What to do with 16 digit twin, non-Mersenne primes?

RienS · 2014-11-14, 13:58

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

TimSorbet · 2014-11-14, 14:34

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 N-1/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 N-1/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.

RienS · 2014-11-14, 15:23

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

R.D. Silverman · 2014-11-15, 00:15

Quote:

Originally Posted by RienS

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

Teach me. Please explain your thoughts as to why you believe that anyone
might want to know? What use is the information?

ewmayer · 2014-11-15, 01:30

My credit card # is a 16-digit prime but is alas not part of a twin-prime pair. Should I publish it anyway?

TimSorbet · 2014-11-15, 01:36

Quote:

Originally Posted by ewmayer

My credit card # is a 16-digit prime but is alas not part of a twin-prime pair. Should I publish it anyway?

Gee, I don't know, why don't you PM it to me and I'll tell you if it's an interesting number?

retina · 2014-11-15, 01:36

Quote:

Originally Posted by ewmayer

My credit card # is a 16-digit prime but is alas not part of a twin-prime pair. Should I publish it anyway?

Post the number here and I'll tell you if it has been compromised.

And just to make sure it is really you please include your expiry date and address details.

ewmayer · 2014-11-15, 02:01

Thanks for the kind offers, folks - the recipient of said CC# could publish a number theory paper, "How to turn a 16-digit prime into an abundant number."

But, with multiple offers already in the, um, offing, I'm afraid I'm gonna have to ask for pot-sweeteners to help me make up my mind. Offers of marriage and dutiful housekeeping from dis-royalled 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.

LaurV · 2014-11-15, 05:28

Add me to the PM list too, and don't forget the three digits on the back of the card.
Thanks.

CRGreathouse · 2014-11-15, 06:05

Quote:

Originally Posted by ewmayer

My credit card # is a 16-digit prime but is alas not part of a twin-prime pair. Should I publish it anyway?

Hmm, 249393770611256 16-digit 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!

LaurV · 2014-11-15, 06:36

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.

2014-11-14, 13:58	#1
RienS Nov 2014 2³ Posts	What to do with 16 digit twin, non-Mersenne 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

2014-11-14, 14:34	#2
TimSorbet Account Deleted "Tim Sorbera" Aug 2006 San Antonio, TX USA 11×389 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 N-1/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 N-1/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 TimSorbet on 2014-11-14 at 14:39

2014-11-15, 05:28	#9
LaurV Romulan Interpreter "name field" Jun 2011 Thailand 10273₁₀ 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 2014-11-15 at 05:28 Reason: (forgot to say thank you) :P

2014-11-15, 06:36	#11
LaurV Romulan Interpreter "name field" Jun 2011 Thailand 10,273 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 2014-11-15 at 06:42

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2014-11-14, 15:23	#3
RienS Nov 2014 2³ 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

2014-11-15, 01:30	#5
ewmayer ∂²ω=0 Sep 2002 República de California 5·2,351 Posts	My credit card # is a 16-digit prime but is alas not part of a twin-prime pair. Should I publish it anyway?

2014-11-15, 02:01	#8
ewmayer ∂²ω=0 Sep 2002 República de California 10110111101011₂ Posts	Thanks for the kind offers, folks - the recipient of said CC# could publish a number theory paper, "How to turn a 16-digit prime into an abundant number." But, with multiple offers already in the, um, offing, I'm afraid I'm gonna have to ask for pot-sweeteners to help me make up my mind. Offers of marriage and dutiful housekeeping from dis-royalled 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.