Carol / Kynea Primes - Page 6

rogue · 2016-05-23, 01:12

Quote:

Originally Posted by Batalov

And now, a Kynea prime for b=30, to make a nice pair.
(30¹⁵⁷⁹⁵⁰ + 1)² - 2 is prime

, I mean

.

You're getting ahead of me with bases that don't require as many tests to find a Top 5000 prime.

I have not put together a webpage yet as I've been busy with outdoor stuff. The weather this past weekend was fantastic here. I hope to get something in place by Memorial Day (next week Monday for those non-Americans out there).

lalera · 2016-05-23, 09:06

hi,
here are the results for carol / kynea
b=28, n=1000 to 30000
(28^2520-1)^2-2
(28^5048+1)^2-2
(28^6492-1)^2-2
(28^6577-1)^2-2
(28^22960-1)^2-2
(28^24990+1)^2-2
(28^25528-1)^2-2

Batalov · 2016-05-24, 07:09

Quote:

Originally Posted by Batalov

For b<=2000, only b=640 and b=1656 remain without known primes.

For b<=3000, in addition to b=640 (up to n<=40K) and b=1656 (up to n<=35K), there are three more b = {2264, 2482, 2634} that remain without known C-K primes (up to n<=5100).

For b=2026, the smallest prime is (2026^5526+1)^2-2, the rest have a prime under n<=1000.

rogue · 2016-05-25, 00:10

I'm starting to put together a website for this search. Take a look at http://www.mersenneforum.org/rogue/ckps.html and give me some feedback.

Batalov · 2016-05-26, 06:31

Update:
For b<=3000, there are ~~four~~ three cases: b=1656 (up to n<=45K) and b = {~~2264,~~^{[COLOR=Blue]*[/COLOR]} 2482, 2634} that remain without known C-K primes (up to n<=8000).

However, for b=640, (640^44940+1)^2-2 is prime (252220 digits),
so all b<1656 have at least one known C-K prime!
___________________
^* (2264^10098+1)^2-2 is prime

lalera · 2016-05-27, 08:45

hi,
here are the results for carol / kynea
b=72, n=10000 to 40000
(72^37930-1)^2-2

lalera · 2016-05-28, 20:20

hi,
here are the results for carol / kynea
b=6, n=100000 to 120000
(6^117991-1)^2-2

lalera · 2016-05-29, 14:56

hi,
here are the results for carol / kynea
b=70, n=10000 to 40000
(70^10744-1)^2-2
(70^11260-1)^2-2
(70^19370-1)^2-2

rogue · 2016-05-29, 19:43

lalera, did you only find Carol primes in those bases?

lalera · 2016-05-30, 09:00

Quote:

Originally Posted by rogue

lalera, did you only find Carol primes in those bases?

yes

lalera · 2016-05-30, 09:29

hi,
here are the results for carol / kynea
b=76, n=1000 to 40000
(76^2306+1)^2-2
(76^3081-1)^2-2
(76^35617-1)^2-2
(76^36090-1)^2-2
b=78, n=1000 to 40000
(78^6429-1)^2-2
(78^6853+1)^2-2

2016-05-26, 06:31	#60
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2²×23×103 Posts	Update: For b<=3000, there are ~~four~~ three cases: b=1656 (up to n<=45K) and b = {~~2264,~~^{[COLOR=Blue][/COLOR]} 2482, 2634} that remain without known C-K primes (up to n<=8000). However, for b=640, (640^44940+1)^2-2 is prime (252220 digits), so all b<1656 have at least one known C-K prime! ___________________ ^ (2264^10098+1)^2-2 is prime Last fiddled with by Batalov on 2016-05-29 at 07:28

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2016-05-23, 09:06	#57
lalera Jul 2003 1001100011₂ Posts	hi, here are the results for carol / kynea b=28, n=1000 to 30000 (28^2520-1)^2-2 (28^5048+1)^2-2 (28^6492-1)^2-2 (28^6577-1)^2-2 (28^22960-1)^2-2 (28^24990+1)^2-2 (28^25528-1)^2-2

2016-05-25, 00:10	#59
rogue "Mark" Apr 2003 Between here and the 1100011001011₂ Posts	I'm starting to put together a website for this search. Take a look at http://www.mersenneforum.org/rogue/ckps.html and give me some feedback.

2016-05-27, 08:45	#61
lalera Jul 2003 13×47 Posts	hi, here are the results for carol / kynea b=72, n=10000 to 40000 (72^37930-1)^2-2

2016-05-28, 20:20	#62
lalera Jul 2003 1001100011₂ Posts	hi, here are the results for carol / kynea b=6, n=100000 to 120000 (6^117991-1)^2-2

2016-05-29, 14:56	#63
lalera Jul 2003 1143₈ Posts	hi, here are the results for carol / kynea b=70, n=10000 to 40000 (70^10744-1)^2-2 (70^11260-1)^2-2 (70^19370-1)^2-2

2016-05-29, 19:43	#64
rogue "Mark" Apr 2003 Between here and the 11×577 Posts	lalera, did you only find Carol primes in those bases?

2016-05-30, 09:29	#66
lalera Jul 2003 13×47 Posts	hi, here are the results for carol / kynea b=76, n=1000 to 40000 (76^2306+1)^2-2 (76^3081-1)^2-2 (76^35617-1)^2-2 (76^36090-1)^2-2 b=78, n=1000 to 40000 (78^6429-1)^2-2 (78^6853+1)^2-2