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Is there a effective quick way to generate a large prime of a given length?

'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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,727

I know where you are going with this and it is not necessary.

To answer your question, there is no extremely quick way.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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Where am I going?

```
while True:
randomnumber = random.randrange(2**(length-1),(2**(length))-1)
if primep(randomnumber):
print randomnumber
break
```

Thats all I got from stackoverflow

*Last edited by Agnishom (2013-09-21 21:16:47)*

'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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,727

You think you need a large prime to learn Diffie- Hellman. I can denmonstrate the procedure using a small one.

Thats all I got from stackoverflow

Hohohohohohohahahaha, they are always good for a laugh. To think that such brilliant people can still have a wonderful sense of humor gives me much hope for the human race.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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bobbym wrote:

You think you need a large prime to learn Diffie- Hellman. I can denmonstrate the procedure using a small one.

I can too. But that is not secure enough.

Sorry, I did not get the humor

'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'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,727

I agree. But I thought you wanted to see how it worked?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

I think the only problem is - after Alice and Bob have the shared secret, how do they exchange messages using it?

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: 104,727

I have been waiting to answer that one since yesterday. But it seems I have missed Agnishom today.

**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 wrote:

I think the only problem is - after Alice and Bob have the shared secret, how do they exchange messages using it?

They use a symmetric cypher, like RC4 with the key.

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

I'm not crazy, my mother had me tested.

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Let us take the generally accepted *p* from http://tools.ietf.org/html/rfc2409#section-6.2

`179769313486231590770839156793787453197860296048756011706444423684197180216158519368947833795864925541502180565485980503646440548199239100050792877003355816639229553136239076508735759914822574862575007425302077447712589550957937778424442426617334727629299387668709205606050270810842907692932019128194467627007`

The generator g is

`2`

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

I'm not crazy, my mother had me tested.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hi Agnishom

My number:

`170889576082067697731054176601909874828559452754928289693960008087616417613737398548717155229171096112124599345710842437121675819339812482513978573388985033018038377053945453188374711735023121936105534290646082341664680937820085667262891263915428892361981765346083422852575547729295502827704976423861860303103`

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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Hi anonymnesty,

g[sup]b[/sup] (mod p)

`173419298906489863864646388281941306843742681293608592957943679413527102401811311961611828206757391788738800024670641247258673805804085888390828078173388181181530749311360724611386280929348614725682444473741887149211776384725911058474047582365359321545094524307293842804350322782081718297375589621859722244791`

*Last edited by Agnishom (2013-09-22 16:34:05)*

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

I'm not crazy, my mother had me tested.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hm, just call me Stefy. It's easier for everybody that way.

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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Hi Stefy,

Sorry for the typo. Is what you posted in #11 g[sup]a[/sup] (mod p) ?

How should I use the secret key to message you now? What about RC4?

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

I'm not crazy, my mother had me tested.

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**auyeungyat****Member**- Registered: 2013-09-23
- Posts: 22

I have tested on my computer(Mac on Terminal).That doesn't generate any numbers!

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auyeungyat wrote:

I have tested on my computer(Mac on Terminal).That doesn't generate any numbers!

I am sorry, primep is defined externally. Do you want the full working code?

*Last edited by Agnishom (2013-09-23 03:02:37)*

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

I'm not crazy, my mother had me tested.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Agnishom wrote:

Hi Stefy,

Sorry for the typo. Is what you posted in #11 g[sup]a[/sup] (mod p) ?

How should I use the secret key to message you now? What about RC4?

It is.

Is there something more simple we could try first?

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: 104,727

I have a nice tut on this if you need to see how it is done.

**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: 16,015

Hi bobbym

You can post them, if you want.

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: 104,727

It uses baby sized numbers but maybe that is best for an example.

**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: 16,015

Sure. Any example would suffice, seeing how I am not sure at all how to use the shared secret.

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: 104,727

Neither am I. How about we try to follow their example?

**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: 16,015

Their?

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: 104,727

The video I have. They use an example. They go through the technique step by step. Should be easy to do with a real problem later on.

**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: 16,015

Could you post the link to the video?

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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