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Rudin
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15 Oct 2015, 6:51 pm

Today I was bored so I decided to find interesting properties of the number 23.

I found this property:

23^2=529
23x32=736

If you take the digital sum you'll get 16, in both cases.

23 has the property that if you multiply it by it's digital inverse and square it and then add the digits for both of those, it'll be the same number.

Post a number with an interesting property.


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18 Oct 2015, 1:45 am

The first one that came to mind: 2+2=2x2=2².



Rudin
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18 Oct 2015, 7:31 am

All numbers are interesting. So you just have to pick any number and find an interesting property.

I really hate the number 6.

But 6 is a perfect number. If you add up the factors of six you'll get,

1+2+3+6=12=2x6

In some definitions the factor, 6, is left out.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Rudin
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18 Oct 2015, 7:49 am

This number is a really awesome number. If you take this number to the power of 3^n for some n (if the Riemann Hypothesis is true) and then you round it to the nearest whole positive integer, it will always be a prime.

Here is the sequence:

2, 11, 1361, 2521008887, 16022236204009818131831320183, 4113101149215104800030529537915953170486139623539759933135949994882770404074832568499

Mill's constant=1.3063778838630806904686144926026057129167845851567136443680537599664340537668...


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Rudin
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18 Oct 2015, 7:53 am

Also, if you take the 3^n-th root of the prime generating by that sequence, it tends to Mill's constant.

Evaluate the 81st root of 2521008887 and you'll see what I mean.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


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18 Oct 2015, 8:19 am

Rudin wrote:
This number is a really awesome number. If you take this number to the power of 3^n for some n (if the Riemann Hypothesis is true) and then you round it to the nearest whole positive integer, it will always be a prime.

Here is the sequence:

2, 11, 1361, 2521008887, 16022236204009818131831320183, 4113101149215104800030529537915953170486139623539759933135949994882770404074832568499

Mill's constant=1.3063778838630806904686144926026057129167845851567136443680537599664340537668...


Greek to me!

But the sixth in the sequence contains the number "1492" (when Columbus sailed the ocean blue). So thats kinda funky. :D



Rudin
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18 Oct 2015, 9:28 am

2015 (this year) is the mean of the first 77 squares.

2015=(1^2+2^2+...+77^2)/77


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


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18 Oct 2015, 9:43 am

I find it interesting that every number has infinitely many digits after the point.
1.0000000000... has the same after-digit lengh as pi, we just assume that 1 is 1.0 with infinitely many 0s and not necissarily think about it.



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18 Oct 2015, 9:54 am

Rudin wrote:

Post a number with an interesting property.


495: The street address of my new home. A property. Get it?. :D



Rudin
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18 Oct 2015, 9:55 am

Marvin_the_Martian wrote:
Rudin wrote:

Post a number with an interesting property.


495: The street address of my new home. A property. Get it?. :D


Yes, I get it.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


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18 Oct 2015, 10:09 am

Rudin wrote:
Marvin_the_Martian wrote:
Rudin wrote:

Post a number with an interesting property.


495: The street address of my new home. A property. Get it?. :D


Yes, I get it.


"Jokes" are always funnier when people end up by "explaining" them.



naturalplastic
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18 Oct 2015, 10:42 am

So ...if 495 is your "property" that would mean that 495 is an example of real estate.

So that would mean that the square root of negative 495 would be "imaginary estate".



Rudin
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18 Oct 2015, 10:57 am

naturalplastic wrote:
So ...if 495 is your "property" that would mean that 495 is an example of real estate.

So that would mean that the square root of negative 495 would be "imaginary estate".


I like that joke, quite funny.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


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18 Oct 2015, 11:00 am

91

91 can be expressed as the sum of two cubes (integers) in two different ways.

91= 6^3 + (−5)^3 = 4^3 + 3^3


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


Rudin
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18 Oct 2015, 11:03 am

Not only that. But 91=1+7+2+9 and 1729 is another number that can be expressed as the sum of two cubes in two different ways.

1729=1^3+12^3=9^3+10^3

Also, if you multiply 91 by it's digital inverse (19) it will be 1729.

91x19=1729

That is just really amazing!


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider


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18 Oct 2015, 11:06 am

1729 is also the product of three distinct primes (sphenic number).

It is also a Carmichael number. Meaning it is an exception to Fermat's primality test. Watch Numberphile for an explanation.


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"God may not play dice with the universe, but something strange is going on with prime numbers."

-Paul Erdos

"There are two types of cryptography in this world: cryptography that will stop your kid sister from looking at your files, and cryptography that will stop major governments from reading your files."

-Bruce Schneider