mersenneforum.org  

Go Back   mersenneforum.org > Prime Search Projects > And now for something completely different

Reply
 
Thread Tools
Old 2016-04-15, 17:28   #1
rogue
 
rogue's Avatar
 
"Mark"
Apr 2003
Between here and the

10111100110112 Posts
Default 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
rogue is online now   Reply With Quote
Old 2016-04-16, 22:26   #2
NorbSchneider
 
NorbSchneider's Avatar
 
"Norbert"
Jul 2014
Budapest

1428 Posts
Default 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
NorbSchneider is offline   Reply With Quote
Old 2016-04-18, 18:39   #3
wombatman
I moo ablest echo power!
 
wombatman's Avatar
 
May 2013

33158 Posts
Default 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
wombatman is offline   Reply With Quote
Old 2016-04-18, 22:28   #4
lalera
 
lalera's Avatar
 
Jul 2003

2·3·101 Posts
Default

Quote:
Originally Posted by wombatman View Post
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
lalera is offline   Reply With Quote
Old 2016-04-20, 08:30   #5
axn
 
axn's Avatar
 
Jun 2003

4,789 Posts
Default 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).
axn is offline   Reply With Quote
Old 2016-04-20, 08:55   #6
axn
 
axn's Avatar
 
Jun 2003

112658 Posts
Default

Quote:
Originally Posted by rogue View Post
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
axn is offline   Reply With Quote
Old 2016-04-20, 17:20   #7
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

2×4,591 Posts
Default

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]
Batalov is offline   Reply With Quote
Old 2016-04-21, 17:34   #8
lalera
 
lalera's Avatar
 
Jul 2003

25E16 Posts
Default

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
lalera is offline   Reply With Quote
Old 2016-04-21, 18:08   #9
lalera
 
lalera's Avatar
 
Jul 2003

25E16 Posts
Default

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
lalera is offline   Reply With Quote
Old 2016-04-28, 22:36   #10
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Cambridge (GMT/BST)

2·3·7·137 Posts
Default

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
henryzz is offline   Reply With Quote
Old 2016-04-29, 00:10   #11
WMHalsdorf
 
WMHalsdorf's Avatar
 
Feb 2005
Bristol, CT

33×19 Posts
Default

(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
WMHalsdorf is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Carol / Kynea Coordinated Search - Reservations rogue And now for something completely different 260 2020-12-02 14:25
Distribution of Mersenne primes before and after couples of primes found emily Math 34 2017-07-16 18:44
Carol / Kynea search (Near-power primes) rogue And now for something completely different 37 2016-06-18 17:58
a 18+ Christmas carol science_man_88 Lounge 10 2010-12-13 23:26
possible primes (real primes & poss.prime products) troels munkner Miscellaneous Math 4 2006-06-02 08:35

All times are UTC. The time now is 13:48.

Fri Dec 4 13:48:59 UTC 2020 up 1 day, 10 hrs, 0 users, load averages: 2.51, 2.30, 2.24

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.