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Carol/Kynea new records   Message List  
Reply | Forward Message #14584 of 21095 |
Re: [PrimeNumbers] Re: Carol/Kynea new records

Predrag,
Thank you.
(Sorry if this seems off-topic and seems like poetry - it probably is) Carol G.
Kirnon is my best female friend in the whole wide world. She was the first girl
to steal my heart when we were in high school. Therefore, since math is my love
and she is my love, I named the first set of numbers after her. The second set,
and really the second set, because I encountered them days after is named for
the baby girl that had the greatest inpact on my life so far, Kynea R. Griffith
(she is ten years old now). I hope some day when people talk about Carol and
Kynea numbers, they will know a little bit about the two. Hopefully soon, I
will include a biography of the two on Steven Harvey's site.

-----Cletus Emmanuel

pminovic <pminovic@...> wrote:
Cletus,
Sorry, I was not aware of your GC, but I found it now at the bottom
of Steven Harvey's CK page. By the way, the comment "Generalized
Carol" was attached to Ballinger's base 6 GC when I submitted my
prime. At the time it was already confirmed to be prime. I guess the
editor of the site removed the comment manually since he doesn't
approve such "unofficial" comments (?).

Bt the way, who are Carol and Kynea and why are these forms named
after them?

And congrats on your large PRP, (2^148330+1)^4-2, the largest
reported so far.

Regards,
Predrag


--- In primenumbers@yahoogroups.com, Cletus Emmanuel <cemmanu@y...>
wrote:
> Congrats to the two of you on your findings. I went to the Top-
5000 and did not see the comments next to either number....
> There is Generalized Carol Number in the form ---> GC = (273*2^k -
1)^2 - 2. This form is more dense than the regular Carol Number. GC
is prime for k=100935 with 60774 digits, 607 digits more than Ray's.




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Mon Feb 23, 2004 5:11 pm

cemmanu
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Forward
Message #14584 of 21095 |
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Congrats to Ray Ballinger who just reported the largest GenCarol prime so far: (6^38660-1)^2-2 60167 digits! Yesterday I found the new largest Kynea prime: ...
pminovic
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Feb 20, 2004
5:29 am

Congrats to the two of you on your findings. I went to the Top-5000 and did not see the comments next to either number.... There is Generalized Carol Number...
Cletus Emmanuel
cemmanu
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Feb 20, 2004
4:35 pm

... 1)^2 - 2. Just how "general" can these types be? Is (N*2^1-1)^2-2 a valid GC? I mean any old odd number squared minus two... Paul ps congrats!...
Paul Underwood
paulunderwooduk
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Feb 21, 2004
9:34 am

Yes, somebody already mentioned the N^2-2 form and the related puzzle on the primes puzzle site. But if N is just any odd number the primality cannot be...
pminovic
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Feb 21, 2004
4:23 pm

Cletus, Sorry, I was not aware of your GC, but I found it now at the bottom of Steven Harvey's CK page. By the way, the comment "Generalized Carol" was...
pminovic
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Feb 21, 2004
4:46 pm

... Actually someday I do hope to allow unofficial comments on primes; but for now there are only database fields for official comments. The requiements for...
Chris Caldwell
primemogul
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Feb 21, 2004
5:50 pm

RE: A068357: primes of the form p*q+p-q with prime p,q. Are really the primes 2,3,11,23,47,53,59,71,79,83,101,107,131,163,167,173,179,191,223,227,23 ...
Zak Seidov
seidovzf
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Feb 22, 2004
2:20 am

Let's break this down and look closely... Let k=p*q+p-q, so k should be on the list if it is prime. Then k-1=p*q+p-q-1=(p-1)*(q+1), or k=(p-1)*(q+1)+1. Now, if...
Joseph Moore
jtpk
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Feb 22, 2004
4:37 am

In a message dated 22/02/04 02:21:54 GMT Standard Time, seidovzf@... ... You want to /prove/ that 71 (for example) is not of this form. Assume the...
mikeoakes2@...
mikeoakes2
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Feb 22, 2004
10:06 am

Thanks, Mike! Really, writing p=(n-1)/(q+1)+1, we need to check prime q's only up to n-2! Easy if you know what to do! Thanks again, Zak ... seidovzf@y... ... ...
Zak Seidov
seidovzf
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Feb 22, 2004
3:06 pm

Predrag, Thank you. (Sorry if this seems off-topic and seems like poetry - it probably is) Carol G. Kirnon is my best female friend in the whole wide world....
Cletus Emmanuel
cemmanu
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Feb 23, 2004
5:11 pm

Congrats on your new Kynea find... -->2/23/4 Minovic finds (2^102435+1)^2-2, 61673 digits. That should be Kynea 43 and the previous one listed below is Kynea...
Cletus Emmanuel
cemmanu
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Feb 23, 2004
5:45 pm

Cletus, Thank you. You won't beleive it but I just ran into yet another Kynea prime: (2^108888+1)^2-2, 65558 digits. The range appears to be populated with...
pminovic
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Feb 24, 2004
2:45 pm

Pregrag, Great! With every find, I feel good inside. I haven't found a Carol/Kynea prime since 2002, and yet I feel connected to every find. That is because...
Cletus Emmanuel
cemmanu
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Feb 24, 2004
5:07 pm

Dear prime gurus, is this Mathematica's prime really prime: 17911135064090123664377811162569837 (Sloan's A092540), thanks, Zak...
Zak Seidov
seidovzf
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Feb 27, 2004
3:52 pm

... Hash: SHA1 ... Yes, PARI/GP says so. Décio ... Version: GnuPG v1.2.3 (GNU/Linux) iD8DBQFAP2zmFXvAfvngkOIRAosFAJ921iJammIUgcu5uNN4WR3dBxNa3ACfT/as ...
Décio Luiz Gazzoni...
decio@...
Send Email
Feb 27, 2004
4:14 pm

Thanks, Filho! Zak...
Zak Seidov
seidovzf
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Feb 27, 2004
7:59 pm

When you call this a "Mathematica's prime," does that mean that this is a prime you've tested using Mathematica's (probabilistic) PrimeQ method? If so, the...
Alan Eliasen
aeliasen
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Feb 27, 2004
11:06 pm

But PrimeQ works for n < 10^16 (?), Zak ... this is a ... method? If so, ... less than, ... mail. ... onsLinks/StandardPackages/NumberTheory/PrimeQ.html ... a...
Zak Seidov
seidovzf
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Feb 28, 2004
12:34 am

... I think you may have misinterpreted a passage in the documentation. It notes the following: * PrimeQ first tests for divisibility using small primes, then...
Alan Eliasen
aeliasen
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Feb 28, 2004
1:29 am
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