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## #1 2013-04-27 16:56:39

mathaholic
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### Sexy primes

Sexy primes are two prime numbers, wherein their difference is 6. I got this from a video on YouTube : http://www.youtube.com/watch?v=WJ12DYBuazY

Now, examples of sexy primes :
5 and 11
11 and 17
...

Sexy triplets :
5 11 17
11 17 23
...

5 11 17 23
11 17 23 29

Sexy quintuplets :
5 11 17 23 29

There are no sexy primes that are groups of 6. That's it! Discuss about it!

246 pages on Prime Numbers Wiki (+1)

## #2 2013-04-27 21:47:15

Agnishom
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### Re: Sexy primes

I got this from wolfram mathworld.
I don't think they are much sexy...

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #3 2013-04-28 14:44:43

mathaholic
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### Re: Sexy primes

I saw it from YouTube, because pf six, that sound like "gender". That's why they're called sexy primes. )

246 pages on Prime Numbers Wiki (+1)

## #4 2013-04-28 19:32:42

Agnishom
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### Re: Sexy primes

Yeah I know..

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #5 2013-04-28 22:13:50

mathaholic
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### Re: Sexy primes

Oh. No abs, right?

246 pages on Prime Numbers Wiki (+1)

## #6 2013-04-28 23:22:33

Agnishom
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### Re: Sexy primes

Is 6 the smallest possible common difference in AP of more than three primes?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #7 2013-04-29 04:29:25

Nehushtan
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### Re: Sexy primes

#### Agnishom wrote:

Is 6 the smallest possible common difference in AP of more than three primes?

Is such a sequence possible?

Last edited by Nehushtan (2013-04-29 04:30:51)

## #8 2013-04-29 06:18:11

bobbym

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### Re: Sexy primes

There are many with a common difference of 6, but none smaller.

Proof is easy.

Hint: Combinatorics is the model! Step out of the box or maybe jump into it.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #9 2013-04-29 22:59:10

anonimnystefy
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### Re: Sexy primes

Well, first note that the common difference must be an even number, and if it is less than 6, then it must be either 2 or 4. Also notice that if two numbers differ by 2, 4 or 8, they have different remainders modulo 3. This means that in three numbers in an AP with common difference 2 or 4, one will surely be divisible by 3. It is now easily proved that an AP of 4 or more terms and common difference 2 or 4 cannot exist.

There are only two AP's of 3 terms and those are 3, 5, 7 and 3, 7, 11.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #10 2013-04-30 10:46:09

Agnishom
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### Re: Sexy primes

Thanks for the proof

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #11 2013-04-30 10:47:47

bobbym

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### Re: Sexy primes

There is one that I came up with that is quite simple.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #12 2013-04-30 10:51:59

anonimnystefy
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### Re: Sexy primes

And that is?

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #13 2013-04-30 10:53:03

bobbym

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### Re: Sexy primes

Boxes and dashes like in combinatorics!

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #14 2013-04-30 11:01:07

Agnishom
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### Re: Sexy primes

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #15 2013-04-30 11:11:39

bobbym

Online

### Re: Sexy primes

We can view the number line in terms of boxes and dashes. The boxes are multiples of three, the dashes are the two numbers between each multiple of 3 that is greater than 3.

WLOG we can presume the lowest prime is located at position1 or position2. See the diagram. If we start at positon1 and count off 2 from it we see in the top drawing that not even a prime pair is possible from this position.

If we start from position2 and count off by 2 we see that a prime triplet with constant difference of two is also impossible

If there is no possible prime triplet with difference of two ( after 3, 5 and 7 )there is obviously no quadraplets, quintuplets etc. That concludes the proof.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #16 2013-04-30 11:14:36

anonimnystefy
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### Re: Sexy primes

That is the same as my proof.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #17 2013-04-30 11:16:15

bobbym

Online

### Re: Sexy primes

But it does not require any mathematical jargon or concepts other than counting.

Proof that there is no triplet with common difference 4.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #18 2013-04-30 11:20:50

anonimnystefy
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### Re: Sexy primes

It is the same proof worded differently.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #19 2013-04-30 11:23:50

bobbym

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### Re: Sexy primes

Hi anonimnystefy;

I did not offer it as a superior proof. I said it was a different one. Someone, like me for instance can understand this one a little easier. This is almost a proof without words.

Also, it is not the same proof. Yours uses words like modulo and AP. This one does not need to.

I think it also solves harder problems easier.

For instance: if I asked whether there were any 7 tuplets with a difference of 2,4,4,4,4,2, I can answer that very quickly by drawing more boxes and more dashes. No math required. Answer is no!

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #20 2013-04-30 11:54:46

mathaholic
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### Re: Sexy primes

Are those about the "theorem" of the sexy primes? Whatever.

246 pages on Prime Numbers Wiki (+1)

## #21 2013-04-30 12:31:30

anonimnystefy
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### Re: Sexy primes

Hi bobbym

It is the same proof. If you do not see that, it just means you haven't read my proof at all.

The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

## #22 2013-04-30 13:40:42

Agnishom
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### Re: Sexy primes

I am not getting bobbym's proof

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #23 2013-04-30 14:11:06

bobbym

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### Re: Sexy primes

Hi Agnishom;

boxes = multiples of 3, starting at 6. Dashes are the 2 numbers between every multiple of 3, like 16 and 17 is between 15 and 18. The lowest prime in our quadruplet has to be at position1 or position2.

Hi anonimnystefy;

I did not look at your proof because I was too busy writing up mine. I still think mine is easier to answer future questions and requires nothing but the ability to draw boxes and lines,

Did you see the question I asked in post#19? With mine, it is snap.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.

## #24 2013-04-30 19:28:18

ElainaVW
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### Re: Sexy primes

Nice idea, I tried it on 2 4 4 4 4 2 and it worked fine.

## #25 2013-04-30 19:35:14

bobbym

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### Re: Sexy primes

Hi;

Welcome to the forum! AdministratorM? bobbym is fine here. I am glad you tried it, just keep in mind that it is more useful for proving what doesn't work then what does.

In mathematics, you don't understand things. You just get used to them.
Some cause happiness wherever they go; others, whenever they go.
If you can not overcome with talent...overcome with effort.