Carol / Kynea Primes - Page 8

wombatman · 2016-07-02, 05:53

For base 26:

Code:

(26^75993+1)^2-2 is prime! (15529.3052s+0.0087s)

215057 digits.

rogue · 2016-07-06, 22:24

(2^688042-1)^2-2 is prime at 414243 digits. This is a new record for that form and will enter the top 5000 in the 2700 range.

paulunderwood · 2016-07-06, 22:37

Quote:

Originally Posted by rogue

(2^688042-1)^2-2 is prime at 414243 digits. This is a new record for that form and will enter the top 5000 in the 2700 range.

Congrats for another one!

rogue · 2016-07-17, 02:10

I have been very lucky.

(2^695631-1)^2-2 is prime at just over 418,800 digits. It will be around 2600 in the Top 5000.

henryzz · 2016-07-27, 08:04

For base 24:

Code:

(24^20047-1)^2-2 is 3-PRP!

BotXXX · 2016-11-24, 17:31

Following http://www.mersenneforum.org/showpos...4&postcount=69

(2010^3+1)^2-2 is 3-PRP! (0.0000s+0.0001s)
Primality testing (2010^3+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 1+sqrt(13)
Running N+1 test using discriminant 13, base 2+sqrt(13)
(2010^3+1)^2-2 is prime! (0.0227s+0.0010s)

(2010^3-1)^2-2 is 3-PRP! (0.0000s+0.0006s)
Primality testing (2010^3-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 11
Running N+1 test using discriminant 17, base 1+sqrt(17)
Running N+1 test using discriminant 17, base 2+sqrt(17)
(2010^3-1)^2-2 is prime! (0.0242s+0.0014s)

(2010^35-1)^2-2 is 3-PRP! (0.0018s+0.0001s)
Primality testing (2010^35-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N+1 test using discriminant 23, base 1+sqrt(23)
(2010^35-1)^2-2 is prime! (0.0311s+0.0004s)

(2010^1967-1)^2-2 is 3-PRP! (3.4481s+0.0003s)
Primality testing (2010^1967-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 17
Running N+1 test using discriminant 29, base 1+sqrt(29)
Running N+1 test using discriminant 29, base 2+sqrt(29)
(2010^1967-1)^2-2 is prime! (32.5536s+0.0007s)

OpenPFGW 3.8.0 on Windows with an Intel Core i7-3667U
Just to get a feeling of cksieve and openpwfg (a long long time ago), after the initial start sieve (-P1e9) I checked 1 <= n <= 2000. The above are the 4 primes found. Will continue to sieve and test this base.

To keep the format of http://www.mersenneforum.org/rogue/ckps.html :
base 2010 (-1) 3 35 1967
base 2010 (+1) 3

BotXXX · 2017-01-20, 16:10

(2010^30505+1)^2-2 is 3-PRP! (1158.2858s+0.0108s)
Primality testing (2010^30505+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
(2010^30505+1)^2-2 is prime! (7971.5683s+0.0110s)

201528 digits - ie too small for the top 5 .. ;)

BotXXX · 2017-03-06, 10:08

Current primes (for both bases upto n = 40.000)

base 316 (-1) 1 5 27 183 5331 14854 17396
base 316 (+1) 9 41 360 521 6421

base 2010 (-1) 3 35 1967
base 2010 (+1) 3 30505

(316^1-1)^2-2 is 3-PRP! (0.0000s+0.0001s)
Primality testing (316^1-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
(316^1-1)^2-2 is prime! (0.0001s+0.0008s)

(316^5-1)^2-2 is 3-PRP! (0.0000s+0.0007s)
Primality testing (316^5-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 17, base 1+sqrt(17)
Running N+1 test using discriminant 17, base 2+sqrt(17)
(316^5-1)^2-2 is prime! (0.0283s+0.0004s)

(316^9+1)^2-2 is 3-PRP! (0.0000s+0.0001s)
Primality testing (316^9+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Running N+1 test using discriminant 13, base 2+sqrt(13)
(316^9+1)^2-2 is prime! (0.0276s+0.0006s)

(316^27-1)^2-2 is 3-PRP! (0.0003s+0.0002s)
Primality testing (316^27-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 2+sqrt(13)
Running N+1 test using discriminant 13, base 3+sqrt(13)
(316^27-1)^2-2 is prime! (0.0456s+0.0004s)

(316^41+1)^2-2 is 3-PRP! (0.0008s+0.0003s)
Primality testing (316^41+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Running N+1 test using discriminant 13, base 2+sqrt(13)
(316^41+1)^2-2 is prime! (0.0338s+0.0004s)

(316^183-1)^2-2 is 3-PRP! (0.0147s+0.0001s)
Primality testing (316^183-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)
Running N+1 test using discriminant 11, base 3+sqrt(11)
(316^183-1)^2-2 is prime! (0.1514s+0.0004s)

(316^360+1)^2-2 is 3-PRP! (0.0625s+0.0002s)
Primality testing (316^360+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Running N+1 test using discriminant 13, base 2+sqrt(13)
(316^360+1)^2-2 is prime! (0.4942s+0.0004s)

(316^521+1)^2-2 is 3-PRP! (0.1391s+0.0002s)
Primality testing (316^521+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 13, base 1+sqrt(13)
Running N+1 test using discriminant 13, base 2+sqrt(13)
(316^521+1)^2-2 is prime! (1.0966s+0.0004s)

(316^5331-1)^2-2 is 3-PRP! (18.1007s+0.0008s)
Primality testing (316^5331-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 11, base 2+sqrt(11)
Running N+1 test using discriminant 11, base 3+sqrt(11)
(316^5331-1)^2-2 is prime! (148.4876s+0.0012s)

(316^6421+1)^2-2 is 3-PRP! (28.4269s+0.0010s)
Primality testing (316^6421+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Running N+1 test using discriminant 29, base 2+sqrt(29)
Running N+1 test using discriminant 29, base 4+sqrt(29)
(316^6421+1)^2-2 is prime! (261.8544s+0.0013s)

(316^14854-1)^2-2 is 3-PRP! (152.9047s+0.0040s)
Primality testing (316^14854-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 17, base 1+sqrt(17)
Running N+1 test using discriminant 17, base 2+sqrt(17)
(316^14854-1)^2-2 is prime! (1238.4924s+0.0034s)

(316^17396-1)^2-2 is 3-PRP! (185.3647s+0.0047s)
Primality testing (316^17396-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 2+sqrt(13)
Running N+1 test using discriminant 13, base 3+sqrt(13)
(316^17396-1)^2-2 is prime! (1956.7175s+0.0038s)

Dylan14 · 2017-04-16, 01:30

For base 50, 1 <= n <= 50000, I found the following primes:

Code:

 (50^1-1)^2-2
 (50^3-1)^2-2
 (50^4+1)^2-2
 (50^4-1)^2-2
 (50^9-1)^2-2
 (50^31-1)^2-2
 (50^38+1)^2-2
 (50^66-1)^2-2
 (50^93+1)^2-2
 (50^115-1)^2-2
 (50^120+1)^2-2
 (50^430-1)^2-2
 (50^1233-1)^2-2
 (50^2546-1)^2-2
 (50^2674-1)^2-2
 (50^4396+1)^2-2
 (50^6360-1)^2-2
 (50^11459+1)^2-2
 (50^25887+1)^2-2

sweety439 · 2017-04-18, 18:40

I searched bases 42, 44, 46 and 48 and found those primes: (for n>100)

(42^195-1)^2-2
(42^255-1)^2-2
(42^713-1)^2-2
(42^119+1)^2-2
(44^1288-1)^2-2
(44^195+1)^2-2
(44^1482+1)^2-2
(46^269-1)^2-2
(46^1304-1)^2-2
(48^207+1)^2-2
(48^329+1)^2-2
(48^1153+1)^2-2

Continue searching...

sweety439 · 2017-04-19, 19:17

Found another prime:

(44^1947-1)^2-2

2016-07-02, 05:53	#78
wombatman I moo ablest echo power! May 2013 29·61 Posts	For base 26: Code: (26^75993+1)^2-2 is prime! (15529.3052s+0.0087s) 215057 digits.

2016-07-27, 08:04	#82
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 1011011111000₂ Posts	For base 24: Code: (24^20047-1)^2-2 is 3-PRP!

2017-04-18, 18:40	#87
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 5×7×83 Posts	I searched bases 42, 44, 46 and 48 and found those primes: (for n>100) (42^195-1)^2-2 (42^255-1)^2-2 (42^713-1)^2-2 (42^119+1)^2-2 (44^1288-1)^2-2 (44^195+1)^2-2 (44^1482+1)^2-2 (46^269-1)^2-2 (46^1304-1)^2-2 (48^207+1)^2-2 (48^329+1)^2-2 (48^1153+1)^2-2 Continue searching... Last fiddled with by sweety439 on 2017-04-18 at 18:53

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2016-07-06, 22:24	#79
rogue "Mark" Apr 2003 Between here and the 11×577 Posts	(2^688042-1)^2-2 is prime at 414243 digits. This is a new record for that form and will enter the top 5000 in the 2700 range.

2016-07-17, 02:10	#81
rogue "Mark" Apr 2003 Between here and the 18CB₁₆ Posts	I have been very lucky. (2^695631-1)^2-2 is prime at just over 418,800 digits. It will be around 2600 in the Top 5000.

2016-11-24, 17:31	#83
BotXXX Aug 2003 Europe 2×97 Posts	Following http://www.mersenneforum.org/showpos...4&postcount=69 (2010^3+1)^2-2 is 3-PRP! (0.0000s+0.0001s) Primality testing (2010^3+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) (2010^3+1)^2-2 is prime! (0.0227s+0.0010s) (2010^3-1)^2-2 is 3-PRP! (0.0000s+0.0006s) Primality testing (2010^3-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 11 Running N+1 test using discriminant 17, base 1+sqrt(17) Running N+1 test using discriminant 17, base 2+sqrt(17) (2010^3-1)^2-2 is prime! (0.0242s+0.0014s) (2010^35-1)^2-2 is 3-PRP! (0.0018s+0.0001s) Primality testing (2010^35-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N+1 test using discriminant 23, base 1+sqrt(23) (2010^35-1)^2-2 is prime! (0.0311s+0.0004s) (2010^1967-1)^2-2 is 3-PRP! (3.4481s+0.0003s) Primality testing (2010^1967-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 17 Running N+1 test using discriminant 29, base 1+sqrt(29) Running N+1 test using discriminant 29, base 2+sqrt(29) (2010^1967-1)^2-2 is prime! (32.5536s+0.0007s) OpenPFGW 3.8.0 on Windows with an Intel Core i7-3667U Just to get a feeling of cksieve and openpwfg (a long long time ago), after the initial start sieve (-P1e9) I checked 1 <= n <= 2000. The above are the 4 primes found. Will continue to sieve and test this base. To keep the format of http://www.mersenneforum.org/rogue/ckps.html : base 2010 (-1) 3 35 1967 base 2010 (+1) 3

2017-01-20, 16:10	#84
BotXXX Aug 2003 Europe 11000010₂ Posts	(2010^30505+1)^2-2 is 3-PRP! (1158.2858s+0.0108s) Primality testing (2010^30505+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 7 Running N+1 test using discriminant 17, base 1+sqrt(17) (2010^30505+1)^2-2 is prime! (7971.5683s+0.0110s) 201528 digits - ie too small for the top 5 .. ;)

2017-03-06, 10:08	#85
BotXXX Aug 2003 Europe 2×97 Posts	Current primes (for both bases upto n = 40.000) base 316 (-1) 1 5 27 183 5331 14854 17396 base 316 (+1) 9 41 360 521 6421 base 2010 (-1) 3 35 1967 base 2010 (+1) 3 30505 (316^1-1)^2-2 is 3-PRP! (0.0000s+0.0001s) Primality testing (316^1-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] (316^1-1)^2-2 is prime! (0.0001s+0.0008s) (316^5-1)^2-2 is 3-PRP! (0.0000s+0.0007s) Primality testing (316^5-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 5 Running N+1 test using discriminant 17, base 1+sqrt(17) Running N+1 test using discriminant 17, base 2+sqrt(17) (316^5-1)^2-2 is prime! (0.0283s+0.0004s) (316^9+1)^2-2 is 3-PRP! (0.0000s+0.0001s) Primality testing (316^9+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) (316^9+1)^2-2 is prime! (0.0276s+0.0006s) (316^27-1)^2-2 is 3-PRP! (0.0003s+0.0002s) Primality testing (316^27-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N-1 test using base 5 Running N+1 test using discriminant 13, base 2+sqrt(13) Running N+1 test using discriminant 13, base 3+sqrt(13) (316^27-1)^2-2 is prime! (0.0456s+0.0004s) (316^41+1)^2-2 is 3-PRP! (0.0008s+0.0003s) Primality testing (316^41+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) (316^41+1)^2-2 is prime! (0.0338s+0.0004s) (316^183-1)^2-2 is 3-PRP! (0.0147s+0.0001s) Primality testing (316^183-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 2+sqrt(11) Running N+1 test using discriminant 11, base 3+sqrt(11) (316^183-1)^2-2 is prime! (0.1514s+0.0004s) (316^360+1)^2-2 is 3-PRP! (0.0625s+0.0002s) Primality testing (316^360+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) (316^360+1)^2-2 is prime! (0.4942s+0.0004s) (316^521+1)^2-2 is 3-PRP! (0.1391s+0.0002s) Primality testing (316^521+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 13, base 1+sqrt(13) Running N+1 test using discriminant 13, base 2+sqrt(13) (316^521+1)^2-2 is prime! (1.0966s+0.0004s) (316^5331-1)^2-2 is 3-PRP! (18.1007s+0.0008s) Primality testing (316^5331-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 11, base 2+sqrt(11) Running N+1 test using discriminant 11, base 3+sqrt(11) (316^5331-1)^2-2 is prime! (148.4876s+0.0012s) (316^6421+1)^2-2 is 3-PRP! (28.4269s+0.0010s) Primality testing (316^6421+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Running N+1 test using discriminant 29, base 2+sqrt(29) Running N+1 test using discriminant 29, base 4+sqrt(29) (316^6421+1)^2-2 is prime! (261.8544s+0.0013s) (316^14854-1)^2-2 is 3-PRP! (152.9047s+0.0040s) Primality testing (316^14854-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 17, base 1+sqrt(17) Running N+1 test using discriminant 17, base 2+sqrt(17) (316^14854-1)^2-2 is prime! (1238.4924s+0.0034s) (316^17396-1)^2-2 is 3-PRP! (185.3647s+0.0047s) Primality testing (316^17396-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Running N+1 test using discriminant 13, base 2+sqrt(13) Running N+1 test using discriminant 13, base 3+sqrt(13) (316^17396-1)^2-2 is prime! (1956.7175s+0.0038s)

2017-04-19, 19:17	#88
sweety439 "99(4^34019)99 palind" Nov 2016 (P^81993)SZ base 36 5531₈ Posts	Found another prime: (44^1947-1)^2-2