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**mathaholic****Member**- From: Earth
- Registered: 2012-11-29
- Posts: 3,014

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

...

Sexy quadruplets :

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!

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**mathaholic****Member**- From: Earth
- Registered: 2012-11-29
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I saw it from YouTube, because pf six, that sound like "gender". That's why they're called sexy primes. )

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**mathaholic****Member**- From: Earth
- Registered: 2012-11-29
- Posts: 3,014

Oh. No abs, right?

Mathaholic | 17th most active poster | 681st most recent person to join MIFF | Person | rrr's classmate

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,616

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.**

**If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

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.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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Thanks for the proof

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

**If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

And that is?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,616

Boxes and dashes like in combinatorics!

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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Please go ahead

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,616

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.**

**If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

That is the same as my proof.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,616

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.**

**If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

It is the same proof worded differently.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,616

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.**

**If it ain't broke, fix it until it is.**

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**mathaholic****Member**- From: Earth
- Registered: 2012-11-29
- Posts: 3,014

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

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

Hi bobbym

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

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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I am not getting bobbym's proof

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,616

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.**

**If it ain't broke, fix it until it is.**

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 461

Hi AdministratorM

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 96,616

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.**

**If it ain't broke, fix it until it is.**

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