mersenneforum.org Carol / Kynea Primes
 Register FAQ Search Today's Posts Mark Forums Read

 2016-04-15, 17:28 #1 rogue     "Mark" Apr 2003 Between here and the 10111001100002 Posts Carol / Kynea Primes I've started this thread to capture Carol / Kynea primes. Use this thread to post reservations. Please go here to get a complete list of Carol and Kynea primes. You can continue to post new primes in this thread. Admin edit: Here are links to Wikipedia about these primes: https://en.wikipedia.org/wiki/Carol_number https://en.wikipedia.org/wiki/Kynea_number Last fiddled with by gd_barnes on 2018-02-21 at 20:48 Reason: admin edit
 2016-04-16, 22:26 #2 NorbSchneider     "Norbert" Jul 2014 Budapest 25·3 Posts Carol / Kynea Primes I search base 38 up to n=70,000. I reached n=5,000 and found 7 new PRPs: (Carol) (38^1-1)^2-2, 4 digits (38^2-1)^2-2, 7 digits (38^13-1)^2-2, 42 digits (38^560-1)^2-2, 1770 digits (Kynea) (38^6+1)^2-2, 19 digits (38^279+1)^2-2, 882 digits (38^3490+1)^2-2, 11027 digits
 2016-04-18, 18:39 #3 wombatman I moo ablest echo power!     May 2013 33038 Posts Base 26 Double-checked the range from n=1 to n=14083. Found the following primes (3-PRP and N-1/N+1 via PFGW): Code: (26^8+1)^2-2 (26^78+1)^2-2 (26^79+1)^2-2 (26^111+1)^2-2 (26^159-1)^2-2 (26^879-1)^2-2 (26^4744-1)^2-2 (26^5276+1)^2-2 (26^5602-1)^2-2 (26^8226+1)^2-2
2016-04-18, 22:28   #4
lalera

Jul 2003

25216 Posts

Quote:
 Originally Posted by wombatman Double-checked the range from n=1 to n=14083. Found the following primes (3-PRP and N-1/N+1 via PFGW): Code: (26^8+1)^2-2 (26^78+1)^2-2 (26^79+1)^2-2 (26^111+1)^2-2 (26^159-1)^2-2 (26^879-1)^2-2 (26^4744-1)^2-2 (26^5276+1)^2-2 (26^5602-1)^2-2 (26^8226+1)^2-2
... and
(26^1+1)^2-2
(26^2+1)^2-2

 2016-04-20, 08:30 #5 axn     Jun 2003 2×13×181 Posts Update on bases 12 and 18 base 12 searched upto 30,000 (continuing to 50,000) Code: (12^1+1)^2-2 (12^2+1)^2-2 (12^3-1)^2-2 (12^8+1)^2-2 (12^29-1)^2-2 (12^51-1)^2-2 (12^60+1)^2-2 (12^513+1)^2-2 (12^1047+1)^2-2 (12^7021+1)^2-2 (12^7506+1)^2-2 (12^7824-1)^2-2 (12^15456-1)^2-2 (12^22614-1)^2-2 (12^28312-1)^2-2 base 18 searched upto 26,000 (sieved upto 100,000, continuing till i'm bored) Code: (18^1+1)^2-2 (18^2-1)^2-2 (18^8-1)^2-2 (18^10+1)^2-2 (18^21+1)^2-2 (18^25+1)^2-2 (18^30-1)^2-2 (18^31+1)^2-2 (18^98-1)^2-2 (18^110-1)^2-2 (18^185-1)^2-2 (18^912-1)^2-2 (18^1083+1)^2-2 (18^2514-1)^2-2 (18^4074-1)^2-2 (18^10208-1)^2-2 (18^15123-1)^2-2 (18^19395-1)^2-2 All proven primes, and available in factordb (the larger ones apparently cannot be proven in factordb, even though N+1 is adequately factored).
2016-04-20, 08:55   #6
axn

Jun 2003

2×13×181 Posts

Quote:
 Originally Posted by rogue Carol Primes (b^n-1)^2-2: Code:  base 2 (n < 100000) 2, 3, 4, 6, 7, 10, 12, 15, 18, 19, 21, 25, 27, 55, 129, 132, 159, 171, 175, 315, 324, 358, 393, 435, 786, 1459, 1707, 2923, 6462, 14289, 39012, 51637 2 (n > 100000) 100224, 108127, 110953, 175749, 185580, 226749, 248949, 253987, 520363 6 6, 7, 20, 47, 255, 274, 279, 308, 1162, 2128, 3791, 9028, 9629, 10029, 13202, 38660, 46631, 48257 10 8, 21, 123, 4299, 6128, 11760, 18884, 40293 14 1, 6, 13, 45, 74, 240, 553, 12348, 13659 22 8, 35, 88, 503, 8642, 8743, 14475 26 159, 879, 4744, 5602 38 1, 2, 13, 560 204 5, 7, 40, 11867, 14458, 1752, 18929 Kynea Primes (b^n+1)^2-2: Code:  base 2 (n < 100000) 1, 2, 3, 5, 8, 9, 12, 15, 17,18, 21, 23, 27, 32, 51, 65, 87, 180, 242, 467, 491, 501, 507, 555, 591, 680, 800, 1070, 1650, 2813, 3281, 4217, 5153, 6287, 6365, 10088, 10367, 37035, 45873, 69312 2 (n > 100000) 102435, 106380, 108888, 110615, 281621, 369581, 376050, 442052 6 9, ,12, 30, 49, 56, 115, 118, 376, 432, 1045, 1310, 6529, 7768, 8430, 21942, 26930, 33568 10 22, 123, 351, 1061 14 1, 5, 60, 72, 118, 181, 245, 310, 498, 820, 962, 2212, 3928, 584, 5937 22 3, 166, 814, 1851, 2197, 3172, 3865, 19791 26 1, 2, 8, 78, 79, 111, 5276, 8226 38 6, 279, 3490 204 40, 3645, 23750
Mark, some of the smaller primes seem to be missing from this list (possibly because cksieve sieves them out). I have generated all primes for 6 <= b <= 100, n <= 64 using PARI/GP.

Carol
Code:
6:1,2,6,7,20,47
10:1,8,21
12:3,29,51
14:1,6,13,45
18:2,8,30
20:1,2,53
22:1,8,35
24:2,27
26:
28:1,22
30:1,6,19,30
34:1,4
38:1,2,13
40:4,15,39
42:3,6,14,15,29
44:1,7,30
46:12
48:1,2,4,6,12,13
50:1,3,4,9,31
52:2,14,24
54:9,17
56:1,2,3,11
58:
60:2,5
62:1
66:12
68:4,59
70:1,5,9,18,24
72:1,9
74:
76:1,2,32,37,51
78:1,2
80:
82:24
84:4
86:3,39
88:2,5,9
90:1,5,43
92:3,4,6,60
94:1,2
96:5
98:2,21
Kynea
Code:
6:1,2,3,4,9,12,30,49,56
10:22
12:1,2,8,60
14:1,5,60
18:1,10,21,25,31
20:1,15,44
22:3
24:24
26:1,2,8
28:1,2,11,15
30:2,3,57
34:1,2,14,29,61
38:6
40:2,49
42:1,3,4
44:3
46:1,54
48:1
50:4,38
52:3,5
54:1
56:8,14
58:2,21,35
60:1,9,21,49
62:1,2
66:
68:1,3,6,32
70:1,7,11
72:
74:1,3
76:1,2,3,22,29
78:3,5,13
80:29,34,45
82:3,9
84:
86:8,18,36
88:1,40
90:11
92:1,2
94:5
96:2,13,15,54
98:4,12,35

 2016-04-20, 17:20 #7 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 100011101000112 Posts Here is my small extension to Anand's table above. So far I have these (I run them all together sorted by size) Carol Primes (b^n-1)^2-2: Code: 10: 1,8,21,123,4299,6128,11760,18884,40293 (known) [79631] 20: 1,2,53,183,1281,1300,8041,29936 [61385] 30: 1,6,19,30,166,495,769,826,1648,3993 [53812] 40: 4,15,39,138,2153,4084,5639 [50000] Kynea Primes (b^n+1)^2-2: Code: 10: 22,351,1061 (known) [79631] 20: 1,15,44,77,141,208,304,1169,3359,5050,22431,34935 [61385] 30: 2,3,57,129,171,9837,30359 [53812] 40: 2,49,144,825,2856,2996,5166,7824,9392,40778 [50000]
 2016-04-21, 17:34 #8 lalera     Jul 2003 2×33×11 Posts hi, here are the results for carol / kynea b=6, n=1 to 50000 Code: (6^1-1)^2-2 (6^2-1)^2-2 (6^6-1)^2-2 (6^1+1)^2-2 (6^2+1)^2-2 (6^3+1)^2-2 (6^4+1)^2-2 (6^7-1)^2-2 (6^9+1)^2-2 (6^12+1)^2-2 (6^20-1)^2-2 (6^30+1)^2-2 (6^47-1)^2-2 (6^49+1)^2-2 (6^56+1)^2-2 (6^115+1)^2-2 (6^118+1)^2-2 (6^255-1)^2-2 (6^274-1)^2-2 (6^279-1)^2-2 (6^308-1)^2-2 (6^376+1)^2-2 (6^432+1)^2-2 (6^1045+1)^2-2 (6^1162-1)^2-2 (6^1310+1)^2-2 (6^2128-1)^2-2 (6^3791-1)^2-2 (6^6529+1)^2-2 (6^7768+1)^2-2 (6^8430+1)^2-2 (6^9028-1)^2-2 (6^9629-1)^2-2 (6^10029-1)^2-2 (6^13202-1)^2-2 (6^21942+1)^2-2 (6^26930+1)^2-2 (6^33568+1)^2-2 (6^38660-1)^2-2 (6^46631-1)^2-2 (6^48257-1)^2-2 please keep my reservation for base 6
 2016-04-21, 18:08 #9 lalera     Jul 2003 11228 Posts hi, here are the results for carol / kynea b=74, n=1 to 20000 Code: (74^1+1)^2-2 (74^3+1)^2-2 (74^183-1)^2-2 (74^694+1)^2-2 (74^2300-1)^2-2 (74^3855-1)^2-2 continuing
 2016-04-28, 22:36 #10 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 2·3·5·191 Posts Base 24 tested until n=10k primes: Code: (24^24+1)^2-2 (24^27-1)^2-2 (24^92-1)^2-2 (24^321+1)^2-2 (24^971+1)^2-2 (24^984+1)^2-2 (24^4950-1)^2-2
 2016-04-29, 00:10 #11 WMHalsdorf     Feb 2005 Bristol, CT 10018 Posts (120^6-1)^2-2 (120^7-1)^2-2 (120^11-1)^2-2 (120^12-1)^2-2 (120^12+1)^2-2 (120^16+1)^2-2 (120^168-1)^2-2 (120^236+1)^2-2 (120^1501+1)^2-2 (120^2249+1)^2-2 (120^2750-1)^2-2 (120^3421+1)^2-2 Currently up to 7000

 Similar Threads Thread Thread Starter Forum Replies Last Post rogue And now for something completely different 258 2020-10-06 14:46 emily Math 34 2017-07-16 18:44 rogue And now for something completely different 37 2016-06-18 17:58 science_man_88 Lounge 10 2010-12-13 23:26 troels munkner Miscellaneous Math 4 2006-06-02 08:35

All times are UTC. The time now is 03:14.

Tue Oct 20 03:14:47 UTC 2020 up 40 days, 25 mins, 0 users, load averages: 1.76, 1.74, 1.77