an infinite process as 3 and 6 represent 5 dimensions and 5 forces. Each 9 of Set (2) Column B will divide into the number that produced it, in set one Column B. As 18 is dividable by 9, likewise with 72, 108, 270, and so on. The integer 9 represents the velocity for the construction of the universe. All prime numbers reduced to a single integer by addition will give us one of these six time integers 1, 2, 4, 5, 7, and 8, from 1/7 and 6/7, infinite repeating sets of 6 time integers, as in Set (2). Column A and C we have 2, 5, and 8 and 1, 4, and 7. Our B Column of Set One Produces the Zeros of the Riemann Zeta Function From our B column of even numbers between our two primes we are minus one to our first twin prime, and plus one to our second twin prime, so that we have minus one and plus one, giving us the zeros of the Zeta function for every set of twin primes, an infinite process. We can produce them and also delete them. 6

7 3, 6, and 9 of set (2) column (B) came from column (B) of set (1) and represent even numbers that are related to primes numbers. On page 3 our (C) result gave us an infinite repeating set of 1 through 9 where each set totaled 45, our infinite time integers 1, 2, 4, 5, 7, and 8 gave us 27, so that we have the application of 3/5 and 2/5. We have shown that 3 and 6 are 5 dimensional numbers, this is why our infinite set of even numbers of set (1) column (B) will always be evenly dividable by 3 and 6, an infinite process. We now want to show by just 3 sets how even numbers are related to twin primes, another infinite process. A. B. C. D. E. F /36 = 2/3.666 infinite /54 = 2/3.666 infinite /90 = 2/3.666 infinite Columns B, and D, are primes, columns A, C, and E are even numbers related to primes. F gives us the totals for each line, primes 24 and even numbers 36, for our first line, to get our ratio set of 2/3. The totals of even numbers for each line will always be evenly divided by 3, 6, and 9, an infinite process related to all sets of twin primes. Twin primes applications of 5 sets represents five dimensions and 5 forces. For even numbers related to all single odd numbers and primes like 23, as 23 gives us 22, 23, 24, so that our ratio is 23/46 = ½, the infinite ½ parts of the Zeta function. Here is where Fermat s Last Theorem shows up, as there, we are minus 1/3, giving us our infinite ratio of 2/3, shown here. In our Poincare One Geometry we have 3 vertical time lines, where our central time line represents the ½ line from both the left and right side vertical lines. Our central time line represents the real Zeta Function, as we can both construct and delete the zero s of the Zeta Function. From Fermat s Last Theorem we have 2 positive sets of 81, that corresponds to the 162 outcomes of our probability models B, C, D, E, and F that were produced from our probability model A, M-Theory that gave us both the mass structure and our Poincare One Geometry of our universe. 81 is also mass of the w+ and w- particles in GeV that can be found at plus or minus 2, the w+ and w- break up into 3 sets of 27 GeV, the lowest state for Bosons. 7

8 They claim that the Higgs Field Mass is 126 GeV, however, it can t produce the mass of the top quark of 174 GeV. We show the Higgs Field Mass to be 189 GeV that totals 18-9, related to the velocity integer 9, our fifth force. The real Pi is proven by Geometry, see Item 41. Back to P Versus NP We have shown that NP infinite, and that P is finite, our first set. So then, how is it related to the universe? Our total of the first set (P) is 45, related to our Poincare One Geometry that gives us the mass location for our dual constructed universe, where we have 12 sphere lines, 6 for each half of the universe. Then we have 22 wave structure lines on the surface of our 2 spheres. That gives us 34 curved lines, plus our 11 (straight) time lines that gives us our total of 45. The total of our infinite time integers is 27, that corresponds to the 27 faces of our Poincare One Geometry. 27 is also the lowest state of inflated Bosons, where they produced protons and neutrons, for the mass structure of our universe. Then we have our total of prime numbers of 17 for our first set of (P) that gives us the 17 curved lines of constructions for each ½ of our network structure parts of our Poincare One Geometry, of 10 points, (black holes) 34 curved lines, and 25 faces for our total of 69. With Quantum Math forming dual fractions we have 69 = 6/9 = 2/3, infinite. Galaxies lie on our 3 dimensional wave structure lines, giving us the yang-mills mass gap for the construction of our universe. For our Poincare One Geometry, see M-Theory part one. A Positive Proof for Fermat s Last Theorem Fermat s last theorem states that X N +Y N =Z N, has no non-zero solutions for N, when N is greater than 2. There are hundreds of pages of mathematics that prove that Fermat s last theorem is true. That proof is accepted by most everyone in mathematics, it s long and complicated. Is it possible that it could be incorrect? Yes it is. 8

9 We are going to use a real physical experiment to show a positive proof for Fermat s last theorem. We are going to use 81 coins (pennies) as this result can break up into other applicable math results. 81 coins give us 3 4. Here we have 3 results, 81 heads, 81 tails and 81 coins, so that we have a 2 to 1 ratio between 81 heads, and 81 tails on 81 coins, all three are 3 4. Now, we have 81 heads, + 81 tails, divided by 2, for our 2 to 1 ratio, that gives us =3 4. Each part; heads, tails, and coins, are 1/3 each. The numbers involved are 81, and is heads and tails, and 81 is coins. See Fermat s proof that 3 4, is impossible. A lot of mathematics was constructed, thinking that his proof was correct. Who would ever accept a non-complicated result, on just one page. This also solves the A, B, C, Conjecture, Beals Conjecture, as well as the 1/3, 2/3 Conjecture. New for Algebra We can use the same integers if their representations are all distinctly different, as in this case heads, tails, and coins. They are different, yet equal, like our results. We go forward in time by multiplication of Pi to get every circumference length. Then backwards from times direction by dividing by Pi ( ) that can be applied to our countable numbers 1, 2, 3... in rotation. So then, does it terminate, or is it infinite. Although we can show what prime numbers are related to, there may not be a pattern for finding the prime numbers, as other odd numbers can also end in one of our 6 integers 1, 2, 4, 5, 7, or is also the lowest state for inflated Bosons where they produced protons and neutrons for the mass structure of our universe. 3, 6, and 9 also represent even numbers related to prime numbers. Richard Eicholtz October 5,

Item 8. Constructing the Square Area of Two Proving No Irrationals. 6 Total Pages

Item 8. Constructing the Square Area of Two Proving No Irrationals. 6 Total Pages Item 8 Constructing the Square Area of Two Proving No Irrationals 6 Total Pages 1 2 We want to start with Pi. How Geometry Proves No Irrations They call Pi the ratio of the circumference of a circle to