
Sexy prime - lelf
https://en.wikipedia.org/wiki/Sexy_prime
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azhenley
Numberphile video on sexy primes:
[https://youtu.be/WJ12DYBuazY](https://youtu.be/WJ12DYBuazY)

This is one of my favorite youtube channels. They make videos on various math
topics that are understandable by laypeople.

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jakobegger
Is there any practical use to these classifications? It seems to me that lager
primes are distributed more or less randomly, so I don't really see the point
of looking for constellations like this. Am I missing something?

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LanceH
Number theory is always pointless until an application is found and it becomes
a separate field of research.

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amelius
I guess the question is more: what makes these primes more interesting than,
say, cousin (differ by 4) or twin (differ by 2) primes, or any other differ-
by-n primes.

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LanceH
In this case, nothing that I know of. Again, that's the kind of math that is
classified as "number theory". It's just pure investigation of relationships
between numbers. Occasionally you gain some insight that is useful.

A lot of cryptography used to be just number theory until computers came along
and were powerful enough to make use of it. How to tell if something if
someting is divisible by 3. Checksums as used on credit cards. Euler's
algorighm.

No, sexy primes don't really have a point other than they are identified and
there is probably some unused conjecture that they are infinite in number.

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enedil
Using Euclid's algorithm (not Euler's) is certainly not the easiest way of
checking for divisibility by 3 - a number is divisible by 3 if and only if
it's sum of digits is divisible by 3. You can repeat the process until you
have one digit.

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amelius
But what if you start with a binary representation?

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firethief
Do it in quaternary. Add pairs of bits.

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avnerium
Or you can form the alternating sum of the bits, e.g. for 0b10011001 you
calculate 1-0+0-1+1-0+0-1 = 0 which is divisible by three. (That's similar to
the divisibility test by 11 of a number in base-10, or more generally testing
if a number in base `b` is divisible by b+1)

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ecesena
Last year both my sister and I, and my mom and dad had sexy prime years. The
coolest thing is that all my family of 5 had a prime number of years, pretty
incredible. I wrote about it here: [https://medium.com/@0x0ece/primes-twin-
primes-and-my-moms-bd...](https://medium.com/@0x0ece/primes-twin-primes-and-
my-moms-bday-14188d149b57)

~~~
hughdbrown
Last year my family was all prime: 5, 7, 47, and 53. Six years from now, we
will be 11, 13, 53, and 59. And then 36 year from now when the kids are
approaching middle age.

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anonytrary
> In an arithmetic progression of five terms with common difference 6, one of
> the terms must be divisible by 5, because 5 and 6 are relatively prime.
> Thus, the only sexy prime quintuplet is (5,11,17,23,29); no longer sequence
> of sexy primes is possible.

Pretty neat.

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nitramm
This page contains visualization of sexy primes up to 1 million -
[https://prime-numbers.info/article/sexy-primes#visualization](https://prime-
numbers.info/article/sexy-primes#visualization)

You can also compare their density with normal primes on this page -
[https://prime-numbers.info/special/visual-type-
comparison#se...](https://prime-numbers.info/special/visual-type-
comparison#sexy-prime--prime--1)

Best thing is that you can enjoy those videos for 11 hours. :)

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joshuawright11
Sounds like the name of an Amazon adult streaming service

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userbinator
Before reading the article I thought it would be about prime numbers which
encode erotic images in a similar fashion to
[https://en.wikipedia.org/wiki/Illegal_prime](https://en.wikipedia.org/wiki/Illegal_prime)
. (in which case if the image depicts a minor, it would be a sexy illegal
prime...)

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kyle-rb
Website displaying random pairs: [http://primes.sexy](http://primes.sexy)

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topkai22
This is clickbait done right.

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ngcc_hk
Interesting we call, a topic never will know as it is not too sexy. Just
number even one may say, but why they have patterns.

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sonofgod
Now earwormed to the tune of "baby shark".

Also, Mersenne Prime, Happy Prime, Lucky Prime etc...

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diminoten
They didn't have the guts to call a prime triplet involving a sexy prime a
threeway or ménage à trois? Boo!

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bthrn
Came here to say that. I was going to recommend it be called a prime threesome
though.

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throwawaymath
They're primes which are separated by exactly six non-prime numbers. It
remains an open question whether or not there are infinitely many sexy primes.

More generally, see the article on prime gaps:
[https://en.m.wikipedia.org/wiki/Prime_gap](https://en.m.wikipedia.org/wiki/Prime_gap)

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jfk13
> They're primes which are separated by exactly six non-prime numbers.

That doesn't match what the article says: "prime numbers that differ from each
other by six". So they're separated by five other numbers (which are not
necessarily all non-primes).

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LanceH
Separated by five natural numbers.

