Prime factorization using double slit experiment from Young

1. Prime factorization using double-slit experiment
Chris De Corte
chrisdecorte@yahoo.com
KAIZY BVBA
Beekveldstraat 22
9300 Aalst, Belgium
26 November 2013
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2. The goal of this document is to open up a discussion whether any physics experiments can
be set up to split up composite numbers.
For the time being the following are mainly theoretical experiments showing the relationship
between primes and composites.
The paper is still a draft version and might be revised.
A
This is my first L TEX experience ...
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3. CONTENTS
CONTENTS
Contents
1 Double slit interference
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2 Prime factorization formula
4
3 Comparing composite and prime frequencies
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4 Example
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5 Conclusion
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A Other experiments
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B references
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4. 2
PRIME FACTORIZATION FORMULA
In the next chapters, we will work out the prime factorization using double-slit experiment.
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Double slit interference
In the next picture, we summarize the experiment of Young with regard to the double slit
interference. Our pattern will have a top at y = 0 and in general for:
y=
mλD
mD
=
d
fd
(1)
In formula 1, we replaced the wavelength λ with 1/f , f being the frequency.
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Prime factorization formula
The general formula to write a composite number using its prime components is as follows:
k
n = p α1 p α2 · · · p αk =
1 2
k
p αi
i
(2)
i=1
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5. 5
CONCLUSION
To work more easily in this document, we will use an easier version of the above formula to
find the first divisor as follows:
fc = f1 .f2
(3)
In the above formula we deliberately replaced already the n and p with f being the frequency.
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Comparing composite and prime frequencies
Writing out formula (1) for fc and f1 , we get:
yc =
mc Dc
fc dc
(4)
y1 =
m1 D1
f1 d1
(5)
and:
When we target a maximum of the first prime frequency on the same spot as a maximum of
the composite frequency, we get:
y1 = yc
(6)
Which results in:
m1 D1 dc
f1 = fc
mc Dc d1
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(7)
Example
We worked out an example below though many different scenario’s would be possible:
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Conclusion
Prime factorization using double-slit experiment is an interesting theoretical subject.
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6. A
A
OTHER EXPERIMENTS
Other experiments
The double-slit experiment is probably only an example. Other experiments could be worked
out with same results. Example(s): on the standing waves of a guitar we can clearly see that
the 6th harmonic is a composite of the second and third harmonic.
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7. B
REFERENCES
Another example is using Wolfram Alpha. In the next example we show how one might try to
find the primes of the number 59531327 by checking if the function sin(P i ∗ 59531327/x)2 +
0.1 ∗ abs(sin(P i ∗ x)) has zero roots between 1 and 59531326:
B
references
• http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html
• http://en.wikipedia.org/wiki/Double-slite xperimenthttp : //en.wikipedia.org/wiki/F undamentalt heo
• http://www.wolframalpha.com
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