Number theory, citation 2103.0181
Instantly Factorize Any Product Of
Two Small Or Large Twin Prime Numbers.
Simple Method -
72 is the constant integer used in the process to find repeated addition in the
series.
First Step –
Repeated Addition Series.
Following the steps ask your colleague to add 72 and 36 as show below.
72 * 1 = 72 + 36 = 108
72 * 2 = 144 + 36 = 180
72 * 3 = 216 + 36 = 252
72 * 4 = 288 + 36 = 324 ......... 'Last Sum Of Series'
Counting can be done as many times like 72 *5 , 72 * 6, 72 * 7 ........ and
one time adding 36 for each series.
Series can go up to infinity.
Last sum of series is 324.
Second Step -
Finding ‘r ‘ Total Sum Of Series -
Ask your colleague to add all the sums together with number 35 to get total
sum of series ' r ' as shown below.
108+ 180 + 252 + 324 + 35 = 899 ...... 35 is the constant to be
added at last in total sum of series each time you calculate this series.
Here we get r = 899
Now get this two information from your colleague .
1) Last sum of series ie 324.
2) Total sum of series ie 899 .
You should know this to calculate the formula.
Therefore,
Ask your colleague to show the last sum of series i.e 324 and the total sum of
series i.e 899.
Note - Total sum of series is also a product of some two twin prime numbers
or prime number and composite number or may be of two composite
numbers.
So 899 is the product of p*q = 899 which we don’t know yet and we are going
to factorize it to know p & q using formula explained below.
Third step -
Now, ask your colleague that, 'Can they immediately guess what is the
multiple factors of given total sum of series is, without factorizing ?'
Answer for your colleague must be 'no', since no one can easily guess or
reverse the p * q = n if the ''n ' is any large integer.
But wait, using my new researched method you can factor in few minutes, no
matter what large integer 'n' is.
So without showing your colleague, calculate the process explained below.
Calculation Process – Finding ‘s’.
There are two method to find ' s ’.
1) First method -
Notice the above 'repeated 72 series', those bold highlighted integers 72 * 1,
72 * 2, 72 * 3, 72 * 4 ........
Series of Integers in line i.e 1,2, 3, 4.....
Find the last integer i.e 4
Substitute 4 with 0 of 0.83 (constant).
We get 4.83
Therefore, s = 4.83.
Each time you calculate to find ' s’ always find the last integer in the line as
explained above.
2) Second Method -
You know that last sum of series is 324. ( you got the information from
your colleague)
Taking 324 / 72 = 4.5
Get the left hand side integer before the decimal point i.e 4.
Substitute 4 with 0 of 0.83 (constant).
As per second method, we get s = 4.83
Next,
Apply the ‘r’ and ‘s’ in the below formula.
r / s = m
m/ 6 = n
Where,
‘r’ is the total sum of series.
‘s’ in this case is the substitution of 4 with 0 of 0.83 constant to get as 4.83.
6 is the constant in the formula.
We got r = 899, s = 4.83
Finding ' m ' -
r / s = m
899 / 4.83 = 186.12836....
Notice integer on the left hand side before the decimal point i.e 186
So, consider only those integers as ' m ' and ignore integers on the right
hand side of decimal point.
Therefore, m = 186
Finding ' n ' -
m / 6 = n
186 / 6 = 31
n = 31 ....... is the answer.
Check it dividing 899 by 31.
899/ 31 = 29
So the factors of 899 is 31, 29.
Immediately show the answer to your colleague.
One can surprise their colleague with this method.
This method works even for factorizing any larger product of multiplied twin primes. One can try checking.
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Could you give me some tips to solve it? Thanks in advance.
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Tina here. This is my first ever post on such a forum and would apologise in advance for my lack of formal clarity and perhaps very amateurish presentation etc.
But I have a burgeoning interest in the beautiful mystery and potential of mathematics and reason in general.
And would love that anyone might direct me in my latest field of curiosity, which is....well...."things to do with primes."
I may not be able to formalise my question very well....as intimated....and do understand in general that people often may not even be sure what they are asking..
But here goes....
Consider, if you would.....the number 2*3*5*7*11*13*17*19*23 = 223092870 ( the product of the first 9 primes).. Call this number: N
Firstly. Am I correct in assuming that there are 3*5*9*11*15*17*21 pairs of numbers which can be summed to make N, where neither is divisible by any of the primes which make its product? Call that X
If so....what is the mathematical reference to this fact? Is this related to both the Chinese Number Theorem and something called Euler's totient? (yes...I am a bit of a math noob, but I will learn)
Secondly: Is it the case that there is also the same number of numbers X which are also divisible by 2? Call this XE
I am mainly interested in how to determine how many pairs XE, are also divisible by some other number, such as 29 or 16 for example.....
What is the math for predicting that kind of thing?
Thank you so much in advance for you tolerance of this relative intrusion into a formalised world with a less than formal approach and presentation.
Tina
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Campanelle: No hints for this one, good luck.
Casarecce/Gemelli: The only difference between them is the topographic helical pitch. Cavalieri's principle is more than likely at play here, but you might have to use it a bit differently.
But what if you had a moving vector field? For instance, let's say you had the centre of some galaxy, about which all the stars around it were orbiting, moving through space. Obviously in the reference frame that is that moving galaxy, the velocity of that centre is zero. But in some external reference frame not moving parallel to that galaxy, that centre is not zero. Does there have to be some other point in that galaxy, then, at which the velocity is zero in the other reference frame, or is there some means by which literally no point in that galaxy has a zero point?
Not sure whether this is better suited to the math or physics board; thought I'd put it here since I assume chemistry and geology have used for the math of rotational dynamics as well.
]]>He talks about R as relating a term to its successive term in a sequence - using the sum of first "n" odd numbers equaling n^2 as an example.
I'm not sure how he defines "R" to start with in this example.
Then introduces R^{xn}, which relates a sequence of numbers together??
I'm not sure if I'm reading his notation correctly.
Any input on this passage would be helpful.
There is link to the book below.
http://strangebeautiful.com/other-texts/russell-anal-matter.pdf
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Thank you in advance to those who will respond
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(Did the math on that it works to make a perfect circle)
2. a 45 degree angle or C can be found by starting at the top corner of quadrant 4 and bottom corner of quadrant 2 and having C be crossing (0,0), so a and b are doubled. Then you can get the other diagonal through 3 and 1 quadrants using the same formula for a curve, now you have 3 dimensions and 2 angled slices of a sphere that cross at 4 points
3. We need them to cross at 8 points because we want to put 8 more spheres around the first one, we want 8 more spheres because of the fact that the dividend between the formula for the volume of sphere over the same formula only with r halved will always yield 8 meaning 8 spheres can surround one sphere in twice the volume without any of the radii crossing but only a maximum of 8
4. So you need 4 more diagonals at 4 45/2 degree angles between the two 45 degree diagonals, these 6 3D slices of the sphere that are angled will intersect at 8 points: these points can be changed by changing the viewing angle of the whole sphere longitudinally using (x-x/2, y) for quandrant 1. These points can be calculated where two slices have the same value using the lateral transformations (x-x/n, y+y/n) for quadrant 1.
5. These 8 new spheres are either closer to you than the original or further away, depth, we express this using y2=y1-y1/r over x2=x1-x1/r where r=C/2 all for quadrant 1.
The instructions I gave for the coordinates of those spheres don't become connected to "various physical phenomena and equations" until gravitons are introduced. Which were tricky to put in there, because they are created by the collapse of the spheres into each other and therefore produce a net drag on them and each other much like particles. A system like the universe can naturally comes into form.
Actually doing the math for gravitons in that way however was tricky. When we said that the x and y parameters of an outside sphere was x2=x1-x1/r (for the spheres touching the inner one at it's back half as opposed to it's front half) where r=C(pythagorean for quadrant 1 of the first sphere)/2 we were saying the radii of the outer sphere and inner sphere were touching. Keep in mind we are always starting at the centeral sphere which is why when we put spheres around a single outer layer of 9 we only need the two diagonal discs to create for points where there are 32 more spheres in front and 32 more in back relative to the original central sphere we started with.
When we take the form y2=y1-2y1/r we are placing the center of an outer sphere at the radial surface of the inner sphere. When this happens one of the discs of an outer sphere & one in the inner sphere are the same x & y values at 2 points (found using lateral transformations), top & bottom.
Saying top is x2, y2 and bottom is x1,y1 if where stacking in the quadrant 1 direction the center for your graviton is found with (y2+y1)/2 and (x2+x1)/2 and the length of your x and y coordinates in it's first quadrant is also found by finding the average of the height and width of quad 1 for the two spheres that are crossing through one another.
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Thanks in advance.
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Is a Fourier transform of a real function is still always real? I suppose the idea is that the imaginary component decays to 0 as you take the integral from -infinity to infinity so that it evaluates to a single finite real number, or actually, does the output of a the Fourier transform of a real valued function need to be real? Why do I generally see absolute value arguments in proving well-defined properties if complex functions have even more possible they can take? If you take an absolute value that only tells you anything about the magnitude of uncountably infinite numbers.
]]>If Obj1 have weight X_{1}=0.7 from Method1 and weight Y_{1}=0.5 from Method2
similarly, Obj2 have weight X_{2}=0.5 from Method 1 and weight Y_{2}=0.7 from method2
My objective is to Rank the obj1 and Obj2 according to there weight values determined from Method1 and Method2.
Can anyone help me to tell the defined mathematical formula to get the,
Rank of Obj1 = ?
Rank of Obj2= ?
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\[ f''(x) = \frac{f(x+2dx) -2(f+dx) + f(x)}{(dx)^2} \]
I am using a finite difference approximation called "Second order forward" from the link, I use dx instead of h:
https://en.wikipedia.org/wiki/Finite_difference#Higher-order_differences
]]>frac{1}{8\sqrt{2}\cos{\frac{\phi-\phi_0}{2}}(1-\sin{\frac{\phi-\phi_0}{2}})\sqrt{1-\sin{\frac{\phi-\phi_0}{2}}}} = \frac{1}{[1+\cos{(\phi-\phi_0)}]^2}.
\begin{equation}
\frac{1}{8\sqrt{2}\cos{\frac{\phi-\phi_0}{2}}(1-\sin{\frac{\phi-\phi_0}{2}})\sqrt{1-\sin{\frac{\phi-\phi_0}{2}}}} = \frac{1}{[1+\cos{(\phi-\phi_0)}]^2}.
\end{equation}
I have checked the two functions by numerical calculation to a graph and see that two functions give exactly the same shape with the $\phi\leq \pi$ as shown in the figure.
\begin{figure}[!t]
\centering
\includegraphics[scale=1]{Nonuniform-ka20-E.eps}
\caption{Comparison between two functions}
\end{figure}
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I am trying to read a research paper: PrivateJobMatch: A Privacy-Oriented Deferred Multi-Match Recommender System for Stable Employment :
https://faculty.ucmerced.edu/frusu/Papers/Conference/2019-recsys-private-job-match.pdf
QuoteIn this paper, we introduce PrivateJobMatch
(Figure 2) – a privacy-oriented deferred multi-match recommender
system – which generates stable pairings (candidate, job description),
rather than recommendations that are best-fit for individual
candidates/employers. PrivateJobMatch combines the flexibility of
decentralized markets with the wise pairing of centralized matching
by adapting DAA into a recommender system that generates a
ranked list of candidates for employers – and vice-versa – in the
order of expected match quality.
On one hand it says:
Quotewhich generates stable pairings (candidate, job description), rather than recommendations
And on the other hand it says:
Quotewith the wise pairing of centralized matching by adapting DAA into a recommender system
I feel the above two views are conflicting because on one side it says that PrivateJobMatch does not generate recommendations and on the other hand, it says, it is adapting DAA into recommender system.
I can't understand how PrivateJobMatch utilizes the features of decntralized markets.
Somebody please guide me.
Zulfi.
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