There are currently 241 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 241 known triples with q>1.4:last update: 2019-03-02

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
141.410225.8826.62FR2019030225​678​107·​2238154​536​3535322​714​43·​83
151.412825.7926.78FR2010052225​55​75​113​292​347238​978​109121312​197​2939
161.412325.1625.91TD20030804294​221323·​132​2312​89·​1471729​516​119​79
171.415724.6925.63TD20030804322​97872510​11·​2910​109237​893​1672​1823
181.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
191.450124.3628.64FR20081220233​536​3167228​329​11399257​74​1312​523
201.405324.3224.13FR2014081529105·​135​194​232​2332​301591235​310​117​53
211.401724.2423.67TD2003080436​74​43·​16421512​4396259​41·​73939
221.402924.0623.56AN199303125·​673​1272​192191318​37·​2772·​315​72​3110
231.435824.0226.70TD2003080434​72​41225​227759​118​BIG
241.415823.9224.63TD2003080427​54​722194​37·​474​536314​11·​139​191·​7829
251.451923.7627.92FR20070803313​6151710​832​2719·​151012·​33​517​712
261.422923.5924.86FR201002253117​6029245​56​839238​73​176​432​1573
271.433623.2225.37TD2003080411·​1038245​37​29·​37·​1997511​710​79·​3892
281.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
291.452023.0826.93FR20100809220​233537·​598​47292324​56​19·​23·​2512
301.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
311.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
321.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
331.411722.7622.74FR20100625221​317​3152​418​170532119​61·​712​4313
341.410322.6722.51TD2003080454​532​594​10124​11·​2315314​712​463·​1531
351.442822.6125.37TD20030804198​434​1492215​523​101313​13·​292​376​911
361.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
371.409022.3622.00FR20130603436​672​29209318​79​29·​37329​58​177​234
381.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
391.409021.7021.17TD2003080474321​112​134​138493226​57​383·​15792
401.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
411.465321.6025.90FR2016120433​241358​119​19·​613215​172​331·​10614
421.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
431.415121.5121.44AN1993031226​52​713​132​46334​43121112​3892​6841
441.423121.4722.06TD20030804317​113·​4912513​11·​13·​1982·​36​718​1249
451.416121.2821.23AN19930312322​37·​20474928​527132​316​1034​113
461.403121.2420.11TD2003080422​34​1633​10061514313119​294​1013
471.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
481.409421.1720.54TD20030804211​34​1014​292211319515​17·​530932
491.404421.1220.08FR20150801230​54​4735​175​293​54137·​112​13·​2311​127
501.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
511.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
521.423420.8821.31TD20030804213​318​2069133​297​2713514​233​31872
531.544420.7931.54AN1993031272​412​31131116​132​792·​33​523​953
541.406120.7319.73AN19930312135​1932·​1112​1123·​76081338​397
551.415820.6820.43TD20030804520​4021240​13·​173​676336​77​113​296
561.457820.5323.64AN19930312512​172​312​16992314​29219​32​11·​1310​47
571.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
581.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
591.407620.2019.20FR2013052572​675​2632​487231​17·​236​29316​515​112
601.402420.0418.62TD20030804211​317​132​19229·​412​83854​472​53·​1076
611.421420.0420.06TD200308043·​5·​13627​75​536​2287113​377​9292
621.438220.0021.32TD200308043·​56​78​5316792·​116​1934​20551
631.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
641.429919.9920.65TD2003080472​23538​1112​47032·​52​132​193​296​532
651.415619.6919.19AN19930312246​2339​55​117​312​431911​59·​7207
661.404919.5418.20TD2003080435​516​19375​232​2334​1321248​432​67
671.509419.4926.17TD200308041310​37237​195​714​223226​512​1873
681.436519.3220.26TD20030804174​1964110​1559212​315​5·​29·​15672
691.411419.2318.30TD20030804311​72​37·​4728​173​1012​191452​3537
701.438119.1720.18TD20030804226​114​763956​2311318​474​7879
711.492419.1524.26AN1993031222​1132​1310​17·​151·​442359​1396
721.404819.1317.70TD2003080457​237​1493318​39072252​32​331
731.433119.1019.71TD20030804711​19512​1019·​71512228​312​113​67
741.406318.8317.45TS 221​1031178​235​151314​52​432​3133
751.422018.8018.52TD2003080434​236​10132247​53​1927·​1317​1373
761.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
771.409718.6117.43AN1993031251222​321​432​52859710​133​172​1512
781.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
791.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
801.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
811.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
821.429917.9918.02AN1993031229​37·​97555​7·​897320​174​3323
831.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
841.400017.7015.71TD200308041742·​712​293​74339​56​135​23·​191
851.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
861.429417.5817.46TD20030804220​79·​9753​76​111034​137​86632
871.412917.5416.33KV 13·​73339​55​895219​72​315​467
881.434917.5017.71TD20030804317​809227​1195·​74​135​59·​10972
891.414417.4416.31AN1993031237​514​72251​112295​73·​4192​1039
901.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
911.428417.3817.13TD20030804294214​33​31·​472​1993712​41532
921.503317.3722.12TS MH 27​238199​8572322​13·​472​263
931.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
941.441517.3417.93AN1993031273​295​151224​516​97·​919327​134
951.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
961.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
971.420817.0916.28TD20030804213​712​3373713​11172321​133​732
981.522217.0822.92AN19930312318​23·​2269173​29·​318210​52​715
991.440316.9817.38AN19930312235​72​172​19327​1072515​372​2311
1001.408916.9715.40AN19930312212315​192​732​33435·​413​1935
1011.431316.8716.66AN19930312227​75326​11·​19·​13952​136​434​179
1021.432316.8616.71TD20030804217​13373​117​432​5801317​176​23
1031.433516.8116.72AN1993031253​81111912​29219​33​174​2332
1041.400316.7914.68AN19930312518​635932​476​73327​1910​79
1051.411616.6915.25JB JB AN199303123·​132​1049239​292​107193​1396
1061.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
1071.406416.6314.85AN19930312219​3673517​197·​281132​2516
1081.404016.5714.64AN19930312512​22728​3·​73​237​4111·​195​675
1091.432116.4916.23TS 317​6777​113​2272​547214​57​176
1101.412316.4014.94TD2003080454​17·​3493717​109235​35​3037
1111.453316.3217.29AN199303121362·​34​74​119​2357​1034​2399
1121.407116.2814.49TD20030804113​315​101·​4791078231​34​56​7
1131.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
1141.401316.0513.89TD2003080479​134210​233​1734312​5·​116​2371
1151.443516.0216.28AN1993031222​114​17517​1357734​239​71
1161.401316.0013.83KV 36​112​47·​35921713221​54​27492
1171.434015.9315.62AN19930312119​4324​236​47·​2772514​72​134
1181.447615.7816.21TS 317221​56​23·​7993472​3075
1191.491615.7818.79AN1993031273213​77​9412316​1033​127
1201.623515.7026.86JB JB1994040119·​13077·​292​31828​322​54
1211.437915.6515.47TD2003080478​13·​893313​53​114​14992·​1912
1221.416315.6214.24TD20030804172​475​73231​593·​137​47232
1231.424615.5314.59TD20030804227​80957​76​135323​36251
1241.442015.5115.53AN1993031225​112​199515​372​4737​711​743
1251.433515.3714.87AN1993031225​31856​710​232119​691·​1433
1261.430215.3614.68JB JB1994040136​72​13·​1272238​61·​137511​196
1271.431815.3514.76TS 614​149223​13·​29538​5·​74​734
1281.410015.2113.42AN19930312213​313​11313·​29·​436​673520​17
1291.421415.1513.94TS 67·​2633310​59​233210​76​132​413
1301.410914.9813.19TD20030804229​13511​269335​72​176​3307
1311.404014.9612.81AN1993031239​10328​112​135​412​47514​533
1321.400814.9212.61AN19930312234​712714​123124​52​112​297
1331.427514.7013.72AN19930312614220​413​832322​5·​19·​167
1341.416414.6813.13JB JB19940401414​33941312​197223​59​29
1351.422114.5013.20KV 17·​19433​510​72​293213​137​613
1361.455014.4814.86TS 232​315225​7·​1093319​52​192​29
1371.407414.4712.43AN1993031232​233237​2932215​52​135​312
1381.448014.4214.42AN19930312112​4359​72​134​9723​3·​737
1391.454414.3914.70TS AR 78​2707210​510​293318​114​43
1401.402014.3312.02AN19930312233​539​76​312​97112​193​1274
1411.465714.2715.11HtR PM 174​67219​1374315​53​13·​892
1421.432914.1313.29AN1993031222176​17·​82092512​7432
1431.410814.0412.12AN1993031213·​2943·​710​19425​5·​432​1394
1441.456213.9814.24AN19930312225​193·​515​1033117​133​472
1451.401313.9411.55TS 2227·​676​1373·​54​135​3532
1461.401213.9311.54AN19930312229​732​312​734​349515​532
1471.420313.7212.18AN19930312313221​54​199278​832​1307
1481.413213.6311.75JB JB AN1993031236​1573​2832310230​52​112​13
1491.420813.6012.07TD200308042334​439215​31958​175​71
1501.419313.5911.99AN19930312194​37234​514​7928​315​732
1511.402013.4911.09AN199303123·​514​19972​115​174​41230​134
1521.400313.3210.84AN19930312214​313​57·​296​712119​132​53
1531.431613.2812.18AN19930312174​793​211229​23·​292519
1541.430413.2112.04AN199303121932·​56​192​1193239​138
1551.536713.0516.74HtR PM 5329​317​132115​17·​313​137
1561.444213.0312.44HtR PM 219​26383·​167554​297
1571.457813.0213.03AN1993031236​512216​13·​594711​47·​113
1581.481312.9714.04AN19930312514​1925​3·​713117​372​353
1591.421012.8911.25JD2005112323938​132​23558​1512​863
1601.407812.8610.65AN1993031222​1373​415​181314​5·​673
1611.416812.8110.98AN1993031239​433513​532327​73​236
1621.407212.7910.55JB JB19940401241212​34​56​1181118​134
1631.417612.7310.92JB JB1994040156​160929​314​13315234
1641.431112.4911.20AN1993031229​192596​7333​57​72​313
1651.465512.3612.48AN19930312712214​673​461313​11·​194
1661.410712.2910.15JB JB19940401672​2399313​107326​515
1671.421012.0810.32AN1993031229​373​8939​59​311036
1681.416111.949.96JB JB AN199303123·​54​59911·​238222​593
1691.428411.7710.25AN19930312514​1136​75​132​251221​234
1701.418211.749.83JB JB1994040113·​349923934​511​139
1711.401411.719.17TS AR 310​54​401136​473229​312
1721.441811.5710.52AN19930312316​232213​292​37359​114​13
1731.489211.4912.24AN19930312224117​19·​292311​53​73​41
1741.404511.459.01AN19930312631226​5·​29233​710​37
1751.415611.349.29AN1993031273513​18124​3·​11·​132​195
1761.431211.239.72KV 21139​73​113​1929·​2774
1771.426811.059.36JB JB AN199303123125​510​1923·​75​113​412
1781.497610.9911.82BdW1988010652​7937713218​37​132
1791.457110.8610.19AN1993031232​5224​173​314710​257
1801.428910.829.17JB JB19940401732211​114​133311​55​7·​17
1811.450010.819.88AN19930312133​53​77​23213​114​13·​41
1821.403510.698.18AN1993031233​1325​11·​192​73352​711
1831.420010.688.71AN1993031223339​57​3127​73​13·​174
1841.405410.678.23AN19930312224​355·​195​592710​167
1851.402210.678.12AN19930312312​5679​31229​115​571
1861.415310.588.45HtR PM 3·​234513​312·​74​1993
1871.455110.549.72JB JB1994040132​116235195​13883
1881.429010.448.74AN1993031232172​116​1992·​138​17
1891.411710.328.05AN1993031279336​7·​11·​135218​433
1901.400610.057.43AN19930312134176​463221​732
1911.58089.9213.01JB JB AN19930312283511​13228​38​173
1921.44629.858.59AN1993031232​57​79229​13117​192
1931.52709.7811.02AN1993031213·​196230​5313​112​31
1941.45099.778.64JB JB1994040135​73213​233​5953​196
1951.42349.687.73JB JB AN1993031252​11133​14832229​32
1961.42189.677.66JB JB AN1993031224​59512​1933​112​175
1971.41899.637.54JB JB AN1993031272217​181238​8092
1981.42769.607.75JB JB AN1993031273115​157222​310​75
1991.44149.608.15AN199303123132·​17·​4153·​57​75
2001.40909.607.22JB JB AN199303127283522​312​17·​109
2011.43629.557.94AN199303122·​13576​1732313​472
2021.45269.438.28BdW19880106219​13·​103711311​53​112
2031.43849.407.84JB JB19940401119·​5093219​34​59
2041.50289.289.55JB JB AN1993031223958​173210​374
2051.40659.206.75NE JK 7932​57​133216​192​67
2061.44779.187.84AN19930312897·​118220​33​53
2071.42049.097.01AN1993031278​19215​52​3723·​177
2081.40618.956.49AN19930312216​41·​71315​72197
2091.41458.816.56XG 311​547·​116​43217​173
2101.43308.686.89JB JB AN1993031231235​5925​234​53
2111.47448.487.70AN199303121316​723​11·​23·​533
2121.40718.395.96JB JB AN1993031239​16323​116​17512
2131.42968.346.44AN1993031239​2976​432224​13
2141.47138.337.44JB JB AN1993031234​19911823​57​73
2151.40438.285.79AN19930312139​72​19727​57​19
2161.42718.126.15AN1993031231078​2329​5092
2171.44337.696.04JB JB AN1993031232​193511217​373
2181.62607.6810.18BdW1985092011232​56​73221​23
2191.47417.506.48JB JB AN1993031272210​11·​53234​58
2201.44107.465.74JB JB AN1993031234​232315215​53​7
2211.42167.445.33AN1993031257115​132215​72​17
2221.44977.325.76GF 13·​55​472218​79
2231.43917.285.52BdW19880106124​37​54758​72
2241.40617.134.73JB JB AN199303125·​72132​433211​38
2251.42836.985.00JB JB AN199303121173​16722·​314
2261.62996.818.64ER198701012310​109235
2271.41376.684.45JB JB AN1993031226​5·​137314136
2281.46196.685.29BdW1988010627​5276​41136
2291.41336.684.44JB JB AN199303125237​13328​1372
2301.45136.024.39JB JB AN1993031235​756​67220
2311.40585.853.56AN1993031213329​37232​57
2321.44335.713.95BdW198801061212​5335​72​43
2331.44515.593.86JB JB AN199303122·​132583·​194
2341.48895.414.25BdW1988010611239​13211​53
2351.41275.253.13BdW198801065311210​173
2361.43504.933.10BdW19880106210​75738​13
2371.54714.774.17BdW1988010673310211​29
2381.48294.523.18BdW198801063721538​5
2391.56793.642.89BdW1988010612·​3754​7
2401.45573.381.86BdW19880106125​3·​5274
2411.42662.110.76BdW1988010635327

AN  Abderrahmane Nitaj  100
AR  Andrej Rosenheinrich  4
BdW  Benne de Weger  14
ER  Eric Reyssat  1
FR  Frank Rubin  31
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.