20141114, 13:58  #1 
Nov 2014
2^{3} Posts 
What to do with 16 digit twin, nonMersenne primes?
Hi all,
I found a triplet prime pair with 16 digits. It is nowhere mentioned on the internet and I can't figure it out how i have to test it in Prime95 (to many digits plus it's no Mersenne prime.) Any suggestions how to test it and what should I do with it? I'm new in this stuff greetings and many thanks, RienS 
20141114, 14:34  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
4278_{10} Posts 
16 digit primes can be trivially proven by computers. E.g. you can use PARI/GP, FactorDB, or Wolfram Alpha. The largest prime triplet has 16737 digits.
Proving larger numbers prime can be done by N1/N+1 tests using PFGW (among others), or ECPP using Primo (if you choose the numbers right, only one out of the 3 will need to slower ECPP, the others can use the fast N1/N+1 tests). Note that ECPP should only be run after you've already shown the number is PRP ("Probable Prime"), e.g. by using PFGW. Your discovery would not be considered interesting to the world at large (unlike if, say, you found a triplet large enough to compete with those in the top 20 list I linked earlier), so there's not really anything you "should do with it" after you find (and verify) it other than admire it yourself. Last fiddled with by MiniGeek on 20141114 at 14:39 
20141114, 15:23  #3 
Nov 2014
2^{3} Posts 
Thanks a lot for the information.
I used WolframAlpha and it seems to be a twin, not a triplet. If you want to know, the twin prime was 4324902831411101 and 4324902831411103 
20141115, 00:15  #4  
"Bob Silverman"
Nov 2003
North of Boston
1D28_{16} Posts 
Quote:
might want to know? What use is the information? 

20141115, 01:30  #5 
∂^{2}ω=0
Sep 2002
República de California
3·7·13·43 Posts 
My credit card # is a 16digit prime but is alas not part of a twinprime pair. Should I publish it anyway?

20141115, 01:36  #6 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
10266_{8} Posts 

20141115, 01:36  #7  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2×17×193 Posts 
Quote:
And just to make sure it is really you please include your expiry date and address details. 

20141115, 02:01  #8 
∂^{2}ω=0
Sep 2002
República de California
2DDB_{16} Posts 
Thanks for the kind offers, folks  the recipient of said CC# could publish a number theory paper, "How to turn a 16digit prime into an abundant number."
But, with multiple offers already in the, um, offing, I'm afraid I'm gonna have to ask for potsweeteners to help me make up my mind. Offers of marriage and dutiful housekeeping from disroyalled Nigerian princesses, that sort of thing. But now back to the hard work on my own upcoming NT manuscript, "On the distribution of even palindromic primes." It's gonna be a model of both profundity and succinctness. 
20141115, 05:28  #9 
Romulan Interpreter
"name field"
Jun 2011
Thailand
17×19×31 Posts 
Add me to the PM list too, and don't forget the three digits on the back of the card.
Thanks. Last fiddled with by LaurV on 20141115 at 05:28 Reason: (forgot to say thank you) :P 
20141115, 06:05  #10 
Aug 2006
3·1,993 Posts 
Hmm, 249393770611256 16digit primes, of which 240266784156262 aren't twins. Probably only a tenth have a valid Luhn checksum, so that leaves you with only 44.5 bits of entropy!

20141115, 06:36  #11 
Romulan Interpreter
"name field"
Jun 2011
Thailand
17·19·31 Posts 
Actually much less, according with the ISO7812, considering that the first number can't be any, and some combinations are not possible, etc, which may leave as less as 37 bits of entropy, [edit: if we know his bank we can go as low as 26 bits, there are only ~8 digits which are truly random there, related to the account and secondary cards] etc.
Last fiddled with by LaurV on 20141115 at 06:42 
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