Part 1, longest CC's
Part 2, smallest existing CC's of given length
Part 3, largest known CC's of given length:
2 3 4
5 6 7
8 9 10
11 12 13
14 15 16
17
Part 4, record history for length: 2 3 4
5 6 7
8 9 10
11 12 13
14 15 16
17
Part 5, programs that were used
Links
Cunningham Chain records (last updated: October 17th, 2009) ----------------------------------------------------------- NEWSFLASH: Tom Wu improved the Sophie Germain (CC2, 1st kind) record. Note: A large CC of length n will be also listed in the section(s) for CC of length n-1, n-2, ..., if it is large enough. A Cunningham Chain (abbreviation: CC) is a sequence of nearly doubled primes. One distinguishes between Cunningham Chains of length n of the 1st kind: n primes, each which is twice the proceeding one plus one; for example (p, 2p+1, 4p+3, 8p+7) is a CC of length 4 of the 1st kind, if each of the four numbers is prime, Cunningham Chains of length n of the 2nd kind: n primes, each which is twice the proceeding one minus one; for example (p, 2p-1, 4p-3, 8p-7) is a CC of length 4 of the 2nd kind, if each of the four numbers is prime, In the following "CC2" stands for "Cunningham Chain of length 2", "CC3" stands for "Cunningham Chain of length 3" and so on. Only the first member of each CC is shown below! As far as the programs that were used to find the CC are known to me they are written in brackets! Some of the records are marked with a short form for month/year instead of the year! Part 1, longest CC's: --------------------- Jaroslaw Wroblewski found CC's of length 17: 2759832934171386593519 (22 digits, CC17, 1st kind, 05/08) 1302312696655394336638441 (25 digits, CC17, 2nd kind, 06/08) 127806074555607670094731 (24 digits, CC17, 2nd kind, 06/08) 40244844789379926979141 (23 digits, CC17, 2nd kind, 06/08) Tony Forbes found a CC of length 16 in 1997: 3203000719597029781 (19 digits, CC16, 2nd kind, 12/97) Phil Carmody and Paul Jobling found a CC16, 1st kind: 810433818265726529159 (21 digits, CC16, 1st kind, 02/02) Part 2, smallest existing CC's of given length: ----------------------------------------------- 810433818265726529159 (21 digits, CC16, 1st kind, Carmody/Jobling, 02/02) 3203000719597029781 (19 digits, CC16, 2nd kind, Forbes, 12/97) 69257563144280941 (17 digits, CC15, 2nd kind, Jobling, 1999) 95405042230542329 (17 digits, CC14, 1st kind, Jobling, 1999) 107588900851484911 (18 digits, CC14, 2nd kind, Jobling, 1999) 4090932431513069 (16 digits, CC13, 1st kind, Brennen, 1998) 758083947856951 (15 digits, CC13, 2nd kind, Loeh, 1989) 554688278429 (12 digits, CC12, 1st kind, Loeh, 1989) 216857744866621 (15 digits, CC12, 2nd kind, Loeh, 1989) 665043081119 (12 digits, CC11, 1st kind, Loeh, 1989) 1389122693971 (13 digits, CC11, 2nd kind, Loeh, 1989) 26089808579 (11 digits, CC10, 1st kind, Loeh, 1989) 205528443121 (12 digits, CC10, 2nd kind, Loeh, 1989) 85864769 (8 digits, CC9, 1st kind, Loeh, 1989) 857095381 (9 digits, CC9, 2nd kind, Loeh, 1989) 19099919 (8 digits, CC8, 1st kind, Nelson/Meeus, 1980/81) 15514861 (8 digits, CC8, 2nd kind, Lalout/Meeus, 1980/81) 1122659 (7 digits, CC7, 1st kind, Lehmer) 16651 (5 digits, CC7, 2nd kind, Lehmer) Part 3, largest known CC's of given length: ------------------------------------------- CC2, 1st kind: -------------- 607095*2^176311-1, 53081 digits, 09/09, Wu(LLR) 48047305725*2^172403-1, 51910 digits, 01/07, Underbakke(TwinGen/LLR) 137211941292195*2^171960-1, 51780 digits, 05/06, Jarai/Farkas/Csajbok/Kasza/Jarai CC2, 2nd kind: -------------- 581627055*2^93181+1, 28060 digits, 08/09, Augustin(NewPGen/PFGW) 3853775193*2^80000+1, 24092 digits, 05/07, Nair(NewPGen/LLR) 1504084599*2^78341+1, 23593 digits, 04/04, Sun(PRP/NewPGen/Proth) CC3, 1st kind: -------------- 164210699973*2^26326-1, 7937 digits, 08/06, Paridon(NewPGen/PFGW) 3020255265*2^20023-1, 6038 digits, 04/05, Sun(NewPGen/PFGW) 16219299585*2^16612-1, 5011 digits, 01/05, Paridon(NewPGen/PFGW) CC3, 2nd kind: -------------- 2366867925*2^17206+1, 5189 digits, 10/04, Sun(NewPGen/PFGW) 1793349831*2^15255+1, 4602 digits, 07/04, Sun(NewPGen/PFGW) 1110159213*2^15164+1, 4574 digits, 10/02, Angel/Augustin/Jobling(NewPGen/PRP/Proth) CC4, 1st kind: -------------- 119184698*5501#-1, 2354 digits, 06/05, Sun(NewPGen/PFGW) 5226562112*3067#-1, 1315 digits, 08/04, Sun(NewPGen/PFGW) 23985240*3067#-1, 1313 digits, 07/04, Sun(NewPGen/PFGW) CC4, 2nd kind: -------------- 1453501013*4127#+1, 1770 digits, 03/05, Sun(NewPGen/PrimeForm) 153344568*4001#+1, 1711 digits, 04/04, Sun(NewPGen/PrimeForm) 131853904032*3061#+1, 1313 digits, 01/03, Broadhurst(PrimeForm) CC5, 1st kind: -------------- 357487161295*1693#-1, 727 digits, 15/05/08, Augustin(NewPGen/PFGW) 5641833966*1657#-1, 712 digits, 07/09, Augustin(NewPGen/PFGW) 7951551045*1637#-1, 709 digits, 07/09, Augustin(NewPGen/PFGW) CC5, 2nd kind: -------------- 2559793087*1499#+1, 645 digits, 10/09, Augustin(NewPGen/PFGW) 23253485008*1493#+1, 643 digits, 10/09, Augustin(NewPGen/PFGW) 19594193737*1481#+1, 630 digits, 09/09, Augustin(NewPGen/PFGW) CC6, 1st kind: -------------- 687237198*1013#+1566180686069, 431 digits, 05/08, Wolter/Andersen(Primo) 33692909611*977#-1, 417 digits, 10/04, Augustin(NewPGen/PFGW) 1093794440403*677#-1, 296 digits, 06/08, Augustin(NewPGen/PFGW) CC6, 2nd kind: -------------- 37783362904*1097#+1, 475 digits, 06/06, Augustin(NewPGen/PFGW) 974518244*823#+24864599761, 351 digits, 04/08, Wolter/Andersen(Primo) 703632724*787#+94265010841, 336 digits, 09/04, Andersen(Primo) CC7, 1st kind: -------------- 1178137903623*661#-1, 291 digits, 07/08, Augustin(NewPGen/PFGW) 1283378648*547#+24329885579, 232 digits, 04/06, van Willegen/Andersen(Primo) 14180848107*487#-1, 211 digits, 11/04, Augustin(NewPGen/PFGW) CC7, 2nd kind: -------------- 668302064*593#+786153598231, 251 digits, 05/08, Wolter/Andersen(Primo) 414792720846*557#+1, 237 digits, 03/06, Augustin(NewPGen/PFGW) 782350985*503#+2189997811, 218 digits, 02/06, Andersen(Primo) CC8, 1st kind: -------------- 2*65728407627*431#-1, 186 digits, 08/05, Augustin(NewPGen/PFGW) 1352438530*311#+5705699, 135 digits, 05/04, Alm/Andersen(Primo) 2*441202409405*239#-1, 108 digits, 03/09, Augustin(NewPGen/PFGW) CC8, 2nd kind: -------------- 269149854*311#+1565403841, 134 digits, 05/04, Alm/Andersen(Primo) 2*2668770761558*241#+1, 112 digits, 02/09, Augustin(NewPGen/PFGW) 177497325593*229#+1, 103 digits, 06/02, Augustin(NewPGen/PFGW) CC9, 1st kind: -------------- 65728407627*431#-1, 185 digits, 08/05, Augustin(NewPGen/PFGW) 441202409405*239#-1, 108 digits, 03/09, Augustin(NewPGen/PFGW) 117739809608*233#-1, 105 digits, 03/09, Augustin(NewPGen/PFGW) CC9, 2nd kind: -------------- 2668770761558*241#+1, 111 digits, 02/09, Augustin(NewPGen/PFGW) 2*1070828503293*239#+1, 109 digits, 07/09, Augustin(NewPGen/PFGW) 745395266*211#+1503602101, 94 digits, 05/04, Alm/Andersen(Primo) CC10, 1st kind: --------------- 1324846487162*223#-1, 99 digits, 05/09, Augustin(NewPGen/PFGW) 3462418*151#+5286829397849, 66 digits, 05/04, Alm/Andersen(Primo) 9440733252109*127#-1, 62 digits, 11/08, Augustin(NewPGen/PFGW) CC10, 2nd kind: --------------- 1070828503293*239#+1, 109 digits, 07/09, Augustin(NewPGen/PFGW) 145683282311*181#+1, 84 digits, 10/05, Augustin(NewPGen/PFGW) 3886637*151#+26473215718951, 66 digits, 05/04, Alm/Andersen(Primo) CC11, 1st kind: --------------- 4608461*107#+178414906509839, 50 digits, 05/04, Alm/Andersen(Primo) 2*(4431659*89#+440181861259139)+1, 42 digits, 02/06, Andersen(Primo) 4988343*89#+334478187443399, 42 digits, 02/06, Andersen(Primo) CC11, 2nd kind: --------------- 2*13931865163581*127#+1, 63 digits, 12/08, Augustin(NewPGen/PFGW) 22101339771043*127#+1, 62 digits, 12/08, Augustin(NewPGen/PFGW) 2*(8428860*127#+212148902055091)-1, 56 digits, 02/06, Andersen(Primo) CC12, 1st kind: --------------- 4431659*89#+440181861259139, 42 digits, 02/06, Andersen(Primo) 2*1753286498051*71#-1, 40 digits, 12/05, Augustin(NewPGen/PFGW) 1307465*79#+11500298799989, 37 digits, 05/04, Alm/Andersen(Primo) CC12, 2nd kind: --------------- 13931865163581*127#+1, 62 digits, 12/08, Augustin(NewPGen/PFGW) 8428860*127#+212148902055091, 56 digits, 02/06, Andersen(Primo) 2878012319891*107#+1, 55 digits, 11/08, Augustin(NewPGen/PFGW) CC13, 1st kind: --------------- 1753286498051*71#-1, 39 digits, 12/05, Augustin(NewPGen/PFGW) 11817507788772*41#-1, 28 digits, 12/08, Augustin(NewPGen/PFGW) 1162623*59#+90771380489789, 28 digits, 05/04, Andersen(Primo) CC13, 2nd kind: --------------- 2*335898524600734221050749906451371-1, 33 digits, 08/08, Andersen(Primo) 331145128052665930985806878883831, 33 digits, 08/08, Andersen(Primo) 252380597488715185263747869755861, 33 digits, 08/08, Andersen (Primo) CC14, 1st kind: --------------- 9510321949318457733566099, 25 digits, 06/04, Andersen(Primo) 25514979074338597984139, 23 digits, 10/04, Alm/Andersen(Primo) 23138440739489691595979, 23 digits, 10/04, Alm/Andersen(Primo) CC14, 2nd kind: --------------- 335898524600734221050749906451371, 33 digits, 08/08, Andersen(Primo) 2*28320350134887132315879689643841-1, 32 digits, 17/06/08, Wroblewski 36027516322668108492823293067201, 32 digits, 17/06/08, Wroblewski CC15, 1st kind: --------------- 662311489517467124375039, 24 digits, 29/05/08, Wroblewski 196426752643710966405599, 24 digits, 28/05/08, Wroblewski 11993367147962683402919, 23 digits, 10/04, Alm/Andersen(Primo) CC15, 2nd kind: --------------- 28320350134887132315879689643841, 32 digits, 17/06/08, Wroblewski 2*2368823992523350998418445521-1, 28 digits, 26/06/08, Wroblewski 71838292723844326926417601, 26 digits, 12/06/08, Wroblewski CC16, 1st kind: --------------- 91304653283578934559359, 23 digits, 29/05/08, Wroblewski 2*2759832934171386593519+1, 22 digits, 27/05/08, Wroblewski 892390227741617675069, 21 digits, 02/02, Carmody/Jobling(GenSv) CC16, 2nd kind: --------------- 2368823992523350998418445521, 28 digits, 26/06/08, Wroblewski 20193491108493165642344881, 26 digits, 12/06/088, Wroblewski 2*1302312696655394336638441-1, 25 digits, 10/06/08, Wroblewski CC17, 1st kind: --------------- 2759832934171386593519, 22 digits, 27/05/08, Wroblewski CC17, 2nd kind: --------------- 1302312696655394336638441, 25 digits, 10/06/08, Wroblewski 127806074555607670094731, 24 digits, 05/06/08, Wroblewski 40244844789379926979141, 23 digits, 05/06/08, Wroblewski Part 4, record history ----------------------- CC2, 1st (Sophie Germain): -------------------------- 53081 digits, 09/09, Wu(LLR) (607095*2^176311-1) 51910 digits, 01/07, Underbakke(TwinGen/LLR) (48047305725*2^172403-1) 51780 digits, 05/06, Jarai/Farkas/Csajbok/Kasza/Jarai (137211941292195*2^171960-1) 36523 digits, 01/05, Predrag Minovic(TwinGen/LLR) (7068555*2^121301-1) 34547 digits, 01/03, Underbakke(TwinGen/PRP/Proth) (2540041185*2^114729-1) 29628 digits, 11/02, Angel/Augustin/Jobling(NewPGen/PFGW) (18912879*2^98395-1) 24432 digits, 08/02, Angel/Augustin/Jobling(NewPGen/PFGW/Proth) (1213822389*2^81131-1) 20013 digits, 02/01, Underbakke(NewPGen/Proth) (109433307*2^66452-1) 18075 digits, 03/00, Indlekofer/Jarai/Wassing (3714089895285*2^60000-1) 9853 digits, 01/00, Lifchitz (18131*22817#-1) 9825 digits, 1999, KerchnerIII(Proth) (18458709*2^32611-1) 7285 digits, 1999, KerchnerIII(Proth) (14516877*2^24176-1) 7119 digits, 1998, Gallot (72021*2^23630-1) 5726 digits, 1998, Ballinger(Proth) (276311*2^19003+1) 5122 digits, 1998, KerchnerIII(Proth) (92305*2^16998+1) 5082 digits, 1995, Dubner (8069496435*10^5072-1) 4932 digits, 1995, Jarai/Indlekofer (470943129*2^16352-1) 4536 digits, 1994, Dubner (5415312903*10^4526-1) 3010 digits, 1993, Dubner (47013511545*10^2999-1) 2039 digits, 1992, Dubner (2926924*10^2032+1) 1863 digits, 1990, Dubner (713851138*10^1854+1) 1812 digits, 1987, Keller (39051*2^6001-1) CC2, 2nd: --------- 28060 digits, 08/09, Augustin(NewPGen/PFGW) (581627055*2^93181+1) 24092 digits, 05/07, Nair(NewPGen/LLR) (3853775193*2^80000+1) 23593 digits, 04/04, Sun(PRP/NewPGen/Proth) (1504084599*2^78341+1) 15840 digits, 12/03, Sun(PRP/NewPGen/Proth) (863710323*2^52588+1) 15060 digits, 11/03, Chaffy(Proth) (55003425*2^50000+1) 15000 digits, 2003, Rouse(Proth) (164581485*2^49800+1) 12116 digits, 11/00, Augustin/Jobling(NewPGen/PRP) (675558849*2^40217+1) 10264 digits, 1998, Lifchitz/Gallot (16769025*2^34071+1) 7190 digits, 1993, Young (but recognized as CC2 many years later) (15015*2^23870+1) CC3: ---- 7937 digits, 08/06, Paridon(NewPGen/PFGW) (164210699973*2^26326-1) 6038 digits, 04/05, Sun(NewPGen/PFGW) (3020255265*2^20023-1) 5189 digits, 10/04, Sun(NewPGen/PFGW) (2366867925*2^17206+1) 4807 digits, 07/04, Sun(NewPGen/PFGW) (2288999415*2^15937-1) 4574 digits, 10/02, Angel/Augustin/Jobling(NewPGen/PRP/Proth) (1110159213*2^15164+1) 3713 digits, 09/02, Herranen(PFGW) (5040102231*2^12301-1) 3710 digits, 07/02, Angel/Augustin/Jobling(NewPGen/PFGW/Proth) (268382583*2^12294-1) 3086 digits, 09/01, Angel/Augustin/Jobling(NewPGen/PRP/Proth) (1838313165*2^10219-1) 3052 digits, 08/01, Angel/Augustin/Jobling(NewPGen/PRP/Proth) (1531785651*2^10107+1) 2475 digits, 2000, Nikkel,St./Nikkel,T.(Proth) (1361835195*2^8191+1) 2006 digits, 06/00, Augustin/Jobling(NewPGen/PFGW) (1568753260*4673#+1) 2004 digits, 2000, Scott/Gallot (1999446945*2^6626-1) 1515 digits, 1998, Roonguthai(Proth) (734257203*2^5000+1) 1213 digits, 20/5/98, Roonguthai(Proth) (384205437*2^4000-1) 1000 digits, 7/5/98, Roonguthai(Proth 4.01) (651358155*2^3291-1) CC4: ---- 2354 digits, 06/05, Sun(NewPGen/PFGW) (119184698*5501#-1) 1770 digits, 03/05, Sun(NewPGen/PrimeForm) (1453501013*4127#+1) 1711 digits, 04/04, Sun(NewPGen/PrimeForm) (153344568*4001#+1) 1313 digits, 01/03, Broadhurst(PrimeForm) (131853904032*3061#+1) 1308 digits, 10/02, Angel/Augustin/Jobling(NewPGen/PFGW) (1707223185*3049#-1) 1303 digits, 09/02, Angel/Augustin/Jobling(NewPGen/PFGW) (356701232*3041#+1) 1117 digits, 09/01, Frind(NewPGen/PFGW) (433098705*2633#-1) 1019 digits, 08/00, Augustin/Jobling(NewPGen/PFGW) (742155874*2381#-1) 506 digits, 17/6/00, Augustin(NewPGen/PFGW) (92406026*1187#+1) 429 digits, 10/6/00, Augustin(NewPGen/PFGW) (35443364*1013#-1) 301 digits, 01/00, Augustin(Proth) (164285535*2^972+1) 241 digits, 10/99, Augustin(Proth) (723592485*2^770+1) CC5: ---- 727 digits, 05/08, Augustin(NewPGen/PFGW) (357487161295*1693#-1) 613 digits, 11/04, Augustin(NewPGen/PFGW) (1719674368*1447#+1) 540 digits, 09/04, Andersen(Primo) (496391760*1277#+325305140161) 509 digits, 02/02, Augustin(NewPGen/PFGW) (51946113*1193#+1) 460 digits, 11/01, Augustin(NewPGen/PFGW) (148809453*1069#-1) 422 digits, 08/01, Frind(NewPGen/PFGW) (828114253*991#-1) 407 digits, 08/00, Augustin(NewPGen/PFGW) (504856309*953#-1) 339 digits, 07/00, Augustin(NewPGen/PFGW) (427383180*797#-1) 257 digits, 20/06/00, Augustin(NewPGen/PFGW) (1217763452*601#-1) 207 digits, 07/06/00, Augustin(NewPGen/PFGW) (206262090*479#-1) 115 digits, 03/00, Augustin(NewPGen/Proth) (463419585*2^353-1) 102 digits, 01/00, Augustin(Proth) (518179995*2^308+1) 86 digits, 12/99, Augustin(Proth) (96952995*2^258-1) 78 digits, 11/99, Jobling (9006546615*2^223-1) 76 digits, 10/99, Augustin(Proth) (392651625*2^222+1) CC6: ---- 475 digits, 06/06, Augustin(NewPGen/PFGW) (37783362904*1097#+1) 417 digits, 10/04, Augustin(NewPGen/PFGW) (33692909611*977#-1) 336 digits, 09/04, Andersen(Primo) (703632724*787#+94265010841) 318 digits, 09/04, Augustin(NewPGen/PFGW) (42693782492*739#+1) 279 digits, 09/04, Andersen(Primo) (2197316072*647#+105063678721) 222 digits, 01/03, Chaffey (6302319587*509#+1) 213 digits, 09/01, Augustin(NewPGen/PFGW) (716250935*491#-1) 208 digits, 08/00, Augustin(NewPGen/PFGW) (1056231420*479#+1) 142 digits, 20/06/00, Augustin(NewPGen/PFGW) (388562456*331#+1) 120 digits, 03/06/00, Augustin(NewPGen/PFGW) (2*305372608*271#+1) 85 digits, 26/10/99, Augustin(Proth) (620060805*2^252-1) 56 digits, 19/10/99, Augustin(Proth) (505054485*2^154-1) CC7: ---- 291 digits, 07/08, Augustin(NewPGen/PFGW) (1178137903623*661#-1) 251 digits, 05/08, Wolter/Andersen(Primo) (668302064*593#+786153598231) 237 digits, 03/06, Augustin(NewPGen/PFGW) (414792720846*557#+1) 218 digits, 02/06, Andersen(Primo) (782350985*503#+2189997811) 211 digits, 11/04, Augustin(NewPGen/PFGW) (14180848107*487#-1) 165 digits, 05/04, Alm/Andersen(Primo) (472063086*383#+1236845609) 153 digits, 06/02, Augustin(NewPGen/PFGW) (406605710992*349#-1) 128 digits, 09/01, Augustin(NewPGen/PFGW) (2310290388*283#+1) 123 digits, 08/00, Augustin(NewPGen/PFGW) (1701815519*277#+1) 87 digits, 07/00, Augustin(NewPGen/PFGW) (843616025*193#+1) 69 digits, 06/00, Augustin(NewPGen/PFGW) (1953370903*151#-1) 43 digits, 12/99, Jobling (460668119835*2^101-1) 31 digits, 11/99, Augustin/Jobling(Primeform) (27215953890276787*37#*2^3-1) 27 digits, 10/99, Augustin(Proth) (666325605*2^60+1) CC8: ---- 186 digits, 08/05, Augustin(NewPGen/PFGW) (2*65728407627*431#-1) 135 digits, 05/04, Alm/Andersen(Primo) (1352438530*311#+5705699) 103 digits, 06/02, Augustin(NewPGen/PFGW) (177497325593*229#+1) 82 digits, 06/00, Augustin(NewPGen/PFGW) (548879116*181#-1) 52 digits, 13/6/00, Augustin(NewPGen/PFGW) (1831430532*107#+1) 44 digits, 1/6/00, Augustin(NewPGen/PFGW) (1742368093*89#-1) 25 digits, 03/00, Augustin(NewPGen/Proth) (1360673835*2^50-1) 23 digits, 12/99, Jobling (36097525695*2^41-1) CC9: ---- 185 digits, 08/05, Augustin(NewPGen/PFGW) (65728407627*431#-1) 94 digits, 05/04, Alm/Andersen(Primo) (745395266*211#+1503602101) 58 digits, 04/01, Augustin(NewPGen/PFGW) (2093307780*127#-1) 50 digits, 12/00, Augustin(NewPGen/PFGW) (1061169280*103#+1) 37 digits, 10/00, Augustin(NewPGen/PFGW) (43105142*73#+1) CC10: ----- 109 digits, 07/09, Augustin(NewPGen/PFGW) (1070828503293*239#+1) 99 digits, 05/09, Augustin(NewPGen/PFGW) (1324846487162*223#-1) 84 digits, 10/05, Augustin(NewPGen/PFGW) (145683282311*181#+1) 66 digits, 05/04, Alm/Andersen(Primo) (3886637*151#+26473215718951) 51 digits, 06/02, Augustin(NewPGen/PFGW) (8296886802*103#+1) 39 digits, 15/12/00, Augustin(NewPGen/PFGW) (3440034726*73#-1) 33 digits, 3/12/00, Augustin(NewPGen/PFGW) (1308811392*61#-1) CC11: ----- 63 digits, 12/08, Augustin(NewPGen/PFGW) (2*13931865163581*127#+1) 56 digits, 02/06, Andersen(Primo) (2*(8428860*127#+212148902055091)-1) 53 digits, 12/05, Augustin(NewPGen/PFGW) (792619264990*103#+1) 50 digits, 05/04, Alm/Andersen(Primo) (4608461*107#+178414906509839) CC12: ----- 62 digits, 12/08, Augustin(NewPGen/PFGW) (13931865163581*127#+1) 56 digits, 02/06, Andersen(Primo) (8428860*127#+212148902055091) 42 digits, 02/06, Andersen(Primo) (4431659*89#+440181861259139) 40 digits, 12/05, Augustin(NewPGen/PFGW) (2*1753286498051*71#-1) 37 digits, 05/04, Alm/Andersen(Primo) (1307465*79#+11500298799989) CC13: ----- 39 digits, 12/05, Augustin(NewPGen/PFGW) (1753286498051*71#-1) 31 digits, 05/04, Andersen(Primo) (938719*67#+56461354019071) CC14: ----- 33 digits, 08/08, Andersen(Primo) (335898524600734221050749906451371) 32 digits, 17/06/08, Wroblewski (2*28320350134887132315879689643841-1) 31 digits, 14/06/08, Wroblewski (2354904873485081880414653783011) 31 digits, 06/06/08, Andersen(Primo) (2337673907855670908145009878491) 26 digits, 05/08, Wroblewski (20299226100350079536373721) 25 digits, 06/04, Andersen(Primo) (9510321949318457733566099) 21 digits, 1997, Forbes (385931755250345784479) CC15: ----- 32 digits, 17/06/08, Wroblewski (28320350134887132315879689643841) 26 digits, 12/06/08, Wroblewski (71838292723844326926417601) 25 digits, 10/06/08, Wroblewski (5830768257311375388822241) 25 digits, 05/06/08, Wroblewski (2817673877915370357723841) 24 digits, 29/05/08, Wroblewski (662311489517467124375039) 24 digits, 28/05/08, Wroblewski (196426752643710966405599) 24 digits, 26/05/08, Wroblewski (105998574608115401372161) 23 digits, 25/05/08, Wroblewski (2*15745040405007366603151-1) 23 digits, 10/04, Alm/Andersen(Primo) (11993367147962683402919) 22 digits, ??, Forbes (4678714760875524493409) 20 digits, 09/97, Forbes (54269795934721528591) CC16: ----- 28 digits, 26/06/08, Wroblewski (2368823992523350998418445521) 26 digits, 12/06/08, Wroblewski (20193491108493165642344881) 25 digits, 10/06/08, Wroblewski (2*1302312696655394336638441-1) 24 digits, 08/06/08, Wroblewski (258296136493222766530021) 24 digits, 05/06/08, Wroblewski (2*127806074555607670094731-1) 23 digits, 29/05/08, Wroblewski (91304653283578934559359) 23 digits, 25/05/08, Wroblewski (15745040405007366603151) 21 digits, 02/02, Carmody/Jobling(GenSv) (892390227741617675069) 19 digits, 12/97, Forbes (3203000719597029781) CC17: ----- 25 digits, 10/06/08, Wroblewski (1302312696655394336638441) 24 digits, 05/06/08, Wroblewski (127806074555607670094731) 23 digits, 05/06/08, Wroblewski (40244844789379926979141) 22 digits, 27/05/08, Wroblewski (2759832934171386593519) Part 5, programs that were used: -------------------------------- NewPGen: -------- Sieving program mainly for numbers of the form k*b^n+/-1, k*p#+/-1, written by Paul Jobling. Visit http://www.utm.edu/research/primes/programs/NewPGen/ PFGW: ----- Prime testing program which allows nearly every form of numbers, written by Chris Nash and speeded up with some additional code from G.Woltman and Y.Gallot. Visit http://pages.prodigy.net/chris_nash/primeform.html or http://groups.yahoo.com/group/primeform PRP: ---- Probable primality test program for numbers of the form k*b^n+/-1, written by George Woltman. Visit http://www.mersenne.org/gimps/ Proth: ------ Full primality test program for numbers of the form k*b^n+/-1, written by Yves Gallot. Visit http://www.utm.edu/research/primes/programs/gallot/ GenSv: ------ A Generic Siever for finding ultra-sparse forms, such as exceptionally long Cunningham Chains. Used by Phil Carmody and Paul Jobling for their longest records. No URL yet, sorry. Primo: ------ Primo is a primality proving program based on the ECPP algorithm: Elliptic Curve Primality Proving. It will test numbers that are not of any special form. Visit http://www.ellipsa.net/ TwinGen: -------- TwinGen is a program to rapidly presieve a set of candidates of the form k.2n+/-1 and remove those candidates which are composite; written by David Underbakke. Visit http://primes.utm.edu/bios/page.php?id=440 LLR: ---- Takes an input file from Paul Jobling's NewPgen, and proves the primality of numbers of the form k*.2^n-1 with k < 2^n; written by Jean Penne. Visit http://primes.utm.edu/bios/page.php?id=431 Remark: ------- Sometimes the "old" Primeform was used to test the full primality of the members of the CC, but I have marked them all with PFGW because PFGW is the successor of Primeform. Please send any new records, corrections or remarks to dirk.augustin@gmx.de
This page started as a text file at
http://groups.yahoo.com/group/primenumbers/files/Prime Tables/Cunningham_Chain_records.txt
That file may currently contain an older version and is only accessible to subscribers of the
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Links:
------
Links to Chris Caldwell's The Prime Pages:
The Top Twenty: Cunningham Chain (1st kind) (only titanic primes)
The Top Twenty: Cunningham Chain (2nd kind) (only titanic primes)
The Prime Glossary: Cunningham
Chain
The Prime Links++ list of Cunningham Chain links
Other links about CC's:
Carlos Rivera's The Prime Puzzles & Problem Connection:
Problem 26.- The earliest Cunningham Chains.
Warut Roonguthai's Yves Gallot's Proth.exe and Cunningham Chains.
(archived, last update in 2000)
Eric Weisstein's MathWorld, Cunningham Chain
Joseph McLean's Cunningham Chains
(the primes are small)
Wikipedia: Cunningham chain
Pages with similar records:
Tony Forbes' Prime k-tuplets
Henri Lifchitz'
BiTwin records
Jens Kruse Andersen's
The largest known CPAP's
Jens Kruse Andersen's The Largest Known Simultaneous Primes