Question about prime numbers…

Hello again,

We forgot to ask you a question about prime numbers.

We are indeed releasing a number primality check tool for which there is no actual size limit beyond the one we have imposed for material resource issues.

However, it is often mentioned the existence of ILLEGAL prime numbers and we do not quite understand the meaning of being able to define a number, which ever it may be, illegal.

However, given the nature of our tool which has no processing limit, we do not wish to have any problem with the authorities.

What is your opinion on the issue, do you think we expose ourselves to any risk by releasing such a tool?

Looking forward to hearing from you.

Best regards,


P.S. In attachment you will find a text file contains the 3 previous and the 3 next numbers following the first illegal known one that contains 1401 digits.
Ex0 SySCreationAsked:
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Pawan KumarDatabase ExpertCommented:
Attachment missing.
"What is your opinion on the issue, do you think we expose ourselves to any risk by releasing such a tool?"
If you DO anything you expose yourself to some risk.
You can find some country in which almost anything is illegal.
I do not have a license to practice law anywhere but
I find it hard to believe that any number is illegal. But any number can be put to an illegal use.
there may be some countries where the above distinction is not made.
Dr. KlahnPrincipal Software EngineerCommented:
There are many illegal numbers, not all of them prime.  Use google and search for "illegal numbers" and all will be revealed.
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Ex0 SySCreationAuthor Commented:
Thank for you comments.

Does someone can understand and maybe explain how "Numbers" might be cossidered to be "Illegal" ???

It's only "Numbers", they are part of our univers, how can someone impose some of them to be considered illegal ???

Now if we have the ability produce easily a very quickly most of them (in particular concerning Large Prime Numbers), can we being considered doing illégal things ???

Thanks for your remarks .. ... .....


Ex0 SySCreationAuthor Commented:
Here is the missing attachment, sorry for that...
Ex0 SySCreationAuthor Commented:
For info, all process were made from a standard personal computer, not on any super-computation computer.
☠ MASQ ☠Commented:
Remember this isn't a law site, it's an IT site(!)

The main issue with "illegal primes" is what is the purpose is in publishing them?  
In the case of the DeCSS case legal action was taken because k*256^2+2083 was already in use as the CSS encryptor, the number itself wasn't illegal but it's publication in association with using it to decrypt the security checks on DVDs might have been hence the legal action taken against those who said "unlock your DVDs with this", not individuals who had the number k*256^2+2083 on their computers.

So for example if you generate a prime number which also turns out to be the launch code for a missile, publishing the number should not be illegal, publishing the number saying "use this number to launch a missile"  is more likely to cause you trouble.

Like most criminal law provable intent is the issue, it's not what you have, it's what you do with it!

For those who want the background to "illegal prime numbers" try:
Written at the height of the hysteria around who owns numbers.
There is no way that prime numbers or programs that find them can be classified as illegal.  The Wikipedia article covers this very well.

The use of certain computer programs (like the one that cracks the protection on DVD's) has been deemed illegal in certain jurisdictions.
Publishing such programs would also be a violation.

All the "illegal primes" do is establish a relationship between a proscribed program and large prime number.  The prime number is large enough to publish.  And the binary representation of the prime matches the binary representation of the program.

There is no conceivable problem unless you are starting with a program and actively looking for one of the infinite number of primes that could generate it.
Ex0 SySCreationAuthor Commented:
Thank you all for your answers,

We understood that our tool wont be illegal at all until someone focused on illegal primes only.

Here for example, another little text file includes some other long numbers around the first illegal executable number that is 1811 digits long. (17 previous and 17 next ones)

Do you can confirm that such lists would be legal to be generated ?

Thanks in advance.



Only a lawyer can render a legal opinion.  And if you talk to five lawyers, you may very well find five different legal opinions.

Or you can rely on common sense.  Suppose you live on a very long street.  The houses are numbered consecutively: 1 on the right, 2 on the left, 3 on the right, and so on.  If the street is long enough, somebody on the left will find themselves with an "illegal" address.  Could they be prosecuted for putting their return address on all the Christmas cards they send out?  Should they be?  Is this a crime or a coincidence?
Ex0 SySCreationAuthor Commented:
Thank you d-glitch for your answer.

Of course the common sense would say that we aren't doing any illegal things, but because Cryptography and very large Prime Numbers are both of them concerning some very sensitive fields, we prefer asking questions instead of doing any kind of bad manoevers.

Just a small question : Did you try our tools available on our website (Ex0-Prime-ToolbarAlph@TaV Vault), and if so, what is your opinion about them ?

Thank for your interest and hope to read you soon .. ... .....

I have not tried the tools, and I almost certainly won't.   I have been a Crytography fan for 40+ years, but I'm not even a rank amateur.  However I do follow Don Coppersmith, David Kahn, and Bruce Bruce Schneier.  I think the most relevent article would be Schneier's Snake Oil from 1999:

Your product does seem to display at least three of his warning signs: new math, proprietarty algorithms, and ridiculously long keys.
Ex0 SySCreationAuthor Commented:
Thank you "d-glitch" for your honesty,

We don't really understand how new maths and proprietary algorithms would be a bad think for a new cryptography system ?!

Of course, you talk about ridiculously long keys and it's true, they might be really long depending on the selected user options but we really don't understand why you considered it to be something really ridiculous.

Could you please maybe explain why it might be considered to be ridiculous to use some very long ciphering keys that are not able to or be solved without perfectly  know how our algorithms are working ???

The fact is that they are only generated and used as very small part of our system and they have nothing to do with the main data protection process itself.

Thanks in advance and hope to read you soon .. ... .....


Ex0 SySCreationAuthor Commented:
To d-glitch and of course all others,

As a cryptography lover for more than 40 years, we imagine that you are more intwerested in cryptographic concepts than into algorithms themselves.

We therefore send you a link to our last published article, detailing exactly the main operation steps processes of our "proprietary" system :

Happy reading.


I am interested in cryptography concepts and capabilities, but most particularly in algorithms.  And so I find your 'published articles' interesting for all the wrong reasons.
  • I see that Alph@TaV is extraordinarily complex, but I don't see anything about performance, efficiency, or algorithms.  
  • Complexity is not the same as security.  
  • New and different and proprietary are actually disqualifying characteristics for a security system.
  • The reason PGP, RSA, DES, and AES can be and are trusted is because they have opened themselves to decades of analysis and attacks by the best cryptographers in the world.

You might want to take a look at these two articles from Bruce Schneier and rethink your sales pitch for the savvy consumer:

Good Luck.

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