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
11.420629.8133.15FR20170515313​375​44939255​723​19·​463·​863220​538​61·​1134
21.412129.3831.48FR20100212237​312​91093513​1315​2939723​11·​793345871
31.412629.2531.37FR20100128214​36​424873514​2912​8378​113​477​46109111
41.450228.1434.40IC20080509238​374228​37​114​193​61·​127·​1732518​174​432​48172
51.447428.0333.90FR20070907224​55​475​18121314​19·​103·​5712​4261728​17·​372
61.460627.7835.12IC201006127·​167·​8114​91934​132​2312​674231​53​112​175​1074
71.419227.5329.82FR2007082559​172​234​372​43·​4817314​118​612​1734252​196​1272
81.415027.0428.67JW20090502312​617​3889323​117​1513​173223​56​73​833​3493
91.449426.5631.88FR2010042354​1913​103213​139​29·​2441·​76732319​114​4635
101.401926.5126.54FR2010030511·​198​23·​675​1877312​473​835​1133217​522​10192
111.480526.3635.16FR20101107522​79·​4594932​1318​613223​174​2512​17333
121.414626.3127.65TD20030804718​233325​518​73​173​981439338​134​5233
131.407726.2826.87JW2009042275​61213​137​173​42293313​58​113​53·​732​892​103
141.412825.7926.78FR2010052225​55​75​113​292​347238​978​109121312​197​2939
151.412325.1625.91TD20030804294​221323·​132​2312​89·​1471729​516​119​79
161.415724.6925.63TD20030804322​97872510​11·​2910​109237​893​1672​1823
171.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
181.450124.3628.64FR20081220233​536​3167228​329​11399257​74​1312​523
191.405324.3224.13FR2014081529105·​135​194​232​2332​301591235​310​117​53
201.401724.2423.67TD2003080436​74​43·​16421512​4396259​41·​73939
211.402924.0623.56AN199303125·​673​1272​192191318​37·​2772·​315​72​3110
221.435824.0226.70TD2003080434​72​41225​227759​118​BIG
231.415823.9224.63TD2003080427​54​722194​37·​474​536314​11·​139​191·​7829
241.451923.7627.92FR20070803313​6151710​832​2719·​151012·​33​517​712
251.422923.5924.86FR201002253117​6029245​56​839238​73​176​432​1573
261.433623.2225.37TD2003080411·​1038245​37​29·​37·​1997511​710​79·​3892
271.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
281.452023.0826.93FR20100809220​233537·​598​47292324​56​19·​23·​2512
291.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
301.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
311.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
321.411722.7622.74FR20100625221​317​3152​418​170532119​61·​712​4313
331.410322.6722.51TD2003080454​532​594​10124​11·​2315314​712​463·​1531
341.442822.6125.37TD20030804198​434​1492215​523​101313​13·​292​376​911
351.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
361.409022.3622.00FR20130603436​672​29209318​79​29·​37329​58​177​234
371.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
381.409021.7021.17TD2003080474321​112​134​138493226​57​383·​15792
391.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
401.465321.6025.90FR2016120433​241358​119​19·​613215​172​331·​10614
411.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
421.415121.5121.44AN1993031226​52​713​132​46334​43121112​3892​6841
431.423121.4722.06TD20030804317​113·​4912513​11·​13·​1982·​36​718​1249
441.416121.2821.23AN19930312322​37·​20474928​527132​316​1034​113
451.403121.2420.11TD2003080422​34​1633​10061514313119​294​1013
461.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
471.409421.1720.54TD20030804211​34​1014​292211319515​17·​530932
481.404421.1220.08FR20150801230​54​4735​175​293​54137·​112​13·​2311​127
491.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
501.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
511.423420.8821.31TD20030804213​318​2069133​297​2713514​233​31872
521.544420.7931.54AN1993031272​412​31131116​132​792·​33​523​953
531.406120.7319.73AN19930312135​1932·​1112​1123·​76081338​397
541.415820.6820.43TD20030804520​4021240​13·​173​676336​77​113​296
551.457820.5323.64AN19930312512​172​312​16992314​29219​32​11·​1310​47
561.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
571.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
581.407620.2019.20FR2013052572​675​2632​487231​17·​236​29316​515​112
591.402420.0418.62TD20030804211​317​132​19229·​412​83854​472​53·​1076
601.421420.0420.06TD200308043·​5·​13627​75​536​2287113​377​9292
611.438220.0021.32TD200308043·​56​78​5316792·​116​1934​20551
621.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
631.429919.9920.65TD2003080472​23538​1112​47032·​52​132​193​296​532
641.415619.6919.19AN19930312246​2339​55​117​312​431911​59·​7207
651.404919.5418.20TD2003080435​516​19375​232​2334​1321248​432​67
661.509419.4926.17TD200308041310​37237​195​714​223226​512​1873
671.436519.3220.26TD20030804174​1964110​1559212​315​5·​29·​15672
681.411419.2318.30TD20030804311​72​37·​4728​173​1012​191452​3537
691.438119.1720.18TD20030804226​114​763956​2311318​474​7879
701.492419.1524.26AN1993031222​1132​1310​17·​151·​442359​1396
711.404819.1317.70TD2003080457​237​1493318​39072252​32​331
721.433119.1019.71TD20030804711​19512​1019·​71512228​312​113​67
731.406318.8317.45TS 221​1031178​235​151314​52​432​3133
741.422018.8018.52TD2003080434​236​10132247​53​1927·​1317​1373
751.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
761.409718.6117.43AN1993031251222​321​432​52859710​133​172​1512
771.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
781.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
791.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
801.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
811.429917.9918.02AN1993031229​37·​97555​7·​897320​174​3323
821.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
831.400017.7015.71TD200308041742·​712​293​74339​56​135​23·​191
841.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
851.429417.5817.46TD20030804220​79·​9753​76​111034​137​86632
861.412917.5416.33KV 13·​73339​55​895219​72​315​467
871.434917.5017.71TD20030804317​809227​1195·​74​135​59·​10972
881.414417.4416.31AN1993031237​514​72251​112295​73·​4192​1039
891.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
901.428417.3817.13TD20030804294214​33​31·​472​1993712​41532
911.503317.3722.12TS MH 27​238199​8572322​13·​472​263
921.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
931.441517.3417.93AN1993031273​295​151224​516​97·​919327​134
941.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
951.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
961.420817.0916.28TD20030804213​712​3373713​11172321​133​732
971.522217.0822.92AN19930312318​23·​2269173​29·​318210​52​715
981.440316.9817.38AN19930312235​72​172​19327​1072515​372​2311
991.408916.9715.40AN19930312212315​192​732​33435·​413​1935
1001.431316.8716.66AN19930312227​75326​11·​19·​13952​136​434​179
1011.432316.8616.71TD20030804217​13373​117​432​5801317​176​23
1021.433516.8116.72AN1993031253​81111912​29219​33​174​2332
1031.400316.7914.68AN19930312518​635932​476​73327​1910​79
1041.411616.6915.25JB JB AN199303123·​132​1049239​292​107193​1396
1051.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
1061.406416.6314.85AN19930312219​3673517​197·​281132​2516
1071.404016.5714.64AN19930312512​22728​3·​73​237​4111·​195​675
1081.432116.4916.23TS 317​6777​113​2272​547214​57​176
1091.412316.4014.94TD2003080454​17·​3493717​109235​35​3037
1101.453316.3217.29AN199303121362·​34​74​119​2357​1034​2399
1111.407116.2814.49TD20030804113​315​101·​4791078231​34​56​7
1121.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
1131.401316.0513.89TD2003080479​134210​233​1734312​5·​116​2371
1141.443516.0216.28AN1993031222​114​17517​1357734​239​71
1151.401316.0013.83KV 36​112​47·​35921713221​54​27492
1161.434015.9315.62AN19930312119​4324​236​47·​2772514​72​134
1171.447615.7816.21TS 317221​56​23·​7993472​3075
1181.491615.7818.79AN1993031273213​77​9412316​1033​127
1191.623515.7026.86JB JB1994040119·​13077·​292​31828​322​54
1201.437915.6515.47TD2003080478​13·​893313​53​114​14992·​1912
1211.416315.6214.24TD20030804172​475​73231​593·​137​47232
1221.424615.5314.59TD20030804227​80957​76​135323​36251
1231.442015.5115.53AN1993031225​112​199515​372​4737​711​743
1241.433515.3714.87AN1993031225​31856​710​232119​691·​1433
1251.430215.3614.68JB JB1994040136​72​13·​1272238​61·​137511​196
1261.431815.3514.76TS 614​149223​13·​29538​5·​74​734
1271.410015.2113.42AN19930312213​313​11313·​29·​436​673520​17
1281.421415.1513.94TS 67·​2633310​59​233210​76​132​413
1291.410914.9813.19TD20030804229​13511​269335​72​176​3307
1301.404014.9612.81AN1993031239​10328​112​135​412​47514​533
1311.400814.9212.61AN19930312234​712714​123124​52​112​297
1321.427514.7013.72AN19930312614220​413​832322​5·​19·​167
1331.416414.6813.13JB JB19940401414​33941312​197223​59​29
1341.422114.5013.20KV 17·​19433​510​72​293213​137​613
1351.455014.4814.86TS 232​315225​7·​1093319​52​192​29
1361.407414.4712.43AN1993031232​233237​2932215​52​135​312
1371.448014.4214.42AN19930312112​4359​72​134​9723​3·​737
1381.454414.3914.70TS AR 78​2707210​510​293318​114​43
1391.402014.3312.02AN19930312233​539​76​312​97112​193​1274
1401.465714.2715.11HtR PM 174​67219​1374315​53​13·​892
1411.432914.1313.29AN1993031222176​17·​82092512​7432
1421.410814.0412.12AN1993031213·​2943·​710​19425​5·​432​1394
1431.456213.9814.24AN19930312225​193·​515​1033117​133​472
1441.401313.9411.55TS 2227·​676​1373·​54​135​3532
1451.401213.9311.54AN19930312229​732​312​734​349515​532
1461.420313.7212.18AN19930312313221​54​199278​832​1307
1471.413213.6311.75JB JB AN1993031236​1573​2832310230​52​112​13
1481.420813.6012.07TD200308042334​439215​31958​175​71
1491.419313.5911.99AN19930312194​37234​514​7928​315​732
1501.402013.4911.09AN199303123·​514​19972​115​174​41230​134
1511.400313.3210.84AN19930312214​313​57·​296​712119​132​53
1521.431613.2812.18AN19930312174​793​211229​23·​292519
1531.430413.2112.04AN199303121932·​56​192​1193239​138
1541.536713.0516.74HtR PM 5329​317​132115​17·​313​137
1551.444213.0312.44HtR PM 219​26383·​167554​297
1561.457813.0213.03AN1993031236​512216​13·​594711​47·​113
1571.481312.9714.04AN19930312514​1925​3·​713117​372​353
1581.421012.8911.25JD2005112323938​132​23558​1512​863
1591.407812.8610.65AN1993031222​1373​415​181314​5·​673
1601.416812.8110.98AN1993031239​433513​532327​73​236
1611.407212.7910.55JB JB19940401241212​34​56​1181118​134
1621.417612.7310.92JB JB1994040156​160929​314​13315234
1631.431112.4911.20AN1993031229​192596​7333​57​72​313
1641.465512.3612.48AN19930312712214​673​461313​11·​194
1651.410712.2910.15JB JB19940401672​2399313​107326​515
1661.421012.0810.32AN1993031229​373​8939​59​311036
1671.416111.949.96JB JB AN199303123·​54​59911·​238222​593
1681.428411.7710.25AN19930312514​1136​75​132​251221​234
1691.418211.749.83JB JB1994040113·​349923934​511​139
1701.401411.719.17TS AR 310​54​401136​473229​312
1711.441811.5710.52AN19930312316​232213​292​37359​114​13
1721.489211.4912.24AN19930312224117​19·​292311​53​73​41
1731.404511.459.01AN19930312631226​5·​29233​710​37
1741.415611.349.29AN1993031273513​18124​3·​11·​132​195
1751.431211.239.72KV 21139​73​113​1929·​2774
1761.426811.059.36JB JB AN199303123125​510​1923·​75​113​412
1771.497610.9911.82BdW1988010652​7937713218​37​132
1781.457110.8610.19AN1993031232​5224​173​314710​257
1791.428910.829.17JB JB19940401732211​114​133311​55​7·​17
1801.450010.819.88AN19930312133​53​77​23213​114​13·​41
1811.403510.698.18AN1993031233​1325​11·​192​73352​711
1821.420010.688.71AN1993031223339​57​3127​73​13·​174
1831.405410.678.23AN19930312224​355·​195​592710​167
1841.402210.678.12AN19930312312​5679​31229​115​571
1851.415310.588.45HtR PM 3·​234513​312·​74​1993
1861.455110.549.72JB JB1994040132​116235195​13883
1871.429010.448.74AN1993031232172​116​1992·​138​17
1881.411710.328.05AN1993031279336​7·​11·​135218​433
1891.400610.057.43AN19930312134176​463221​732
1901.58089.9213.01JB JB AN19930312283511​13228​38​173
1911.44629.858.59AN1993031232​57​79229​13117​192
1921.52709.7811.02AN1993031213·​196230​5313​112​31
1931.45099.778.64JB JB1994040135​73213​233​5953​196
1941.42349.687.73JB JB AN1993031252​11133​14832229​32
1951.42189.677.66JB JB AN1993031224​59512​1933​112​175
1961.41899.637.54JB JB AN1993031272217​181238​8092
1971.42769.607.75JB JB AN1993031273115​157222​310​75
1981.44149.608.15AN199303123132·​17·​4153·​57​75
1991.40909.607.22JB JB AN199303127283522​312​17·​109
2001.43629.557.94AN199303122·​13576​1732313​472
2011.45269.438.28BdW19880106219​13·​103711311​53​112
2021.43849.407.84JB JB19940401119·​5093219​34​59
2031.50289.289.55JB JB AN1993031223958​173210​374
2041.40659.206.75NE JK 7932​57​133216​192​67
2051.44779.187.84AN19930312897·​118220​33​53
2061.42049.097.01AN1993031278​19215​52​3723·​177
2071.40618.956.49AN19930312216​41·​71315​72197
2081.41458.816.56XG 311​547·​116​43217​173
2091.43308.686.89JB JB AN1993031231235​5925​234​53
2101.47448.487.70AN199303121316​723​11·​23·​533
2111.40718.395.96JB JB AN1993031239​16323​116​17512
2121.42968.346.44AN1993031239​2976​432224​13
2131.47138.337.44JB JB AN1993031234​19911823​57​73
2141.40438.285.79AN19930312139​72​19727​57​19
2151.42718.126.15AN1993031231078​2329​5092
2161.44337.696.04JB JB AN1993031232​193511217​373
2171.62607.6810.18BdW1985092011232​56​73221​23
2181.47417.506.48JB JB AN1993031272210​11·​53234​58
2191.44107.465.74JB JB AN1993031234​232315215​53​7
2201.42167.445.33AN1993031257115​132215​72​17
2211.44977.325.76GF 13·​55​472218​79
2221.43917.285.52BdW19880106124​37​54758​72
2231.40617.134.73JB JB AN199303125·​72132​433211​38
2241.42836.985.00JB JB AN199303121173​16722·​314
2251.62996.818.64ER198701012310​109235
2261.41376.684.45JB JB AN1993031226​5·​137314136
2271.46196.685.29BdW1988010627​5276​41136
2281.41336.684.44JB JB AN199303125237​13328​1372
2291.45136.024.39JB JB AN1993031235​756​67220
2301.40585.853.56AN1993031213329​37232​57
2311.44335.713.95BdW198801061212​5335​72​43
2321.44515.593.86JB JB AN199303122·​132583·​194
2331.48895.414.25BdW1988010611239​13211​53
2341.41275.253.13BdW198801065311210​173
2351.43504.933.10BdW19880106210​75738​13
2361.54714.774.17BdW1988010673310211​29
2371.48294.523.18BdW198801063721538​5
2381.56793.642.89BdW1988010612·​3754​7
2391.45573.381.86BdW19880106125​3·​5274
2401.42662.110.76BdW1988010635327

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.