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Title: Math/Number Theory/Prime Numbers - Cunningham Chain Records Sequences of nearly doubled primes, maintained by Dirk Augustin.
Deficient_Factorials A summary of searches for primes of the form n!/k+-1 (k above 1), n!/k!+-1 (k above 3) and n!/n#+-1.

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Cunningham Chain records

Cunningham Chain records

Record list created and maintained by Dirk Augustin.Hosted by Jens Kruse Andersen (home)Part 1, longest CC'sPart 2, smallest existing CC's of given lengthPart 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 usedLinksCunningham Chain records (last updated: September 22nd, 2008)-------------------------------------------------------------NEWSFLASH:Jens Kruse Andersen improved the CC14 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 nearlydoubled primes. One distinguishes betweenCunningham 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 knownto me they are written in brackets!Some of the records are marked with a short form for month/yearinstead 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:--------------48047305725*2^172403-1, 51910 digits, 01/07, Underbakke(TwinGen/LLR)137211941292195*2^171960-1, 51780 digits, 05/06, Jarai/Farkas/Csajbok/Kasza/Jarai7068555*2^121301-1, 36523 digits, 01/05, Predrag Minovic(TwinGen/LLR)CC2, 2nd kind:--------------3853775193*2^80000+1, 24092 digits, 05/07, Nair(NewPGen/LLR)1504084599*2^78341+1, 23593 digits, 04/04, Sun(PRP/NewPGen/Proth)964487139*2^78341+1, 23592 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)3409817710*1277#+312503170979, 541 digits, 04/05/08, Wolter/Andersen(Primo)5864262128*1201#-1, 514 digits, 02/06, Chaffey (NewPGen/PFGW)CC5, 2nd kind:--------------1719674368*1447#+1, 613 digits, 11/04, Augustin(NewPGen/PFGW) 496391760*1277#+325305140161, 540 digits, 09/04, Andersen(Primo) 51946113*1193#+1, 509 digits, 02/02, 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) 579166749*211#+6062216159, 93 digits, 05/04, Alm/Andersen(Primo) CC8, 2nd kind:--------------269149854*311#+1565403841, 134 digits, 05/04, Alm/Andersen(Primo) 177497325593*229#+1, 103 digits, 06/02, Augustin(NewPGen/PFGW)2*(745395266*211#+1503602101)-1, 94 digits, 05/04, Alm/Andersen(Primo)CC9, 1st kind:--------------65728407627*431#-1, 185 digits, 08/05, Augustin(NewPGen/PFGW)115467633*211#+28398049679, 93 digits, 05/04, Alm/Andersen(Primo)173972541674*173#-1, 80 digits, 10/05, Augustin(NewPGen/PFGW)CC9, 2nd kind:--------------745395266*211#+1503602101, 94 digits, 05/04, Alm/Andersen(Primo)2*145683282311*181#+1, 85 digits, 10/05, Augustin(NewPGen/PFGW)122930659949*173#+1, 80 digits, 10/05, Augustin(NewPGen/PFGW)CC10, 1st kind:---------------3462418*151#+5286829397849, 66 digits, 05/04, Alm/Andersen(Primo)117935149928*127#-1, 60 digits, 10/05, Augustin(NewPGen/PFGW)1817824393707*109#-1, 57 digits, 11/05, Augustin(NewPGen/PFGW)CC10, 2nd kind:---------------145683282311*181#+1, 84 digits, 10/05, Augustin(NewPGen/PFGW)3886637*151#+26473215718951, 66 digits, 05/04, Alm/Andersen(Primo)81541671823*127#+1, 60 digits, 11/05, Augustin(NewPGen/PFGW)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*(8428860*127#+212148902055091)-1, 56 digits, 02/06, Andersen(Primo)792619264990*103#+1, 53 digits, 12/05, Augustin(NewPGen/PFGW)3554641*107#+60834577934131, 49 digits, 05/04, Alm/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: --------------- 8428860*127#+212148902055091, 56 digits, 02/06, Andersen(Primo)1108761*79#+442133324202571, 37 digits, 05/04, Alm/Andersen(Primo)4*335898524600734221050749906451371-3, 34 digits, 08/08, Andersen(Primo)CC13, 1st kind: --------------- 1753286498051*71#-1, 39 digits, 12/05, Augustin(NewPGen/PFGW)1162623*59#+90771380489789, 28 digits, 05/04, Andersen(Primo)14002442298246316008734639, 26 digits, 06/04, 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, Wroblewski36027516322668108492823293067201, 32 digits, 17/06/08, WroblewskiCC15, 1st kind: --------------- 662311489517467124375039, 24 digits, 29/05/08, Wroblewski196426752643710966405599, 24 digits, 28/05/08, Wroblewski11993367147962683402919, 23 digits, 10/04, Alm/Andersen(Primo)CC15, 2nd kind: --------------- 28320350134887132315879689643841, 32 digits, 17/06/08, Wroblewski2*2368823992523350998418445521-1, 28 digits, 26/06/08, Wroblewski71838292723844326926417601, 26 digits, 12/06/08, WroblewskiCC16, 1st kind: --------------- 91304653283578934559359, 23 digits, 29/05/08, Wroblewski2*2759832934171386593519+1, 22 digits, 27/05/08, Wroblewski892390227741617675069, 21 digits, 02/02, Carmody/Jobling(GenSv)CC16, 2nd kind: --------------- 2368823992523350998418445521, 28 digits, 26/06/08, Wroblewski20193491108493165642344881, 26 digits, 12/06/088, Wroblewski2*1302312696655394336638441-1, 25 digits, 10/06/08, WroblewskiCC17, 1st kind: --------------- 2759832934171386593519, 22 digits, 27/05/08, WroblewskiCC17, 2nd kind: --------------- 1302312696655394336638441, 25 digits, 10/06/08, Wroblewski127806074555607670094731, 24 digits, 05/06/08, Wroblewski40244844789379926979141, 23 digits, 05/06/08, WroblewskiPart 4, record history-----------------------CC2, 1st (Sophie Germain):--------------------------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:---------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:-----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:-----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:-----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 formk*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 formof numbers, written by Chris Nash and speeded up withsome additional code from G.Woltman and Y.Gallot.Visit http://pages.prodigy.net/chris_nash/primeform.htmlor http://groups.yahoo.com/group/primeformPRP:----Probable primality test program for numbers of theform k*b^n+/-1, written by George Woltman.Visit http://www.mersenne.org/gimps/Proth:------Full primality test program for numbers of the formk*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 exceptionallylong Cunningham Chains. Used by Phil Carmody and Paul Jobling for theirlongest 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=440LLR:----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=431Remark:-------Sometimes the "old" Primeform was used to test the fullprimality of the members of the CC, but I have markedthem all with PFGW because PFGW is the successor ofPrimeform.Please send any new records, corrections or remarks todirk.augustin@gmx.deThis page started as a text file athttp://groups.yahoo.com/group/primenumbers/files/Prime Tables/Cunningham_Chain_records.txtThat file may currently contain an older version and is only accessible to subscribers of the Prime Numbers e-mail list.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: CunninghamChainThe Prime Links++ list of Cunningham Chain linksOther 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 chainPages with similar records:Tony Forbes' Prime k-tupletsHenri Lifchitz' BiTwin recordsJens Kruse Andersen's The largest known CPAP'sJens Kruse Andersen's The Largest Known Simultaneous Primes
 

Sequences

of

nearly

doubled

primes,

maintained

by

Dirk

Augustin.

http://hjem.get2net.dk/jka/math/Cunningham_Chain_records.htm

Cunningham Chain Records 2008 November

dvd rental

dvd


Sequences of nearly doubled primes, maintained by Dirk Augustin.

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