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Old 2015-03-25, 23:44   #1
CuriousKit
 
"J. Gareth Moreton"
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Lightbulb What makes a prime worth mentioning?

I want to test my coding efficiency in prime number checking and generation, including ones of more unusual or arbitrary constructions (e.g. ones that can be decoded to reveal images and messages, for example).

My question is... how large should a prime number be to be considered worth posting here?
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Old 2015-03-26, 02:12   #2
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If its most notable feature is its size, then I'd base it off of the smallest numbers on one of these standard lists, based on its type:
  • The Top 5000 primes list for ordinary proven primes (ones where there is an efficient test for numbers of that form), currently 375,000 digits
  • The PRP Top list for PRPs for which there is no easy way to prove it prime, currently 36,291 digits.
  • The Top 20 ECPP page for numbers that are proven prime via ECPP (since ECPP is currently the fastest primality test in practice for general-form numbers), currently 18,662 digits.
Any such prime should also be submitted to the appropriate list. Anything less than that is probably not too interesting by size alone.
Any prime that doesn't fit these criteria, but that you think may be interesting to others for some other reason, could also be posted. Software, especially if it can compete with the common standard prime searching tools (Prime95, PFGW, etc.) would also be interesting. An example of primes that would not be interesting/good to post is ones that can be discovered trivially with standard tools and are not otherwise interesting, whether your software took weeks or seconds to find them.
Primes that can be decoded into images/messages could fall into either category, depending on what you're encoding, if you have a generalized way to encode them, and if you want to spam every random image or message you can find, or just interesting ones (or post the techniques you use to make them, so people can generate their own spam if they like). On the topic of embedding messages in primes, you will probably find this interesting: https://en.wikipedia.org/wiki/Illegal_prime

All just my opinions.

Last fiddled with by Mini-Geek on 2015-03-26 at 02:17
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Old 2015-03-26, 02:21   #3
LaurV
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Say, over a million digits?
And if it is not an illegal prime...


Edit, grrrr... that guy was faster...

Last fiddled with by LaurV on 2015-03-26 at 02:22
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Old 2015-03-26, 02:34   #4
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Also, notable are small but chained primes, e.g. see here (and they haven't made it here yet - they travel by snail-email ), and same is true for k-tuples: twins, triplets, quads, quints, and so on. That's of course (as Dennis Miller used to say) "that's just my opinion. I could be wrong."
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Old 2015-03-26, 02:52   #5
LaurV
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Well.. actually... if you put it like that, the only primes worth mentioning and be posted here are the primes which are part of encryption keys for bank accounts. Post them here together with the account name, bank, etc... whatever may be necessary...
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Old 2015-03-26, 06:07   #6
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Quote:
Originally Posted by LaurV View Post
Well.. actually... if you put it like that, the only primes worth mentioning and be posted here are the primes which are part of encryption keys for bank accounts. Post them here together with the account name, bank, etc... whatever may be necessary...
In that line of thought then all you'd need are the prime factors of the signing keys. After that everything else is a doddle.
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Old 2015-03-26, 11:39   #7
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The article on illegal primes is what caught my attention, I confess!

Hmmm, and some of these numbers may take some time to generate. Thanks for the response chaps - I'll see what I can come up with.
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Old 2015-03-26, 22:27   #8
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The article on illegal primes caught my attention too. The whole thing is bloody silly? How paranoid can the republicans get?

I have a collection of prime numbers. If one of these so-called "illegal" primes appears in that collection, I neither know nor care. If I receive a letter from some lawyer insisting I delete one of those numbers (cease and desist or whatever it is called) I shall ensure that letter goes viral on social media before ceremonially burning it.

What makes a prime worth mentioning? I don't know. Is 2 worth mentioning? (Answer - probably, yes, because it's the only even prime), or 2,147,483,647? or any other that you might think of?
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Old 2015-03-27, 00:15   #9
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Well, that's the nice thing about numbers... they can't be copyrighted or censored in their pure form. So if it just so happens to also represent a valid compressed archive that contains the C source code to a DVD decoder, that's their problem!

Of course, there can still be a danger of harassment or worse upon the disclosure of a Blu-Ray master key or if you generate a prime number that happens to be one of the prime factors of an important RSA key pair (which is incredibly unlikely... usually the sign of the key issuer having a poor random number generator).
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Old 2015-03-27, 00:28   #10
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Quote:
Originally Posted by BudgieJane View Post
The article on illegal primes caught my attention too. The whole thing is bloody silly? How paranoid can the republicans get?
That reminds me of this article which I have posted previously but might be interesting reading for those that haven't seen it yet. [/offtopic]
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Old 2015-04-25, 17:56   #11
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Here is a couple of (PRP) prime partition numbers that are unusually close together:
numbpart(1234626973) and numbpart(1234631715)
Is it worth mentioning? I think, maybe.
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