Cunningham Chain records

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 18 19

Part 4, record history for length: 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Part 5, programs that were used

Links



Cunningham Chain records (last updated: August 16th, 2020) ---------------------------------------------------------- NEWSFLASH: A new record for Cunningham chains of length 2 of the second kind was found by Bela Szekeres, Peter Magyar, Gabor E. Gevay, Gabor Fakas and Antal Jarai. Note: A large Cunningham Chain (abbreviation: 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 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 year-month-day or with month/year instead of the year! Part 1, longest CC's: --------------------- Raanan Chermoni and Jaroslaw Wroblewski found CC's of length 18 and 19: 658189097608811942204322721 (27 digits, CC18, 2nd kind, 2014-MAR-09) 182927793839529342111307801 (27 digits, CC18, 2nd kind, 2014-MAR-08) 117302256313688977973793781 (27 digits, CC18, 2nd kind, 2014-MAR-08) 42008163485623434922152331 (26 digits, CC19, 2nd kind, 2014-MAR-15) 79910197721667870187016101 (26 digits, CC19, 2nd kind, 2014-MAR-23) Jaroslaw Wroblewski found first CC's of length 17 in 2008: 2759832934171386593519 (22 digits, CC17, 1st kind, 2008-MAY) 1302312696655394336638441 (25 digits, CC17, 2nd kind, 2008-JUN) 127806074555607670094731 (24 digits, CC17, 2nd kind, 2008-JUN) 40244844789379926979141 (23 digits, CC17, 2nd kind, 2008-JUN) Tony Forbes found the first CC of length 16 in 1997: 3203000719597029781 (19 digits, CC16, 2nd kind, 1997-DEC) Part 2, smallest existing CC's of given length: ----------------------------------------------- 810433818265726529159 (21 digits, CC16, 1st kind, Carmody/Jobling, 2002-FEB) 3203000719597029781 (19 digits, CC16, 2nd kind, Forbes, 1997-DEC) 90616211958465842219 (20 digits, CC15, 1st kind, Sorenson/Webster, 2017-July-05) 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: -------------- 2618163402417*2^1290000-1, 388342 digits, 2016-FEB-29, Brown(PrimeGrid/TwinGen/LLR) 18543637900515*2^666667-1, 200701 digits, 2012-APR-09, Bliedung(PrimeGrid/TwinGen/LLR) 183027*2^265440-1, 79911 digits, 2010-MAR, Wu(sgsieve/LLR) CC2, 2nd kind: -------------- 3622179275715*2^256002+1, 77077 digits, 2020-MAY-31, Szekeres/Magyar/Gevay/Farkas/Jarai 2570606397*2^252762+1, 76099 digits, 2020-MAY-20, Batalov(NewPGen/PFGW) 352666770^8192+1, 70021 digits, 2020-MAY-04, Larrson (GeneFer/AthGFNSieve/PrivGfnServer/PFGW) CC3, 1st kind: -------------- 1128330746865*2^66439-1, 20013 digits, 2020-FEB-17, Paridon(NewPGen/PFGW) 1815615642825*2^44044-1, 13271 digits, 2016-NOV-11, Angel/Augustin(NewPGen/PFGW) 778965587811*2^36625-1, 11038 digits, 2016-SEP-01, Angel/Augustin(NewPGen/PFGW) CC3, 2nd kind: -------------- 742478255901*2^40067+1, 12074 digits, 2016-SEP-09, Angel/Augustin(NewPGen/PFGW) 996824343*2^40072+1, 12072 digits, 2016-SEP-02, Angel/Augustin(NewPGen/PFGW) 49607430768*11^11005+1, 11472 digits, 2016-12-03, Rischel(NewPGen/TOPS/LLR) CC4, 1st kind: -------------- 13720852541*7877#-1, 3384 digits, 2016-OCT-31, Angel/Augustin(NewPGen/PFGW) 28961560189*7517#-1, 3217 digits, 2016-SEP-09, Angel/Augustin(NewPGen/PFGW) 375967981369*6907#-1, 2971 digits, 2017-MAY-31, Ístlin(NewPGen/PFGW) CC4, 2nd kind: -------------- 49325406476*9811#+1, 4233 digits, 2019-JUL-10, Ístlin(NewPGen/PFGW) 259056632602*7699#+1, 3315 digits, 2019-JUN-01, Batalov(NewPGen/PFGW) 17285145467*6977#+1, 3005 digits, 2016-JUL-26, Angel/Augustin(NewPGen/PFGW) CC5, 1st kind: -------------- 31017701152691334912*4091#-1, 1765 digits, 2016-NOV-03, Balyakin 3387614923*3917#-1, 1680 digits, 2016-OCT-15, Angel/Augustin(NewPGen/PFGW) 199949435137*3499#-1, 1493 digits, 2016-MAR-02, Ístlin(NewPGen/PFGW) CC5, 2nd kind: -------------- 181439827616655015936*4673#+1, 2018 digits, 2016-NOV-08, Balyakin 6413732664*3797#+1, 1630 digits, 2016-SEP-29, Angel/Augustin(NewPGen/PFGW) 646737879652976640*3559#+1, 1535 digits, 2016-MAR-10, Balyakin CC6, 1st kind: -------------- 2799873605326*2371#-1, 1016 digits, 2015-MAR-25, Batalov(NewPGen/PFGW) 37488065464*1483#-1, 633 digits, 2010-MAR, Augustin(NewPGen/PFGW) 1882807711450*1327#-1, 578 digits, 2014-JUL-21, Batalov(NewPGen/PFGW) CC6, 2nd kind: -------------- 52992297065385779421184*1531#+1, 668 digits, 2015-MAY-15, Balyakin 480112483568*1511#+1, 650 digits, 2014-MAR-10, Ístlin(NewPGen/PFGW) 37783362904*1097#+1, 475 digits, 2006-JUN-29, Augustin(NewPGen/PFGW) CC7, 1st kind: -------------- 82466536397303904*1171#-1, 509 digits, 2016-JAN-01, Balyakin 3931472185692005387730944*857#-1, 381 digits, 2015-MAY-15, Balyakin 14317181455772*853#-1, 367 digits, 2014-JUL-24, Batalov(NewPGen/PFGW) CC7, 2nd kind: -------------- 25802590081726373888*1033#+1, 453 digits, 2015-DEC-17, Balyakin 2*2373007846680317952*761#+1, 337 digits, 2016-MAR-10, Balyakin 535617118876*727#+1, 313 digits, 2015-DEC-06, Ístlin(NewPGen/PFGW) CC8, 1st kind: -------------- 89628063633698570895360*593#-1, 265 digits, 2015-DEC-17, Balyakin 2*553374939996823808*593#-1, 260 digits, 2016-MAR-10, Balyakin 5175268103676*557#-1, 238 digits, 2015-NOV-20, Ístlin(NewPGen/PFGW) CC8, 2nd kind: -------------- 2373007846680317952*761#+1, 337 digits, 2016-MAR-10, Balyakin 112156947439087303442563072*491#+1, 230 digits, 2015-MAY-15, Balyakin 1148424905221*509#+1, 224 digits, 2010-AUG, Augustin(NewPGen/PFGW) CC9, 1st kind: -------------- 553374939996823808*593#-1, 260 digits, 2016-MAR-10, Balyakin 40912747216912409971130368*401#-1, 190 digits, 2015-DEC-17, Balyakin 2630705556345975695872*401#-1, 186 digits, 2015-MAY-15, Balyakin CC9, 2nd kind: -------------- 173129832252242394185728*401#+1, 187 digits, 2015-MAY-15, Balyakin 182887101390961871050645934589918687746535370612015546956692154622371784133412186*223#+1, 167 digits, 2013-JUL-23, Primecoin 326715355352350972893381745676353435171008659029059646631240926699147385033998869*193#+1, 158 digits, 2013-JUL-09, Primecoin CC10, 1st kind: --------------- 3696772637099483023015936*311#-1, 150 digits, 2016-MAR-10, Balyakin 380036435653000196587520*311#-1, 149 digits, 2016-JAN-01, Balyakin 1814165079257305081195008*307#-1, 148 digits, 2015-DEC-17, Balyakin CC10, 2nd kind: --------------- 2044300700000658875613184*311#+1, 150 digits, 2016-MAR-10, Balyakin 2*341841671431409652891648*311#+1, 150 digits, 2016-NOV-03, Balyakin 172046770897145546293248*311#+1, 149 digits, 2016-JAN-01, Balyakin CC11, 1st kind: --------------- 73853903764168979088206401473739410396455001112581722569026969860983656346568919*151#-1, 140 digits, 2013-AUG-03, Primecoin 397146194319432735351828361368498572415833839171716172868658515395849798889548375*107#-1, 124 digits, 2013-AUG-06, Primecoin 239744775802122662005054501673219419476327706093461245474933836166272232010143904*107#-1, 123 digits, 2015-SEP-18, Primecoin CC11, 2nd kind: --------------- 341841671431409652891648*311#+1, 149 digits, 2016-NOV-03, Balyakin 19298029794843054654*311#+1, 145 digits, 2015-MAY-15, Balyakin 8026337833619599372491948674562462668692014872229571339857384053514279156849912832*109#+1, 127 digits, 2014-JAN-18, Primecoin CC12, 1st kind: --------------- 288320466650346626888267818984974462085357412586437032687304004479168536445314040*83#-1, 113 digits, 2014-MAY-23, Primecoin 61592551716229060392971860549140211602858978086524024531871935735163762961673908480*71#*-1 , 110 digits, 2013-NOV-02, Primecoin 178811043947926524937518051044987491022433869417704220317907704222148116972528580*71#-1, 107 digits, 2014-FEB-03, Primecoin CC12, 2nd kind: --------------- 906644189971753846618980352*233#+1, 121 digits, 2015-MAY-15, Balyakin 160433998429454286861864982184342218645773889300991352796925862298096263175269000*73#+1, 109 digits, 2013-DEZ-21, Primecoin 3018970250978499232353420274403370309649101023080062032175680183412679387197178760*71#+1, 109 digits, 2014-JAN-25, Primecoin CC13, 1st kind: --------------- 106680560818292299253267832484567360951928953599522278361651385665522443588804123392*61#-1, 107 digits, 2014-JAN-20, Primecoin 130083778959343562529131897703476422909096253953040587242097712006102296570026924*59#-1, 102 digits, 2014-DEZ-06, Primecoin 19313073314471398368420651854042490322517950973521740350204774005412663648863502336*47#-1, 101 digits, 2014-MAY-25, Primecoin CC13, 2nd kind: --------------- 38249410745534076442242419351233801191635692835712219264661912943040353398995076864*47#+1, 101 digits, 2014-MAY-12, Primecoin 33155807057790800775649341859694105808052724705909514418378338523752551896758685696*47#+1, 101 digits, 2014-JUN-07, Primecoin 2*5819411283298069803200936040662511327268486153212216998535044251830806354124236416*47#+1, 100 digits, 2014-MAY-16, Primecoin CC14, 1st kind: --------------- 14340319624001770765457042636973902777444526766562062468716553623575545716736*59#-1, 98 digits, 2018-NOV-20, Primecoin 347622072041723844162287184183914184860957936041436689230785415185462392681984*53#-1, 98 digits, 2018-SEP-24, Primecoin 191342609850856879957449499895670283640890480214837046901752486942672919132160*53#-1, 97 digits, 2018-JUN-24, Primecoin CC14, 2nd kind: --------------- 5819411283298069803200936040662511327268486153212216998535044251830806354124236416*47#+1, 100 digits, 2014-MAY-16, Primecoin 3146591441955217642366698240919518681196313035455968063191643605670902480355328*53#+1, 99 digits, 2018-JUN-10, Primecoin 1585753053589282551631841398385658077743119695490328251925552789038464584491008*53#+1, 98 digits, 2018-SEP-29, Primecoin CC15, 1st kind: --------------- 14354792166345299956567113728*43#-1, 45 digits, 2016-JAN-01, Balyakin 14366587870229772953764096*43#-1, 42 digits, 2015-DEC-17, Balyakin 27353790674175627273118204975428644651729, 41 digits, 2014-APR-25, Wroblewski CC15, 2nd kind: --------------- 67040002730422542592*53#+1, 40 digits, 2016-MAR-10, Balyakin 25939635974573655642*53#+1, 39 digits, 2015-MAY-15, Balyakin 28320350134887132315879689643841, 32 digits, 2008-JUN-17, Wroblewski CC16, 1st kind: --------------- 91304653283578934559359, 23 digits, 2008-MAY-29, Wroblewski 2*2759832934171386593519+1, 22 digits, 2008-MAY-27, Wroblewski 892390227741617675069, 21 digits, 2002-FEB, Carmody/Jobling(GenSv) CC16, 2nd kind: --------------- 2*1540797425367761006138858881-1, 28 digits, 2014-APR-03, Chermoni/Wroblewski 4*658189097608811942204322721-3, 28 digits, 2014-MAR-09, Chermoni/Wroblewski 2614065594356962781728904640, 28 digits, 2014-APR-09, Chermoni/Wroblewski CC17, 1st kind: --------------- 2759832934171386593519, 22 digits, 2008-MAY-27, Wroblewski CC17, 2nd kind: --------------- 1540797425367761006138858881, 28 digits, 2014-APR-03, Chermoni/Wroblewski 2*658189097608811942204322721-1, 28 digits, 2014-MAR-09, Chermoni/Wroblewski 1284167734361435112645318721, 28 digits, 2014-APR-03, Chermoni/Wroblewski CC18, 2nd kind: --------------- 658189097608811942204322721, 27 digits, 2014-MAR-09, Chermoni/Wroblewski 182927793839529342111307801, 27 digits, 2014-MAR-08, Chermoni/Wroblewski 2*79910197721667870187016101-1, 27 digits, 2014-MAR-23, Chermoni/Wroblewski CC19, 2nd kind: --------------- 79910197721667870187016101, 26 digits, 2014-MAR-23, Chermoni/Wroblewski 42008163485623434922152331, 26 digits, 2014-MAR-15, Chermoni/Wroblewski Part 4, record history ----------------------- CC2, 1st (Sophie Germain): -------------------------- 388342 digits, 2016-FEB-29, Brown(PrimeGrid/TwinGen/LLR) (2618163402417*2^1290000-1) 200701 digits, 2012-APR-09, Bliedung(PrimeGrid/TwinGen/LLR) (18543637900515*2^666667-1) 79911 digits, 2010-MAR, Wu(sgsieve/LLR) (183027*2^265440-1) 76424 digits, 2009-NOV-18, Jarai/Farkas/Csajbok/Kasza/Jarai (648621027630345*2^253824-1) 76424 digits, 2009-NOV-02, Jarai/Farkas/Csajbok/Kasza/Jarai (620366307356565*2^253824-1) 53081 digits, 2009-SEP, Wu(LLR) (607095*2^176311-1) 51910 digits, 2007-JAN, Underbakke(TwinGen/LLR) (48047305725*2^172403-1) 51780 digits, 2006-MAY, Jarai/Farkas/Csajbok/Kasza/Jarai (137211941292195*2^171960-1) 36523 digits, 2005-JAN, Predrag Minovic(TwinGen/LLR) (7068555*2^121301-1) 34547 digits, 2003-JAN, Underbakke(TwinGen/PRP/Proth) (2540041185*2^114729-1) 29628 digits, 2002-NOV, Angel/Augustin/Jobling(NewPGen/PFGW) (18912879*2^98395-1) 24432 digits, 2002-AUG, Angel/Augustin/Jobling(NewPGen/PFGW/Proth) (1213822389*2^81131-1) 20013 digits, 2001-FEB, Underbakke(NewPGen/Proth) (109433307*2^66452-1) 18075 digits, 2000-MAR, Indlekofer/Jarai/Wassing (3714089895285*2^60000-1) 9853 digits, 2000-JAN, 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: --------- 77077 digits, 2020-MAY-31, Szekeres/Magyar/Gevay/Farkas/Jarai (3622179275715*2^256002+1) 76099 digits, 2020-MAY-20, Batalov(NewPGen/PFGW) (2570606397*2^252762+1) 70021 digits, 2020-MAY-04, Larrson (GeneFer/AthGFNSieve/PrivGfnServer/PFGW) (352666770^8192+1) 63633 digits, 2019-MAI-24, Batalov(NewPGen/LLR) (556336461*2^211355+1) 52725 digits, 2017-DEC-20, Batalov(NewPGen/PFGW) (7775705415*2^175115+1) 51489 digits, 2016-JUL-12, Nair(NewPGen/LLR) (9985628193*2^171008+1) 51238 digits, 2015-MAR-27, Batalov(NewPGen/LLR) (129431439657*2^170171+1) 48660 digits, 2015-JAN-07, Rajala(NewPGen/PFGW) (185688291*2^161616+1) 47784 digits, 2014-JUL-17, Batalov(NewPGen/LLR) (1579755*2^158712+1) 44652 digits, 2010-JUL, Wu(sgsieve/LLR) (648309*2^148310+1) 40993 digits, 2010-JUN, Wu(sgsieve/LLR) (552903*2^136156+1) 37514 digits, 2009-DEC, Wu(sgsieve/LLR) (163221*2^124600+1) 31430 digits, 2009-NOV, Wu(sgsieve/LLR) (532323*2^104389+1) 28060 digits, 2009-AUG, Augustin(NewPGen/PFGW) (581627055*2^93181+1) 24092 digits, 2007-MAY, Nair(NewPGen/LLR) (3853775193*2^80000+1) 23593 digits, 2004-APR, Sun(PRP/NewPGen/Proth) (1504084599*2^78341+1) 15840 digits, 2003-DEC, Sun(PRP/NewPGen/Proth) (863710323*2^52588+1) 15060 digits, 2003-NOV, Chaffy(Proth) (55003425*2^50000+1) 15000 digits, 2003, Rouse(Proth) (164581485*2^49800+1) 12116 digits, 2000-NOV, 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: ---- 20013 digits, 2020-FEB-17, Paridon(NewPGen/PFGW) (1128330746865*2^66439-1) 13271 digits, 2016-NOV-11, Angel/Augustin(NewPGen/PFGW) (1815615642825*2^44044-1) 12074 digits, 2016-SEP-09, Angel/Augustin(NewPGen/PFGW) (742478255901*2^40067+1) 12072 digita, 2016-SEP-02, Angel/Augustin(NewPGen/PFGW) (996824343*2^40072+1) 11038 digits, 2016-SEP-01, Angel/Augustin(NewPGen/PFGW) (778965587811*2^36625-1) 10713 digits, 2015-MAR-17, Batalov(NewPGen/PFGW) (333645655005*2^35547-1) 10535 digits, 2014-APR, Gevay/Vatai/Farkas/Jarai(PFGW) (5110664609396115*2^34944-1) 10477 digits, 2010-JAN-08, Wu(sgsieve/LLR) (914546877*2^34772-1) 8175 digits, 2009-NOV, Wu(sgsieve/LLR) (379185609*2^27127-1) 7937 digits, 2006-AUG, Paridon(NewPGen/PFGW) (164210699973*2^26326-1) 6038 digits, 2005-APR, Sun(NewPGen/PFGW) (3020255265*2^20023-1) 5189 digits, 2004-OCT, Sun(NewPGen/PFGW) (2366867925*2^17206+1) 4807 digits, 2004-JUL, Sun(NewPGen/PFGW) (2288999415*2^15937-1) 4574 digits, 2002-OCT, Angel/Augustin/Jobling(NewPGen/PRP/Proth) (1110159213*2^15164+1) 3713 digits, 2002-SEP, Herranen(PFGW) (5040102231*2^12301-1) 3710 digits, 2002-JUL, Angel/Augustin/Jobling(NewPGen/PFGW/Proth) (268382583*2^12294-1) 3086 digits, 2001-SEP, Angel/Augustin/Jobling(NewPGen/PRP/Proth) (1838313165*2^10219-1) 3052 digits, 2001-AUG, Angel/Augustin/Jobling(NewPGen/PRP/Proth) (1531785651*2^10107+1) 2475 digits, 2000, Nikkel,St./Nikkel,T.(Proth) (1361835195*2^8191+1) 2006 digits, 2000-JUN, 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, 1998-MAY-20, Roonguthai(Proth) (384205437*2^4000-1) 1000 digits, 1998-MAY-7, Roonguthai(Proth 4.01) (651358155*2^3291-1) CC4: ---- 4233 digits, 2019-JUL-10, Ístlin(NewPGen/PFGW) (49325406476*9811#+1) 3384 digits, 2016-OCT-31, Angel/Augustin(NewPGen/PFGW) (13720852541*7877#-1) 3217 digits, 2016-SEP-09, Angel/Augustin(NewPGen/PFGW) (28961560189*7517#-1) 3005 digits, 2016-JUL-26, Angel/Augustin(NewPGen/PFGW) (17285145467*6977#+1) 2882 digits, 2015-MAR-20, Batalov(NewPGen/PFGW) (28904981097*6703#-1) 2878 digits, 2015-MAR-19, Batalov(NewPGen/PFGW) (35598436282*6701#+1 2835 digits, 2011-FEB, Angel(NewPGen/PFGW) (1249097877*6599#-1) 2354 digits, 2005-JUN, Sun(NewPGen/PFGW) (119184698*5501#-1) 1770 digits, 2005-MAR, Sun(NewPGen/PrimeForm) (1453501013*4127#+1) 1711 digits, 2004-APR, Sun(NewPGen/PrimeForm) (153344568*4001#+1) 1313 digits, 2003-JAN, Broadhurst(PrimeForm) (131853904032*3061#+1) 1308 digits, 2002-OCT, Angel/Augustin/Jobling(NewPGen/PFGW) (1707223185*3049#-1) 1303 digits, 2002-SEP, Angel/Augustin/Jobling(NewPGen/PFGW) (356701232*3041#+1) 1117 digits, 2001-SEP, Frind(NewPGen/PFGW) (433098705*2633#-1) 1019 digits, 2000-AUG, Augustin/Jobling(NewPGen/PFGW) (742155874*2381#-1) 506 digits, 2000-JUN-17, Augustin(NewPGen/PFGW) (92406026*1187#+1) 429 digits, 2000-JUN-10, Augustin(NewPGen/PFGW) (35443364*1013#-1) 301 digits, 2000-JAN, Augustin(Proth) (164285535*2^972+1) 241 digits, 1999-OCT, Augustin(Proth) (723592485*2^770+1) CC5: ---- 2018 digits, 2016-NOV-08, Balyakin (181439827616655015936*4673#+1) 1765 digits, 2016-NOV-03, Balyakin (31017701152691334912*4091#-1) 1680 digits, 2016-OCT-15, Angel/Augustin(NewPGen/PFGW) (3387614923*3917#-1) 1630 digits, 2016-SEP-29, Angel/Augustin(NewPGen/PFGW) (6413732664*3797#+1) 1535 digits, 2016-MAR-10, Balyakin (646737879652976640*3559#+1) 1493 digits, 2016-MAR-02, Ístlin(NewPGen/PFGW) (199949435137*3499#-1) 1342 digits, 2015-DEC-17, Balyakin (26483492454758573330432*3109#+1) 1299 digits, 2015-MAR-25, Batalov(NewPGen/PFGW) (361296035282*3023#-1) 1288 digits, 2015-MAR-21, Batalov(NewPGen/PFGW) (56185437312*3001#+1) 1183 digits, 2012-MAR, Augustin(NewPGen/PFGW) (4250172704*2749#-1) 1140 digits, 2011-JAN, Angel(NewPGen/PFGW) (80670856865*2677#+1) 1116 digits, 2010-JUL, Broadhurst(NewPGen/PFGW) (45008010405*2621#+1) 727 digits, 2008-MAY, Augustin(NewPGen/PFGW) (357487161295*1693#-1) 613 digits, 2004-NOV, Augustin(NewPGen/PFGW) (1719674368*1447#+1) 540 digits, 2004-SEP, Andersen(Primo) (496391760*1277#+325305140161) 509 digits, 2002-FEB, Augustin(NewPGen/PFGW) (51946113*1193#+1) 460 digits, 2001-NOV, Augustin(NewPGen/PFGW) (148809453*1069#-1) 422 digits, 2001-AUG, Frind(NewPGen/PFGW) (828114253*991#-1) 407 digits, 2000-AUG, Augustin(NewPGen/PFGW) (504856309*953#-1) 339 digits, 2000-JUL, Augustin(NewPGen/PFGW) (427383180*797#-1) 257 digits, 2000-JUN-20, Augustin(NewPGen/PFGW) (1217763452*601#-1) 207 digits, 2000-JUN-07, Augustin(NewPGen/PFGW) (206262090*479#-1) 115 digits, 2000-MAR, Augustin(NewPGen/Proth) (463419585*2^353-1) 102 digits, 2000-JAN, Augustin(Proth) (518179995*2^308+1) 86 digits, 1999-DEC, Augustin(Proth) (96952995*2^258-1) 78 digits, 1999-NOV, Jobling (9006546615*2^223-1) 76 digits, 1999-OCT, Augustin(Proth) (392651625*2^222+1) CC6: ---- 1016 digits, 2015-MAR-25, Batalov(NewPGen/PFGW) (2799873605326*2371#-1) 650 digits, 2014-MAR-10, Ístlin(NewPGen/PFGW) (480112483568*1511#+1) 633 digits, 2010-MAR, Augustin(NewPGen/PFGW) (37488065464*1483#-1) 475 digits, 2006-JUN, Augustin(NewPGen/PFGW) (37783362904*1097#+1) 417 digits, 2004-OCT, Augustin(NewPGen/PFGW) (33692909611*977#-1) 336 digits, 2004-SEP, Andersen(Primo) (703632724*787#+94265010841) 318 digits, 2004-SEP, Augustin(NewPGen/PFGW) (42693782492*739#+1) 279 digits, 2004-SEP, Andersen(Primo) (2197316072*647#+105063678721) 222 digits, 2003-JAN, Chaffey (6302319587*509#+1) 213 digits, 2001-SEP, Augustin(NewPGen/PFGW) (716250935*491#-1) 208 digits, 2000-AUG, Augustin(NewPGen/PFGW) (1056231420*479#+1) 142 digits, 2000-JUN-20, Augustin(NewPGen/PFGW) (388562456*331#+1) 120 digits, 2000-JUN-03, Augustin(NewPGen/PFGW) (2*305372608*271#+1) 85 digits, 1999-OCT-26, Augustin(Proth) (620060805*2^252-1) 56 digits, 1999-OCT-19, Augustin(Proth) (505054485*2^154-1) CC7: ---- 509 digits, 2016-JAN-01, Balyakin (82466536397303904*1171#-1) 453 digits, 2015-DEC-17, Balyakin (25802590081726373888*1033#+1) 381 digits, 2015-MAY-15, Balyakin (3931472185692005387730944*857#-1) 367 digits, 2014-JUL-24, Batalov(NewPGen/PFGW) (14317181455772*853#-1) 356 digits, 2010-JUL, Augustin(NewPGen/PFGW) (162597166369*827#-1) 291 digits, 2008-JUL, Augustin(NewPGen/PFGW) (1178137903623*661#-1) 251 digits, 2008-MAY, Wolter/Andersen(Primo) (668302064*593#+786153598231) 237 digits, 2006-MAR, Augustin(NewPGen/PFGW) (414792720846*557#+1) 218 digits, 2006-FEB, Andersen(Primo) (782350985*503#+2189997811) 211 digits, 2004-NOV, Augustin(NewPGen/PFGW) (14180848107*487#-1) 165 digits, 2004-MAY, Alm/Andersen(Primo) (472063086*383#+1236845609) 153 digits, 2002-JUN, Augustin(NewPGen/PFGW) (406605710992*349#-1) 128 digits, 2001-SEP, Augustin(NewPGen/PFGW) (2310290388*283#+1) 123 digits, 2000-AUG, Augustin(NewPGen/PFGW) (1701815519*277#+1) 87 digits, 2000-JUL, Augustin(NewPGen/PFGW) (843616025*193#+1) 69 digits, 2000-JUN, Augustin(NewPGen/PFGW) (1953370903*151#-1) 43 digits, 1999-DEZ, Jobling (460668119835*2^101-1) 31 digits, 1999-NOV, Augustin/Jobling(Primeform) (27215953890276787*37#*2^3-1) 27 digits, 1999-OCT, Augustin(Proth) (666325605*2^60+1) CC8: ---- 337 digits, 2016-MAR-10, Balyakin (2373007846680317952*761#+1) 265 digits, 2015-DEC-17, Balyakin (89628063633698570895360*593#-1) 238 digits, 2015-NOV-20, Ístlin(NewPGen/PFGW) (5175268103676*557#-1) 230 digits, 2015-MAY-15, Balyakin (112156947439087303442563072*491#+1) 224 digits, 2010-AUG, Augustin(NewPGen/PFGW) (1148424905221*509#+1) 186 digits, 2005-AUG, Augustin(NewPGen/PFGW) (2*65728407627*431#-1) 135 digits, 2004-MAY, Alm/Andersen(Primo) (1352438530*311#+5705699) 103 digits, 2002-JUN, Augustin(NewPGen/PFGW) (177497325593*229#+1) 82 digits, 2000-JUN, Augustin(NewPGen/PFGW) (548879116*181#-1) 52 digits, 2000-JUN-13, Augustin(NewPGen/PFGW) (1831430532*107#+1) 44 digits, 2000-JUN-01, Augustin(NewPGen/PFGW) (1742368093*89#-1) 25 digits, 2000-MAR, Augustin(NewPGen/Proth) (1360673835*2^50-1) 23 digits, 1999-DEC, Jobling (36097525695*2^41-1) CC9: ---- 260 digits, 2016-MAR-10, Balyakin (553374939996823808*593#-1) 190 digits, 2015-DEC-17, Balyakin (40912747216912409971130368*401#-1) 187 digits, 2015-MAY-15, Balyakin (173129832252242394185728*401#+1) 185 digits, 2005-AUG, Augustin(NewPGen/PFGW) (65728407627*431#-1) 94 digits, 2004-MAY, Alm/Andersen(Primo) (745395266*211#+1503602101) 58 digits, 2001-APR, Augustin(NewPGen/PFGW) (2093307780*127#-1) 50 digits, 2000-DEZ, Augustin(NewPGen/PFGW) (1061169280*103#+1) 37 digits, 2000-OCT, Augustin(NewPGen/PFGW) (43105142*73#+1) CC10: ----- 150 digits, 2016-MAR-10, Balyakin (3696772637099483023015936*311#-1) 149 digits, 2016-JAN-01, Balyakin (380036435653000196587520*311#-1) 148 digits, 2015-DEC-17, Balyakin (1814165079257305081195008*307#-1) 147 digits, 2015-MAY-15, Balyakin (330951321789825381416704*307#-1) 146 digits, 2013-Sep-27, Primecoin (44598464649019035883154084128331646888059795218766083584048621139159337786287845212160000*149#-1) 140 digits, 2013-AUG-03, Primecoin (2*73853903764168979088206401473739410396455001112581722569026969860983656346568919*151#-1) 130 digits, 2013-JUL-30, Primecoin (462437381164406137571238642026500487143562202130164203468923172902534686193803360*127#+1) 127 digits, 2013-JUL-26, Primecoin (56264173162248110557182990671699794423868532232638543675069282466016594777519178*113#+1) 123 digits, 2013-JUL-19, Primecoin (262499092615905868031715264868904084128264525100784340743363467708299618392967465*107#-1) 115 digits, 2013-JUL-18, Primecoin (124204185879546865064885473789426527077462683918304583642200186747726088560403328*89#+1) 114 digits, 2013-JUL-17, Primecoin (412406801624694938044523477936948391896313088313421313799025296390261745671407240*83#-1) 113 digits, 2013-JUL-13, Primecoin (245733408934030585360992778759621360588058894402905285648919156928156545458241886*83#-1) 109 digits, 2009-JUL, Augustin(NewPGen/PFGW) (1070828503293*239#+1) 99 digits, 2009-MAY, Augustin(NewPGen/PFGW) (1324846487162*223#-1) 84 digits, 2005-OCT, Augustin(NewPGen/PFGW) (145683282311*181#+1) 66 digits, 2004-MAY, Alm/Andersen(Primo) (3886637*151#+26473215718951) 51 digits, 2002-JUN, Augustin(NewPGen/PFGW) (8296886802*103#+1) 39 digits, 2000-DEZ-15, Augustin(NewPGen/PFGW) (3440034726*73#-1) 33 digits, 2000-DEZ-03, Augustin(NewPGen/PFGW) (1308811392*61#-1) CC11: ----- 149 digits, 2016-NOV-03, Balyakin (341841671431409652891648*311#+1) 145 digits, 2015-MAY-15, Balyakin (19298029794843054654*311#+1) 140 digits, 2013-AUG-03, Primecoin (73853903764168979088206401473739410396455001112581722569026969860983656346568919*151#-1) 116 digits, 2013-JUL-26, Primecoin (566002435353389048470195154197633715327639809354150079355350346671860564824949963*89#-1) 113 digits, 2013-JUL-23, Primecoin (174304836888332595142407951525788751329051227164577255527856958439859830598690304*83#-1) 108 digits, 2013-JUL-22, Primecoin (488499712314488417016779441191681704321131667381809511540071609780532612839680260*71#-1) 108 digits, 2013-JUL-20, Primecoin (189431187381152056703213606148620440770958584332732508794815501069120395607727520*71#+1) 102 digits, 2013-JUL-18, Primecoin (107386119837124621814971704624900922741439953979550058923273511670890827552543392*59#-1) 98 digits, 2013-JUL-17, Primecoin (848029410248902405267951124411141542913902774598042414627002939891647628881358680*43#+1) 93 digits, 2013-JUL-16, Primecoin (105391885235180642837566579719340498344767363492888467130937411507174806414446905*37#-1) 91 digits, 2013-JUL-14, Primecoin (244904970375722028798242559069071350723679913437376658289613677305863972540773149*29#+1) 63 digits, 2008-DEZ, Augustin(NewPGen/PFGW) (2*13931865163581*127#+1) 56 digits, 2006-FEB, Andersen(Primo) (2*(8428860*127#+212148902055091)-1) 53 digits, 2005-DEZ, Augustin(NewPGen/PFGW) (792619264990*103#+1) 50 digits, 2004-MAY, Alm/Andersen(Primo) (4608461*107#+178414906509839) CC12: ----- 121 digits, 2015-MAY-15, Balyakin (906644189971753846618980352*233#+1) 113 digits, 2014-MAY-23, Primecoin (288320466650346626888267818984974462085357412586437032687304004479168536445314040*83#-1) 110 digits, 2013-NOV-02, Primecoin (61592551716229060392971860549140211602858978086524024531871935735163762961673908480*71#*-1) 97 digits, 2013-OKT-12, Primecoin (27514366944545993668422567193822444315682837691915196563994783521784099031989503616*41#+1) 97 digits, 2013-JUL-21, Primecoin (263663326886409378473341387047271336974122837948496277769621396327294641140893808*43#+1) 62 digits, 2008-DEZ, Augustin(NewPGen/PFGW) (13931865163581*127#+1) 56 digits, 2006-FEB, Andersen(Primo) (8428860*127#+212148902055091) 42 digits, 2006-FEB, Andersen(Primo) (4431659*89#+440181861259139) 40 digits, 2005-DEZ, Augustin(NewPGen/PFGW) (2*1753286498051*71#-1) 37 digits, 2004-MAY, Alm/Andersen(Primo) (1307465*79#+11500298799989) CC13: ----- 107 digits, 2014-JAN-20, Primecoin (106680560818292299253267832484567360951928953599522278361651385665522443588804123392*61#-1) 94 digits, 2013-SEP-10, Primecoin (10756750720700195380397697188448178460115725467111771468875842964723844354555016704*31#+1) 39 digits, 2005-DEZ, Augustin(NewPGen/PFGW) (1753286498051*71#-1) 31 digits, 2004-MAY, Andersen(Primo) (938719*67#+56461354019071) CC14: ----- 100 digits, 2014-MAY-16, Primecoin (5819411283298069803200936040662511327268486153212216998535044251830806354124236416*47#+1) 41 digits, 2014-APR-25, Wroblewski (2*27353790674175627273118204975428644651729+1) 33 digits, 2008-AUG, Andersen(Primo) (335898524600734221050749906451371) 32 digits, 2008-JUN-17, Wroblewski (2*28320350134887132315879689643841-1) 31 digits, 2008-JUN-14, Wroblewski (2354904873485081880414653783011) 31 digits, 2008-JUN-06, Andersen(Primo) (2337673907855670908145009878491) 26 digits, 2008-MAY, Wroblewski (20299226100350079536373721) 25 digits, 2004-JUN, Andersen(Primo) (9510321949318457733566099) 21 digits, 1997, Forbes (385931755250345784479) CC15: ----- 45 digits, 2016-JAN-01, Balyakin (14354792166345299956567113728*43#-1) 42 digits, 2015-DEC-17, Balyakin (14366587870229772953764096*43#-1) 41 digits, 2014-APR-25, Wroblewski (27353790674175627273118204975428644651729) 32 digits, 2008-JUN-17, Wroblewski (28320350134887132315879689643841) 26 digits, 2008-JUN-12, Wroblewski (71838292723844326926417601) 25 digits, 2008-JUN-10, Wroblewski (5830768257311375388822241) 25 digits, 2008-JUN-05, Wroblewski (2817673877915370357723841) 24 digits, 2008-MAY-29, Wroblewski (662311489517467124375039) 24 digits, 2008-MAY-28, Wroblewski (196426752643710966405599) 24 digits, 2008-MAY-26, Wroblewski (105998574608115401372161) 23 digits, 2008-MAY-25, Wroblewski (2*15745040405007366603151-1) 23 digits, 2004-OCT, Alm/Andersen(Primo) (11993367147962683402919) 22 digits, ??, Forbes (4678714760875524493409) 20 digits, 1997-SEP, Forbes (54269795934721528591) CC16: ----- 28 digits, 2014-APR-03, Chermoni/Wroblewski (2*1540797425367761006138858881-1) 28 digits, 2014-MAR-09, Chermoni/Wroblewski (4*658189097608811942204322721-3) 28 digits, 2008-JUN-26, Wroblewski (2368823992523350998418445521) 26 digits, 2008-JUN-12, Wroblewski (20193491108493165642344881) 25 digits, 2008-JUN-10, Wroblewski (2*1302312696655394336638441-1) 24 digits, 2008-JUN-08, Wroblewski (258296136493222766530021) 24 digits, 2008-JUN-05, Wroblewski (2*127806074555607670094731-1) 23 digits, 2008-MAY-29, Wroblewski (91304653283578934559359) 23 digits, 2008-MAY-25, Wroblewski (15745040405007366603151) 21 digits, 2002-FEB, Carmody/Jobling(GenSv) (892390227741617675069) 19 digits, 1997-DEC, Forbes (3203000719597029781) CC17: ----- 28 digits, 2014-APR-03, Chermoni/Wroblewski (1540797425367761006138858881) 28 digits, 2014-MAR-09, Chermoni/Wroblewski (2*658189097608811942204322721-1) 27 digits, 2014-MAR-08, Chermoni/Wroblewski (465463467291895470464386321) 25 digits, 2008-JUN-10, Wroblewski (1302312696655394336638441) 24 digits, 2008-JUN-05, Wroblewski (127806074555607670094731) 23 digits, 2008-JUN-05, Wroblewski (40244844789379926979141) 22 digits, 2008-MAY-27, Wroblewski (2759832934171386593519) CC18: ----- 27 digits, 2014-MAR-09, Chermoni/Wroblewski (658189097608811942204322721) 27 digits, 2014-MAR-08, Chermoni/Wroblewski (182927793839529342111307801) CC19: ----- 26 digits, 2014-MAR-23, Chermoni/Wroblewski (79910197721667870187016101) 26 digits, 2014-MAR-15, Chermoni/Wroblewski (42008163485623434922152331) 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 sgsieve: -------- A specialized sieving program developed by Tom Wu for sieving of Sophie-Germain candidates over a range of k and n values. It generates NewPGen/LLR-format output. Visit http://primes.utm.edu/bios/code.php?code=L983 PrimeGrid --------- PrimeGrid's primary goal is to bring the excitement of prime finding to the "everyday" computer user. By simply downloading and installing BOINC and attaching to the PrimeGrid project, participants can choose from a variety of prime forms to search. visit http:/www.primegrid.com Primecoin --------- Primecoin, developed by Sunny King, is the first proof-of-work based cryptocurrency that has come up with any kind of workable solution. The central premise of Primecoin is that, instead of useless SHA256 hashes, the proof of work protocol would require miners to find long chains of prime numbers (Cunningham chains and BiTwins). visit http://ppcoin.org/primecoin Remark: ------- Sometimes the "old" Primeform was used to test the full primality of the members of a 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 Please check all primes for full primality before sending them to me. In addition all submitted primes are always double checked by me with PFGW.

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 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: Cunningham Chain



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

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

