.LOG Kynea primes are of the form 4^k+2^(k+1)-1 = (2^x+1)^2-2 Carol Primes are of the form 4^k-2^(k+1)-1 = (2^x-1)^2-2 WHATS NEW: 6/27/5 Rosink completes checking Carol from 275000 to 325000, noprimes. 4/25/5 Harvey completes Carol from 218000 to 219000, no primes. 3/17/5 Rosink reports Carol checked from 275000 to 291799, 297999 to 310768, & 320000 to 325000 3/11/5 Minivic reports Kynea checked to 250000, no primes; Harvey reserves Carol 218000 to 219000. 2/13/5 Harvey completes Carol from 219000 to 220000, no primes. 1/31/5 Harvey completes Carol from 220000 to 230000; reserves Carol from 219000 to 220000. 1/19/5 Lipinski's reservations will expire on 1/31/5, unless I hear from him before then. 1/11/5 Harvey finds new record Carol prime (2^226749-1)^2-2, 136517 digits. 12/29/4 Minovic reports Kynea base 2 checked to 243000. 12/7/4 Emmanuel reports Carol checked to 200000, reserves Carol & Kynea 250001 to 275000. 12/3/4 Minovic reports Kynea checked to 240000, no new primes. 12/2/4 Harvey reserves carol base 2 from 220000 to 230000. 11/18/4 Emmanuel submits new STATUS page for Carol & Kynea primes 11/3/4 Emmanuel reports a new record Carol Prime (2^185580-1)^2-2. This number has a 111731 digits. 10/27/4 Minovic reports Kynea, base 2, checked to 233000, no new primes; reserves same to 250000. 10/8/4 Emanuel reports a new Carol Prime (2^175749 - 1)^2 - 2. (105812 digits), a new record. 9/27/4 Binnekamp reports no more primes detected in Carol 200000-210000 and Carol base -10 from 50000-75000. 9/15/4 Minovic reserves Kynea, base 2, from 220000 to 240000. 9/8/4 Emanuel reports no new Kynea primes up to 220000. 7/29/4 Emmanuel completes Generalized Carol form (273*2^n -1)^2 - 2 up to 120,527, & stops there. 7/1/4 Rosink puts up progress page at http://1202.org:81/carol.htm 6/29/4 Emmanuel finds (273*2^117629 - 1)^2 - 2 is prime!(70825 digits), continuing on to 125000. 6/28/4 Emmanuel completes Kynea base 2 to 200000, reserves same to 220000. 6/14/4 Emmanuel reports (273*2^k - 1)^2 -2 checked up through 117000. 5/7/4 Rosink reserves Carol base 2 from 275000 to 325000. 4/23/4 Rodenkirch reports (2^108127-1)^2-2 is prime!(65099 digits), completes Carol base 2 to 150000. 4/16/4 Emmanuel reports no primes for Kynea base2 in range 150000 to 173000. 4/7/4 Minovic reports Kynea base2 completed to 150000, no new primes. 4/5/4 Ballinger finds (6^48257-1)^2-2 is prime! (digits:75103) 4/2/4 Broadhurst finds (2^85075+1)^3-2 is prime! (76831 digits), new largest Big-Ears prime. 3/31/4 Broadhurst finds (2^79127+1)^3-2 is prime! (71459 digits). 3/28/4 Balinger reports (6^46631-1)^2-2 is prime!(digits:72572) 3/26/4 Minovic reports Kynea, base 2, checked to 137,000. 3/24 Binnekamp reserves base 10 Carol for k= 50000 to 70000. 3/12/4 Binnekamp finds (10^40293-1)^2 -2 ,digits 80586, a near-repdigit prime (nrd) ,consists only of 9's and one 7 near the center of the number. Rodenkirch reports that the latest versions of ck & multisieve agree in output, so the bug looks squashed. 3/11/4 Rodenkirch reports apparent BUG in ck, ranges tested prior to current version(Feb 3 2004) should be resieved. Bug involves numbers being removed from .abc files without factors being found. So the remedy is to compare the factors log with the .abc files to see if any numbers are unaccounted for, or just resieve & prp test numbers not already prp'd. 3/11/4 Minovic finds (2^106380+1)^2-2, 64048 digits; and reserves Kynea 130000 to 150000. 3/10/4 Rodenkirch reserves Carol to 150000. 2/26/4 Binnekamp reports on base 3 generalization,(2^k-1)^3+2 & (2^k+1)^3-2; and reserves Carol base 10, 30300 to 50000. 2/24/4 Minovic finds (2^108888+1)^2-2, 65558 digits 2/23/4 Minovic finds (2^102435+1)^2-2, 61673 digits. 2/19/4 Minovic finds (2^110615+1)^2-2, 66597 digits, largest Kynea. Ballinger finds (6^38660-1)^2-2, 60167 digits. 2/16/4 Harvey finds (22^19791+1)^2-2, 53136 digits! 2/13/4 Minovic reserves base 2 Kynea from 102000 to 130000. 2/10/4 Wolter adandons base 2, to 150000. 2/9/4 Ballinger reports (6^26930+1)^2-2 and (6^33568+1)^2-2, 52242 digits! 2/4/4 Harvey abandons base 10 at 30300, reserves base 22 to 22000. 1/29/4 Minovic finds (14^12348-1)^2-2, 28305 digits & (14^13659-1)^2-2, 31310 digits. 1/26/4 Binnekamp reports (2^110953-1)^2-2 is prime! New record! Marcin Lipinski reserves base 18 to 50000. Binnekamp reserves Carol base 2 to 200000 to 210000. 1/22/4 Emmanuel reserves base 2 both forms from 150001 to 200000. 1/21/4 Minovic reports base 14 results. Phil Carmody releases ck, a carol/kynea base 2 sieve. 1/19/4 Wolter finds (2^100224-1)^2-2 is prime! New record! 1/17/4 Ray Ballinger reports base 6 primes to 10300, reserves to 20000. 1/16/4 Multisieve now supports sieving of (b^k+1)^2-2, and is FAST! 1/8/4 Thomas Wolter reserves both forms base 2 from 100000 to 150000. Titanic primes of these forms with k less than 15000 were discovered by Cletus Emmanuel. Primality confirmed using OpenPFGW. Items in [ ] are [discoverer date]. The top ten: (2^226749-1)^2-2 [Harvey 1/2005] 136517 digits (2^185580-1)^2-2 [Emmanuel 11/2004] 111731 digits (2^175749-1)^2-2 [Emmanuel 10/2004] 105812 digits (2^110953-1)^2-2 [Binnekamp 2004] 66801 digits (2^110615+1)^2-2 [Minovic 2004] 66597 digits (2^108888+1)^2-2 [Minovic 2004] 65558 digits (2^108127-1)^2-2 [Rodenkirch 2004] 65099 digits (2^106380+1)^2-2 [Minovic 2004] 64048 digits (2^102435+1)^2-2 [Minovic 2004] 61673 digits (2^100224-1)^2-2 [Wolter 2004] 60341 digits All Kynea: 1 (2^0+1)^2 - 2 2 4^1+2^2-1 3 4^2+2^(2+1)-1 4 4^3+2^(3+1)-1 5 4^5+2^(5+1)-1 6 4^8+2^(8+1)-1 7 4^9+2^(9+1)-1 8 4^12+2^(12+1)-1 9 4^15+2^(15+1)-1 10 4^17+2^(17+1)-1 11 4^18+2^(18+1)-1 12 4^21+2^(21+1)-1 13 4^23+2^(23+1)-1 14 4^27+2^(27+1)-1 15 4^32+2^(32+1)-1 16 4^51+2^(51+1)-1 17 4^65+2^(65+1)-1 18 4^87+2^(87+1)-1 19 4^180+2^(180+1)-1 20 4^242+2^(242+1)-1 21 4^467+2^(467+1)-1 22 4^491+2^(491+1)-1 23 4^501+2^(501+1)-1 24 4^507+2^(507+1)-1 25 4^555+2^(555+1)-1 26 4^591+2^(591+1)-1 27 4^680+2^(680+1)-1 28 4^800+2^(800+1)-1 29 4^1070+2^(1070+1)-1 30 4^1650+2^(1650+1)-1 31 4^2813+2^(2813+1)-1 32 4^3281+2^(3281+1)-1 33 4^4217+2^(4217+1)-1 34 4^5153+2^(5153+1)-1 35 4^6287+2^(6287+1)-1 36 4^6365+2^(6365+1)-1 37 4^10088+2^(10088+1)-1 38 4^10367+2^(10367+1)-1 39 4^37035+2^37036-1 [Harvey 2002] 40 4^45873+2^45874-1 [Harvey 2002] 41 4^69312+2^69313-1 [Harvey 2002] 42 (2^102435+1)^2-2 [Minovic 2004] 43 (2^106380+1)^2-2 [Minovic 2004] 44 (2^108888+1)^2-2 [Minovic 2004] 45 (2^110615+1)^2-2 [Minovic 2004] checked to 250000, reserved 250001 to 275000(Emmanuel) All Carol: 1 4^2-2^(2+1)-1 2 4^3-2^(3+1)-1 3 4^4-2^(4+1)-1 4 4^6-2^(6+1)-1 5 4^7-2^(7+1)-1 6 4^10-2^(10+1)-1 7 4^12-2^(12+1)-1 8 4^15-2^(15+1)-1 9 4^18-2^(18+1)-1 10 4^19-2^(19+1)-1 11 4^21-2^(21+1)-1 12 4^25-2^(25+1)-1 13 4^27-2^(27+1)-1 14 4^55-2^(55+1)-1 15 4^129-2^(129+1)-1 16 4^132-2^(132+1)-1 17 4^159-2^(159+1)-1 18 4^171-2^(171+1)-1 19 4^175-2^(175+1)-1 20 4^315-2^(315+1)-1 21 4^324-2^(324+1)-1 22 4^358-2^(358+1)-1 23 4^393-2^(393+1)-1 24 4^435-2^(435+1)-1 25 4^786-2^(786+1)-1 26 4^1459-2^(1459+1)-1 27 4^1707-2^(1707+1)-1 28 4^2923-2^(2923+1)-1 29 4^6462-2^(6462+1)-1 30 4^14289-2^(14289+1)-1 [Emmanuel 2002] 31 4^39012-2^(39012+1)-1 [Harvey 2002] 32 4^51637-2^51638-1 [Binnekamp 2002] 33 (2^100224-1)^2-2 [Wolter 2004] 34 (2^108127-1)^2-2 [Rodenkirch 4/2004] 35 (2^110953-1)^2-2 [Binnekamp 2004] 36 (2^175749-1)^2-2 [Emmanuel 10/2004] 37 (2^185580-1)^2-2 [Emmanuel 11/2004] 38? (2^226749-1)^2-2 [Harvey 1/2005] checked to 210000, checked 218000 to 230000, reserved 250001 to 275000(Emmanuel), checked 275000 to 325000. Generalization: (b^k+/-1)^2-2 base 6 reserved to 50000, checked to 33000(Ballinger) (6^6-1)^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(Ballinger 2/4) (6^38660-1)^2-2(Ballinger 2/4) (6^46631-1)^2-2(Ballinger 3/4)(digits:72572) (6^48257-1)^2-2(Ballinger 4/4) (digits:75103) base 10 checked to 70000 (10^8-1)^2-2 (10^21-1)^2-2 (10^22+1)^2-2 (10^123-1)^2-2 (10^351+1)^2-2 (10^1061+1)^2-2 (10^4299-1)^2-2 (10^6128-1)^2-2 (10^11760-1)^2-2 (10^18884-1)^2-2(Harvey 2/4) (10^40293-1)^2 -2[Binnekamp 3/4] base 14 reserved to 35000, checked to 30000(Minovic) (14^1-1)^2-2 (14^6-1)^2-2 (14^13-1)^2-2 (14^45-1)^2-2 (14^74-1)^2-2 (14^240-1)^2-2 (14^553-1)^2-2 (14^12348-1)^2-2 28305 digits (14^13659-1)^2-2 31310 digits (14^1+1)^2-2 (14^5+1)^2-2 (14^60+1)^2-2 (14^72+1)^2-2 (14^118+1)^2-2 (14^181+1)^2-2 (14^245+1)^2-2 (14^310+1)^2-2 (14^498+1)^2-2 (14^820+1)^2-2 (14^962+1)^2-2 (14^2212+1)^2-2 (14^3928+1)^2-2 (14^5844+1)^2-2 (14^5937+1)^2-2 base 22 checked to 22000 (22^3+1)^2-2 (22^8-1)^2-2 (22^35-1)^2-2 (22^88-1)^2-2 (22^166+1)^2-2 (22^503-1)^2-2 (22^814+1)^2-2 (22^1851+1)^2-2 (22^2197+1)^2-2 (22^3172+1)^2-2 (22^3865+1)^2-2 (22^8643-1)^2-2 (22^8743-1)^2-2 (22^14475-1)^2-2 (22^19791+1)^2-2(Harvey, 2/4) base 26, Carol (26*n-1)^2-2, checked to 22500 (26^159-1)^2-2 (26^879-1)^2-2 (26^4744-1)^2-2 (26^5602-1)^2-2(Harvey 12/4) base 26, Kynea (26*n+1)^2-2, checked to 14084 (26^8+1)^2-2 (26^78+1)^2-2 (26^79+1)^2-2 (26^111+1)^2-2 (26^5276+1)^2-2 (26^8226+1)^2-2(Harvey 12/4) Generalization: (b*2^k+/-1)^2-2 base 3 checked to 10000 (3*2^0-1)^2-2 (3*2^15-1)^2-2 (3*2^21-1)^2-2 (3*2^25-1)^2-2 (3*2^70-1)^2-2 (3*2^129-1)^2-2 (3*2^399-1)^2-2 (3*2^511-1)^2-2 (3*2^856-1)^2-2 (3*2^9574-1)^2-2 (3*2^13+1)^2-2 (3*2^19+1)^2-2 (3*2^20+1)^2-2 (3*2^34+1)^2-2 (3*2^37+1)^2-2 (3*2^40+1)^2-2 (3*2^317+1)^2-2 (3*2^1258+1)^2-2 (3*2^1651+1)^2-2 (3*2^3370+1)^2-2 (3*2^3640+1)^2-2 (3*2^3715+1)^2-2 (3*2^6818+1)^2-2 (3*2^6925+1)^2-2 (3*2^8050+1)^2-2 base 273 checked to 117629+ (Emmanuel), reserved to 125000, (273*2^k-1)^2-2, Generalized Carol (273*2^1 - 1)^2 - 2 (273*2^2 - 1)^2 - 2 (273*2^3 - 1)^2 - 2 (273*2^6 - 1)^2 - 2 (273*2^7 - 1)^2 - 2 (273*2^9 - 1)^2 - 2 (273*2^10 - 1)^2 - 2 (273*2^12 - 1)^2 - 2 (273*2^19 - 1)^2 - 2 (273*2^20 - 1)^2 - 2 (273*2^25 - 1)^2 - 2 (273*2^26 - 1)^2 - 2 (273*2^30 - 1)^2 - 2 (273*2^31 - 1)^2 - 2 (273*2^45 - 1)^2 - 2 (273*2^47 - 1)^2 - 2 (273*2^57 - 1)^2 - 2 (273*2^72 - 1)^2 - 2 (273*2^81 - 1)^2 - 2 (273*2^86 - 1)^2 - 2 (273*2^108 - 1)^2 - 2 (273*2^112 - 1)^2 - 2 (273*2^132 - 1)^2 - 2 (273*2^196 - 1)^2 - 2 (273*2^228 - 1)^2 - 2 (273*2^231 - 1)^2 - 2 (273*2^239 - 1)^2 - 2 (273*2^345 - 1)^2 - 2 (273*2^384 - 1)^2 - 2 (273*2^410 - 1)^2 - 2 (273*2^429 - 1)^2 - 2 (273*2^1687 - 1)^2 - 2 (273*2^2245 - 1)^2 - 2 (273*2^2519 - 1)^2 - 2 (273*2^2714 - 1)^2 - 2 (273*2^2816 - 1)^2 - 2 (273*2^3155 - 1)^2 - 2 (273*2^3956 - 1)^2 - 2 (273*2^4319 - 1)^2 - 2 (273*2^4917 - 1)^2 - 2 (273*2^5913 - 1)^2 - 2 (273*2^7854 - 1)^2 - 2 (273*2^8823 - 1)^2 - 2 (273*2^11650 - 1)^2 - 2 (273*2^14320 - 1)^2 - 2 (273*2^18143 - 1)^2 - 2 (273*2^23185 - 1)^2 - 2 (273*2^43834 - 1)^2 - 2 (273*2^46121 - 1)^2 - 2 (273*2^51488 - 1)^2 - 2 (273*2^51972 - 1)^2 - 2 (273*2^100935 - 1)^2 - 2 (Emmanuel, 7/2) (273*2^117629 - 1)^2 - 2 (Emmanuel, 6/4) Generalization: (2^k-1)^3+2(Noddy number) & (2^k+1)^3-2(Big-Ears number) (2^k-1)^3+2 is prime for: 0,1,2,6,10,16,48,70,1196,3958(Binnecamp 2004),57096,59556,62440,70362(Broadhurst 2004)[88000] (2^k+1)^3-2 is prime for: 3,7,11,15,35,16475,26827(Binnekamp 2004),79127(Broadhurst, 3/4),85075(Broadhurst 4/4)[88000] 11:06 AM 6/27/2005