There are currently 240 known ABC triples of quality at least 1.4, which are often called good ABC triples. The next plot counts them by their number of digits. For instance, the graph says that there are 11 good triples where c has 20 digits.

good abc triples graph

The method of ABC@home finds all ABC triples for a given lower bound on the quality and an upper bound on the size. By a run of an early implementation of Jeroen Demeyer from Gent in June 2007 we know that the list of good triples up to 20 digits is now complete. So when new good triples are discovered, only the red part in the plot above will grow. Demeyer's search turned up nine new triples with c of at most 20 digits.

By a completely independent method, Frank Rubin has found a number of new good ABC triples in the last few years, including most of the good triples with more than 20 digits, and all of the good triples with 30 digits.


The 240 known triples with q>1.4:last update: 2017-05-15

Order by quality, date, size or merit.

qualitysizemeritbyona bc
11.62996.818.64ER198701012310​109235
21.62607.6810.18BdW1985092011232​56​73221​23
31.623515.7026.86JB JB1994040119·​13077·​292​31828​322​54
41.58089.9213.01JB JB AN19930312283511​13228​38​173
51.56793.642.89BdW1988010612·​3754​7
61.54714.774.17BdW1988010673310211​29
71.544420.7931.54AN1993031272​412​31131116​132​792·​33​523​953
81.536713.0516.74HtR PM 5329​317​132115​17·​313​137
91.52709.7811.02AN1993031213·​196230​5313​112​31
101.522217.0822.92AN19930312318​23·​2269173​29·​318210​52​715
111.509419.4926.17TD200308041310​37237​195​714​223226​512​1873
121.503317.3722.12TS MH 27​238199​8572322​13·​472​263
131.50289.289.55JB JB AN1993031223958​173210​374
141.497610.9911.82BdW1988010652​7937713218​37​132
151.492419.1524.26AN1993031222​1132​1310​17·​151·​442359​1396
161.491615.7818.79AN1993031273213​77​9412316​1033​127
171.489211.4912.24AN19930312224117​19·​292311​53​73​41
181.48895.414.25BdW1988010611239​13211​53
191.48294.523.18BdW198801063721538​5
201.481312.9714.04AN19930312514​1925​3·​713117​372​353
211.480526.3635.16FR20101107522​79·​4594932​1318​613223​174​2512​17333
221.47448.487.70AN199303121316​723​11·​23·​533
231.47417.506.48JB JB AN1993031272210​11·​53234​58
241.47138.337.44JB JB AN1993031234​19911823​57​73
251.465714.2715.11HtR PM 174​67219​1374315​53​13·​892
261.465512.3612.48AN19930312712214​673​461313​11·​194
271.465321.6025.90FR2016120433​241358​119​19·​613215​172​331·​10614
281.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
291.46196.685.29BdW1988010627​5276​41136
301.460627.7835.12IC201006127·​167·​8114​91934​132​2312​674231​53​112​175​1074
311.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
321.457820.5323.64AN19930312512​172​312​16992314​29219​32​11·​1310​47
331.457813.0213.03AN1993031236​512216​13·​594711​47·​113
341.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
351.457110.8610.19AN1993031232​5224​173​314710​257
361.456213.9814.24AN19930312225​193·​515​1033117​133​472
371.45573.381.86BdW19880106125​3·​5274
381.455110.549.72JB JB1994040132​116235195​13883
391.455014.4814.86TS 232​315225​7·​1093319​52​192​29
401.454414.3914.70TS AR 78​2707210​510​293318​114​43
411.453316.3217.29AN199303121362·​34​74​119​2357​1034​2399
421.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
431.45269.438.28BdW19880106219​13·​103711311​53​112
441.452023.0826.93FR20100809220​233537·​598​47292324​56​19·​23·​2512
451.451923.7627.92FR20070803313​6151710​832​2719·​151012·​33​517​712
461.45136.024.39JB JB AN1993031235​756​67220
471.45099.778.64JB JB1994040135​73213​233​5953​196
481.450228.1434.40IC20080509238​374228​37​114​193​61·​127·​1732518​174​432​48172
491.450124.3628.64FR20081220233​536​3167228​329​11399257​74​1312​523
501.450010.819.88AN19930312133​53​77​23213​114​13·​41
511.44977.325.76GF 13·​55​472218​79
521.449426.5631.88FR2010042354​1913​103213​139​29·​2441·​76732319​114​4635
531.448014.4214.42AN19930312112​4359​72​134​9723​3·​737
541.44779.187.84AN19930312897·​118220​33​53
551.447615.7816.21TS 317221​56​23·​7993472​3075
561.447428.0333.90FR20070907224​55​475​18121314​19·​103·​5712​4261728​17·​372
571.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
581.44629.858.59AN1993031232​57​79229​13117​192
591.44515.593.86JB JB AN199303122·​132583·​194
601.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
611.444213.0312.44HtR PM 219​26383·​167554​297
621.443516.0216.28AN1993031222​114​17517​1357734​239​71
631.44335.713.95BdW198801061212​5335​72​43
641.44337.696.04JB JB AN1993031232​193511217​373
651.442822.6125.37TD20030804198​434​1492215​523​101313​13·​292​376​911
661.442015.5115.53AN1993031225​112​199515​372​4737​711​743
671.441811.5710.52AN19930312316​232213​292​37359​114​13
681.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
691.441517.3417.93AN1993031273​295​151224​516​97·​919327​134
701.44149.608.15AN199303123132·​17·​4153·​57​75
711.44107.465.74JB JB AN1993031234​232315215​53​7
721.440316.9817.38AN19930312235​72​172​19327​1072515​372​2311
731.43917.285.52BdW19880106124​37​54758​72
741.43849.407.84JB JB19940401119·​5093219​34​59
751.438220.0021.32TD200308043·​56​78​5316792·​116​1934​20551
761.438119.1720.18TD20030804226​114​763956​2311318​474​7879
771.437915.6515.47TD2003080478​13·​893313​53​114​14992·​1912
781.436519.3220.26TD20030804174​1964110​1559212​315​5·​29·​15672
791.43629.557.94AN199303122·​13576​1732313​472
801.435824.0226.70TD2003080434​72​41225​227759​118​BIG
811.43504.933.10BdW19880106210​75738​13
821.434917.5017.71TD20030804317​809227​1195·​74​135​59·​10972
831.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
841.434015.9315.62AN19930312119​4324​236​47·​2772514​72​134
851.433623.2225.37TD2003080411·​1038245​37​29·​37·​1997511​710​79·​3892
861.433515.3714.87AN1993031225​31856​710​232119​691·​1433
871.433516.8116.72AN1993031253​81111912​29219​33​174​2332
881.433119.1019.71TD20030804711​19512​1019·​71512228​312​113​67
891.43308.686.89JB JB AN1993031231235​5925​234​53
901.432914.1313.29AN1993031222176​17·​82092512​7432
911.432316.8616.71TD20030804217​13373​117​432​5801317​176​23
921.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
931.432116.4916.23TS 317​6777​113​2272​547214​57​176
941.431815.3514.76TS 614​149223​13·​29538​5·​74​734
951.431613.2812.18AN19930312174​793​211229​23·​292519
961.431316.8716.66AN19930312227​75326​11·​19·​13952​136​434​179
971.431211.239.72KV 21139​73​113​1929·​2774
981.431112.4911.20AN1993031229​192596​7333​57​72​313
991.430413.2112.04AN199303121932·​56​192​1193239​138
1001.430215.3614.68JB JB1994040136​72​13·​1272238​61·​137511​196
1011.429919.9920.65TD2003080472​23538​1112​47032·​52​132​193​296​532
1021.429917.9918.02AN1993031229​37·​97555​7·​897320​174​3323
1031.42968.346.44AN1993031239​2976​432224​13
1041.429417.5817.46TD20030804220​79·​9753​76​111034​137​86632
1051.429010.448.74AN1993031232172​116​1992·​138​17
1061.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
1071.428910.829.17JB JB19940401732211​114​133311​55​7·​17
1081.428411.7710.25AN19930312514​1136​75​132​251221​234
1091.428417.3817.13TD20030804294214​33​31·​472​1993712​41532
1101.42836.985.00JB JB AN199303121173​16722·​314
1111.42769.607.75JB JB AN1993031273115​157222​310​75
1121.427514.7013.72AN19930312614220​413​832322​5·​19·​167
1131.42718.126.15AN1993031231078​2329​5092
1141.426811.059.36JB JB AN199303123125​510​1923·​75​113​412
1151.42662.110.76BdW1988010635327
1161.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
1171.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
1181.424615.5314.59TD20030804227​80957​76​135323​36251
1191.423420.8821.31TD20030804213​318​2069133​297​2713514​233​31872
1201.42349.687.73JB JB AN1993031252​11133​14832229​32
1211.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
1221.423121.4722.06TD20030804317​113·​4912513​11·​13·​1982·​36​718​1249
1231.422923.5924.86FR201002253117​6029245​56​839238​73​176​432​1573
1241.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
1251.422114.5013.20KV 17·​19433​510​72​293213​137​613
1261.422018.8018.52TD2003080434​236​10132247​53​1927·​1317​1373
1271.42189.677.66JB JB AN1993031224​59512​1933​112​175
1281.42167.445.33AN1993031257115​132215​72​17
1291.421420.0420.06TD200308043·​5·​13627​75​536​2287113​377​9292
1301.421415.1513.94TS 67·​2633310​59​233210​76​132​413
1311.421012.8911.25JD2005112323938​132​23558​1512​863
1321.421012.0810.32AN1993031229​373​8939​59​311036
1331.420813.6012.07TD200308042334​439215​31958​175​71
1341.420817.0916.28TD20030804213​712​3373713​11172321​133​732
1351.420629.8133.15FR20170515313​375​44939255​723​19·​463·​863220​538​61·​1134
1361.42049.097.01AN1993031278​19215​52​3723·​177
1371.420313.7212.18AN19930312313221​54​199278​832​1307
1381.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
1391.420010.688.71AN1993031223339​57​3127​73​13·​174
1401.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
1411.419313.5911.99AN19930312194​37234​514​7928​315​732
1421.419227.5329.82FR2007082559​172​234​372​43·​4817314​118​612​1734252​196​1272
1431.41899.637.54JB JB AN1993031272217​181238​8092
1441.418211.749.83JB JB1994040113·​349923934​511​139
1451.417612.7310.92JB JB1994040156​160929​314​13315234
1461.416812.8110.98AN1993031239​433513​532327​73​236
1471.416414.6813.13JB JB19940401414​33941312​197223​59​29
1481.416315.6214.24TD20030804172​475​73231​593·​137​47232
1491.416121.2821.23AN19930312322​37·​20474928​527132​316​1034​113
1501.416111.949.96JB JB AN199303123·​54​59911·​238222​593
1511.415823.9224.63TD2003080427​54​722194​37·​474​536314​11·​139​191·​7829
1521.415820.6820.43TD20030804520​4021240​13·​173​676336​77​113​296
1531.415724.6925.63TD20030804322​97872510​11·​2910​109237​893​1672​1823
1541.415619.6919.19AN19930312246​2339​55​117​312​431911​59·​7207
1551.415611.349.29AN1993031273513​18124​3·​11·​132​195
1561.415310.588.45HtR PM 3·​234513​312·​74​1993
1571.415121.5121.44AN1993031226​52​713​132​46334​43121112​3892​6841
1581.415027.0428.67JW20090502312​617​3889323​117​1513​173223​56​73​833​3493
1591.414626.3127.65TD20030804718​233325​518​73​173​981439338​134​5233
1601.41458.816.56XG 311​547·​116​43217​173
1611.414417.4416.31AN1993031237​514​72251​112295​73·​4192​1039
1621.41376.684.45JB JB AN1993031226​5·​137314136
1631.41336.684.44JB JB AN199303125237​13328​1372
1641.413213.6311.75JB JB AN1993031236​1573​2832310230​52​112​13
1651.412917.5416.33KV 13·​73339​55​895219​72​315​467
1661.412825.7926.78FR2010052225​55​75​113​292​347238​978​109121312​197​2939
1671.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
1681.41275.253.13BdW198801065311210​173
1691.412629.2531.37FR20100128214​36​424873514​2912​8378​113​477​46109111
1701.412325.1625.91TD20030804294​221323·​132​2312​89·​1471729​516​119​79
1711.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
1721.412316.4014.94TD2003080454​17·​3493717​109235​35​3037
1731.412129.3831.48FR20100212237​312​91093513​1315​2939723​11·​793345871
1741.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
1751.411710.328.05AN1993031279336​7·​11·​135218​433
1761.411722.7622.74FR20100625221​317​3152​418​170532119​61·​712​4313
1771.411616.6915.25JB JB AN199303123·​132​1049239​292​107193​1396
1781.411419.2318.30TD20030804311​72​37·​4728​173​1012​191452​3537
1791.410914.9813.19TD20030804229​13511​269335​72​176​3307
1801.410814.0412.12AN1993031213·​2943·​710​19425​5·​432​1394
1811.410712.2910.15JB JB19940401672​2399313​107326​515
1821.410322.6722.51TD2003080454​532​594​10124​11·​2315314​712​463·​1531
1831.410015.2113.42AN19930312213​313​11313·​29·​436​673520​17
1841.409718.6117.43AN1993031251222​321​432​52859710​133​172​1512
1851.409421.1720.54TD20030804211​34​1014​292211319515​17·​530932
1861.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
1871.409022.3622.00FR20130603436​672​29209318​79​29·​37329​58​177​234
1881.409021.7021.17TD2003080474321​112​134​138493226​57​383·​15792
1891.40909.607.22JB JB AN199303127283522​312​17·​109
1901.408916.9715.40AN19930312212315​192​732​33435·​413​1935
1911.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
1921.407812.8610.65AN1993031222​1373​415​181314​5·​673
1931.407726.2826.87JW2009042275​61213​137​173​42293313​58​113​53·​732​892​103
1941.407620.2019.20FR2013052572​675​2632​487231​17·​236​29316​515​112
1951.407414.4712.43AN1993031232​233237​2932215​52​135​312
1961.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
1971.407212.7910.55JB JB19940401241212​34​56​1181118​134
1981.407116.2814.49TD20030804113​315​101·​4791078231​34​56​7
1991.40718.395.96JB JB AN1993031239​16323​116​17512
2001.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
2011.40659.206.75NE JK 7932​57​133216​192​67
2021.406416.6314.85AN19930312219​3673517​197·​281132​2516
2031.406318.8317.45TS 221​1031178​235​151314​52​432​3133
2041.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
2051.40618.956.49AN19930312216​41·​71315​72197
2061.406120.7319.73AN19930312135​1932·​1112​1123·​76081338​397
2071.40617.134.73JB JB AN199303125·​72132​433211​38
2081.40585.853.56AN1993031213329​37232​57
2091.405410.678.23AN19930312224​355·​195​592710​167
2101.405324.3224.13FR2014081529105·​135​194​232​2332​301591235​310​117​53
2111.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
2121.404919.5418.20TD2003080435​516​19375​232​2334​1321248​432​67
2131.404819.1317.70TD2003080457​237​1493318​39072252​32​331
2141.404511.459.01AN19930312631226​5·​29233​710​37
2151.404421.1220.08FR20150801230​54​4735​175​293​54137·​112​13·​2311​127
2161.40438.285.79AN19930312139​72​19727​57​19
2171.404016.5714.64AN19930312512​22728​3·​73​237​4111·​195​675
2181.404014.9612.81AN1993031239​10328​112​135​412​47514​533
2191.403510.698.18AN1993031233​1325​11·​192​73352​711
2201.403121.2420.11TD2003080422​34​1633​10061514313119​294​1013
2211.402924.0623.56AN199303125·​673​1272​192191318​37·​2772·​315​72​3110
2221.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
2231.402420.0418.62TD20030804211​317​132​19229·​412​83854​472​53·​1076
2241.402210.678.12AN19930312312​5679​31229​115​571
2251.402013.4911.09AN199303123·​514​19972​115​174​41230​134
2261.402014.3312.02AN19930312233​539​76​312​97112​193​1274
2271.401926.5126.54FR2010030511·​198​23·​675​1877312​473​835​1133217​522​10192
2281.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
2291.401724.2423.67TD2003080436​74​43·​16421512​4396259​41·​73939
2301.401411.719.17TS AR 310​54​401136​473229​312
2311.401313.9411.55TS 2227·​676​1373·​54​135​3532
2321.401316.0513.89TD2003080479​134210​233​1734312​5·​116​2371
2331.401316.0013.83KV 36​112​47·​35921713221​54​27492
2341.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
2351.401213.9311.54AN19930312229​732​312​734​349515​532
2361.400814.9212.61AN19930312234​712714​123124​52​112​297
2371.400610.057.43AN19930312134176​463221​732
2381.400313.3210.84AN19930312214​313​57·​296​712119​132​53
2391.400316.7914.68AN19930312518​635932​476​73327​1910​79
2401.400017.7015.71TD200308041742·​712​293​74339​56​135​23·​191

AN  Abderrahmane Nitaj  100
AR  Andrej Rosenheinrich  4
BdW  Benne de Weger  14
ER  Eric Reyssat  1
FR  Frank Rubin  30
GF  Gerhard Frey  1
HtR  Herman te Riele  4
IC  Ismael Jiménez Calvo  2
JB JB  Jerzy Browkin, Juliusz Brzezinski  34
JD  Jeroen Demeyer  9
JK  Joe Kanapka  1
JW  Jarek Wroblewski  2
KV  Kees Visser  6
MH  Mathias Hegner  2
NE  Noam Elkies  1
PM  Peter Montgomery  4
TD  Tim Dokchitser  41
TS  Traugott Schulmeiss  17
XG  Xiao Gang  1

Feel free to send me an update.