Carol / Kynea Primes - Page 9

rogue · 2017-04-22, 18:44

sweety439, what range of n are you searching?

sweety439 · 2017-04-23, 14:04

I tested to about n=2000 and found only these primes. At beginning, I decided to search to n=10K, but it will take too much time, so I released it.

rogue · 2017-04-23, 15:47

Quote:

Originally Posted by sweety439

I tested to about n=2000 and found only these primes. At beginning, I decided to search to n=10K, but it will take too much time, so I released it.

If you properly sieved, it should take less than a day to test n=10000.

kar_bon · 2017-04-24, 08:55

Primes for CK Base 44, tested up to n=25K:

(44^8210+1)^2-2
(44^12909-1)^2-2
(44^20502+1)^2-2

vasyannyasha · 2017-04-28, 08:31

base 252 up to n=2000
(252^88-1)^2-2
(252^177+1)^2-2
(252^337-1)^2-2
(252^717-1)^2-2 is 3-PRP! (0.3107s+0.0002s)
(252^1330-1)^2-2 is 3-PRP! (0.9531s+0.0002s)
(252^1468+1)^2-2 is 3-PRP! (1.6530s+0.0002s)
(252^1996-1)^2-2 is 3-PRP! (2.4196s+0.0003s)
please explain
if program write ''(252^1996-1)^2-2 is 3-PRP!'' it means that this number really prime or 50/50?
Pre-thanks
P.S first three really primes.

kar_bon · 2017-04-28, 09:02

With pfgw use the "-tp" option to prove prime.

So
pfgw -q"(252^717-1)^2-2"

will show
(252^717-1)^2-2 is 3-PRP!

but
pfgw64 -tp -q"(252^717-1)^2-2"

will show
Primality testing (252^717-1)^2-2 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 17, base 1+sqrt(17)
(252^717-1)^2-2 is prime! (0.6952s+0.0011s)

rogue · 2017-04-28, 14:26

FYI, you only need to report in increments of 10,000. It will save me time.

vasyannyasha · 2017-04-29, 14:48

Quote:

Originally Posted by rogue

FYI, you only need to report in increments of 10,000. It will save me time.

Ok.
Finally for base 252 from n=1 to n=10000 i find 9 primes(7 Carol primes and 2 Kynea primes).
(252^88-1)^2-2 is prime! (0.0380s+0.0005s)
(252^177+1)^2-2 is prime! (0.0915s+0.0009s)
(252^337-1)^2-2 is prime! (0.2384s+0.0009s)
(252^717-1)^2-2 is prime! (1.2084s+0.0009s)
(252^1330-1)^2-2 is prime! (8.1088s+0.0236s)
(252^1468+1)^2-2 is prime! (8.6567s+0.0053s)
(252^1996-1)^2-2 is prime! (16.5803s+0.0061s)
(252^3095-1)^2-2 is prime! (37.3119s+0.0015s)
(252^6548-1)^2-2 is prime! (159.6788s+0.0013s)

Dylan14 · 2017-06-27, 16:04

For base 50, 50001 <= n <= 100000, the following primes were found:

Code:

 (50^53351-1)^2-2
 (50^69033-1)^2-2
 (50^69157-1)^2-2

rogue · 2017-06-27, 16:24

Thanks. I've been neglecting to post an updated page. I'll try to remind myself to do that tonight.

rogue · 2017-06-27, 23:41

My Carol/Kynea webpage has been updated!

2017-06-27, 16:04	#97
Dylan14 "Dylan" Mar 2017 3·193 Posts	For base 50, 50001 <= n <= 100000, the following primes were found: Code: (50^53351-1)^2-2 (50^69033-1)^2-2 (50^69157-1)^2-2

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2017-04-22, 18:44	#89
rogue "Mark" Apr 2003 Between here and the 2·3²·353 Posts	sweety439, what range of n are you searching?

2017-04-23, 14:04	#90
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 101101100110₂ Posts	I tested to about n=2000 and found only these primes. At beginning, I decided to search to n=10K, but it will take too much time, so I released it.

2017-04-24, 08:55	#92
kar_bon Mar 2006 Germany 101101011100₂ Posts	Primes for CK Base 44, tested up to n=25K: (44^8210+1)^2-2 (44^12909-1)^2-2 (44^20502+1)^2-2

2017-04-28, 08:31	#93
vasyannyasha "Vasiliy" Apr 2017 Ukraine 3²×7 Posts	base 252 up to n=2000 (252^88-1)^2-2 (252^177+1)^2-2 (252^337-1)^2-2 (252^717-1)^2-2 is 3-PRP! (0.3107s+0.0002s) (252^1330-1)^2-2 is 3-PRP! (0.9531s+0.0002s) (252^1468+1)^2-2 is 3-PRP! (1.6530s+0.0002s) (252^1996-1)^2-2 is 3-PRP! (2.4196s+0.0003s) please explain if program write ''(252^1996-1)^2-2 is 3-PRP!'' it means that this number really prime or 50/50? Pre-thanks P.S first three really primes.

2017-04-28, 09:02	#94
kar_bon Mar 2006 Germany 2²×727 Posts	With pfgw use the "-tp" option to prove prime. So pfgw -q"(252^717-1)^2-2" will show (252^717-1)^2-2 is 3-PRP! but pfgw64 -tp -q"(252^717-1)^2-2" will show Primality testing (252^717-1)^2-2 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 17, base 1+sqrt(17) (252^717-1)^2-2 is prime! (0.6952s+0.0011s)

2017-04-28, 14:26	#95
rogue "Mark" Apr 2003 Between here and the 14322₈ Posts	FYI, you only need to report in increments of 10,000. It will save me time.

2017-06-27, 16:24	#98
rogue "Mark" Apr 2003 Between here and the 2·3²·353 Posts	Thanks. I've been neglecting to post an updated page. I'll try to remind myself to do that tonight.

2017-06-27, 23:41	#99
rogue "Mark" Apr 2003 Between here and the 6354₁₀ Posts	My Carol/Kynea webpage has been updated!