quantaum mathematics chapter 9 : oscillating number 130

Chapter 9  oscillating number

as you know about indium function which is a additivie function

ex:  i(10)=i(5)+i(2)=p(5)+p(2)=11+3=14

now if you repeatedly apply then you get a prime number after it goes on incresing. for example

i(38)=i(19)+i(2)=67+3=70

i(i(38))=i(70)=i(7)+i(5)+i(2)=17+11+3=31=i^2(38)

i( i(i(38)))=i(31)=127

after applying it the number keep on increasing but there are certain numbers in which it don't happen

such numbers are called oscillating number

i^n(m)=m 

then m is oscillating number n is natural number also n is called frequency. first oscillating number is 130 in which frequency is 7.

                                                        

i(130)=i(2)+i(5)+i(13)=3+11+41=55

i^2(130)=i(55)=i(5)+i(11)=42

i^3(130)=i(42)=i(7)+i(2)+i(3)=17+3+5=25

i^4(130)=i(25)=2*i(5)=2*11=22

i^5(130)=i(22)=i(11)+i(2)=34

i^6(130)=i(34)=i(17)+i(2)=62

i^7(130)=i(62)=i(31)+i(2)=130

also number that occurs are also oscillating for example

22,25,34,42,55,62  are partially oscillating number with 130

quantaum mathematics Chapter 8 uses of helium function

Chapter 8 Uses of helium Function

there is a lot of uses of helium function in solving prime numbers

1. first use is that it could be use to find the total number of distinct prime factors a number has using euler's totient function.
   

   
2. second use is about finding the number of primes between x(x+1) and (x+1)(x+2), i had found that number of primes between the the given range is equal to h(x(x+1)). it could be further be generalized to x(x+1)+1 and (x+1)(x+2)+1 because the the single value of helium function is almost constant or variation is very slow.
3. third use is in measuring the randomness of prime numbers, it could also be generalized for natural numbers.
   

randomness of prime graph is

it is interesting to note that natural number upto 12 have zero randomness. and the first randomness is found in natural number 13 of unit randomness also unit of randomness is chanchal which itself means randomness.

you can see the variation of blue line and red line .
4. helium function could be used to find the group number of primes.
h(n)=2h+1  n belongs to h group of prime if n is  replaced by 10^m then it is very useful.

quantaum mathematics chapter 7 uses of Random functions

Chapter 7     Uses Of Random Functions

in this chapter you will find about the various uses of random functions.

7.1 uses of The God Function 

1.  used in super conjecture,numerology is fully based on  the god function
2. some properties of god function are , if d(n)=n then n will be prime exception 4
3. it could used to produce random euler's number as

4. d(n) is related to pi as follows

there might be an error please verify it

5. it could be used to calculate the nth term of prime precisely
      n=z*d(pn-1)
113=p(30)
30=2*(d(112))
there exit many kind of above different formulas formulas
6. there are many numbers in which god function becomes equal to 

Quantaum mathematics Chapter 6:quantaum prime conjecture

Chapter 6 The Quantaum Prime conjecture

prime gap is connected to geo function here is what i founded

interesting prime density is itself govern by prime gap itself.

quantaum mathematics chapter 5 : quantaum nth term of prime

Chapter 5 Quantaum nth term of prime

using random function we could find the nth term of prime precisely and accurately also.

to find nth term precisely i had found these formulas

calculating nth term using helium function accurately

calculating nth term Precisely using Random Functions

calculating Nth term of prime using minimum operator and prime gap, also using infinity

note that d(3!)=d(3)+d(2)+d(1)

similarly for others

Quantaum Mathematics: Chapter 4 quantaum geometry

Chapter 4 The Quantaum Geometry

this chapter deals with quantaum geometry.

what quantaum geometry really is?

quantaum geometry is a special kind of co-ordinate geometry in which numbers are replaced with random numbers,on any of the axis.

Types of quantaum plane

m*b^0=m     if  this is satisfied on all 3 axis then it is 3-3 D plane. it is useful in describing the motion of planets to the atom.random number do not exit on any axis.

m*b^m  it will have many but finite value . on the basis of this 3 kind of co-ordinate exit

• 2-3 D plane in which 1 axis has random number plotted on it.
• 1-3 D plane in which 2 axis has random number plotted on it.
• 0-3 D plane in which all 3 axis has random number plotted on it.

Uses of Quantaum Geometry

in near by future we will face many kind of particle and thier random functions, in that case quantaum geometry will be helpful in understanding their random function. i am making few predictions of the use of quantaum geometry.

• electron motion could be understand in 2-3 D plane.
• bosons,photons,etc could be understand in 1-3 D plane.
• the ultimate particle, if exit could be understand in 0-3 D plane

the point of coincident is that at below the minimum label randomness exit , it is also shown in the nature,
in nature atom is the minimum and below minimum that is electron motion random .

 

quantaum mathematics chapter 3 : the theory of minimum

Chapter 3 The theory of Minimum

in this chapter i will prove that randomness exit below the minimum , same as that of atomic level.

the minimum operator

the minimum conjecture:

 it states that if we decrease any number below minimum value then it will behave as a random number.

proof 

so, one thing is proved that below the minimum randomness exist.

Quantaum Mathematics: Chapter 2 : Random Functions in detail

Chapter 2  Random Functions in detail

let's describe random functions in detail, there are only three random functions which do not use prime directly. a list is provided which about random functions and their uses.

• God Function:the name is god because play a very important role in numerology.also has relation with primes,Bernoulli's number.
• Helium Function:it's uses are many, counting number of distinct prime factor we need this, relation to prime,used in producing minium number of a number
• Geo function: small version of god function related as d(n)=g_0*G(n).just like permutations connects combinatorics.used to calculate atomic weight of element,has relation with prime gap.

1.God Function

2.Helium function

3. Geo Function

in next xhapter we gone describe the concept of minimum.

• 
  

The Quantaum Mathematics: Chapter 1 Introduction

                              The Quantaum Mathematics

introduction to quantaum mathematics

to deal with random function, to study algebra of random number, i had developed the quantaum mathematics there is a similarity between quantaum physics.

• in quantaum physics , classical physics laws are not applicable.same as that of quantaum mathematics in which the property of addition , subtraction is not govern by the classical mathematics
• in quantaum physics we deal with the probability of finding an electron in a given region.same that of quantaum mathematics,we deal with probability of addittion,subtraction in random numbers.
• the word quantaum means a fixed energy packet.same as that of quantaum mathematics, we deal with fixed property of random numbers.

yet, there is many things we correlate between quantaum physics and quantaum mathematics.
there is also a new kind of geometry which i call the quantaum geometry.
in next chapter we gone form the basic law of quantaum mathematics.  

Chapter 7 The Prime Gap

Chapter 7 The Prime Gap

following property i had observed

1.  prime gap of primes could be improved

here is one that i have founded.

i=sqrt(-1)

2. maximum repetation of difference of primes in a group is govern by the formula

h(h+1)/2, also which difference occur most could be calculated as

h+1      for h is odd

h+2      for h is even

careful with one exception in group 2

 

Chapter-6 Fibonnaci form of prime

Chapter 6   The Fibonnaci Form of prime

there is a large connection between fibonnaci numbers and prime numbers.
I had founded it devote this discovery to the discover of this sequence,fibonacci

The Fibonnaci form of prime

also i am providing a more useful result

Chapter -1 summary of nth term of prime

Chapter -1  summary of nth term of prime

as we are going back ward that is why chapter -1.
so far we have discussed the two kind of formula for nth prime.theyare

Euclidean form of prime

Euler's form of Prime

o is omicron
in next chapter we gone describe about two more form of primes.

Chapter 5 More Random Functions

Chapter 5  More Random Functions

as you know that random functions are those functions which could not be differentiated. but they have many uses.
let us build some random function using primes.

If    y= p^a*q^b          p ,q   are   prime   then

 I(y)=ap(p)+bp(q)             this  is indium  function   used  in finding the oscillating number.

J(y) = ap^(-1)p+bp^(-1)(q)     this  is  j-function.


sorry about latex hope that you understand. p^(-1)  means p inverse . just like inverse of a function exist.
graph of indium function

graph of j-function

 in next chapter we will deal with the uses of this functions and also extend the  theory of randomness.

Chapter 4 : Random Functions

Chapter 4  Random Functions

you know about what is random number and random function. all random function are logarithmic in nature because we are performing an operation on natural numbers.

2.1 Properties of random function

1. Every random function is logarithmic function with a random base.

2. When any number is divided by 0 it becomes the universal set of random numbers having range (-∞,+∞) .

3. Property of logarithmic are applied in random function.

4.d(1),G(1),h(1),i(1),j(1) have different values..

5. Random numbers have different value for a fixed number but have finite value.

6. Random number-random number≠0 . it don't obey the law of mathematics so it is also called
quantaum mathematics.

 

2.2 GOD function

Let a random number b be defined as    bp=p     where p is prime, and range of b is 1<b≤33 .

Also    d(y) = logb(y)

In simple words if y = p^a*q^b           where p, q are prime   then

  d(y)= a*p+q*b

Graph of god function

2.3 Helium function

Let a random number b_0  be define as

           p=b_0*(p-1)       Having range 1<b_0≤2     and    h(y) = logb_0y

Graph of helium function

2.4    Geo function

Let a random number g0 ,having range from 2≤g0<∞     and it is related to prime as

           g_0∈{2,3,5,7,…}                                              G(y) = logg_0y

Graph of  geo function

If   y = p^a*q^b             where   p , q are prime  then

G(y) = a+b   also    d(y)=g0 G(y)

there are more random function which i will discuss later.