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
11.480526.3635.16FR20101107522​79·​4594932​1318​613223​174​2512​17333
21.460627.7835.12IC201006127·​167·​8114​91934​132​2312​674231​53​112​175​1074
31.450228.1434.40IC20080509238​374228​37​114​193​61·​127·​1732518​174​432​48172
41.447428.0333.90FR20070907224​55​475​18121314​19·​103·​5712​4261728​17·​372
51.420629.8133.15FR20170515313​375​44939255​723​19·​463·​863220​538​61·​1134
61.449426.5631.88FR2010042354​1913​103213​139​29·​2441·​76732319​114​4635
71.544420.7931.54AN1993031272​412​31131116​132​792·​33​523​953
81.412129.3831.48FR20100212237​312​91093513​1315​2939723​11·​793345871
91.412629.2531.37FR20100128214​36​424873514​2912​8378​113​477​46109111
101.419227.5329.82FR2007082559​172​234​372​43·​4817314​118​612​1734252​196​1272
111.415027.0428.67JW20090502312​617​3889323​117​1513​173223​56​73​833​3493
121.450124.3628.64FR20081220233​536​3167228​329​11399257​74​1312​523
131.451923.7627.92FR20070803313​6151710​832​2719·​151012·​33​517​712
141.414626.3127.65TD20030804718​233325​518​73​173​981439338​134​5233
151.452023.0826.93FR20100809220​233537·​598​47292324​56​19·​23·​2512
161.407726.2826.87JW2009042275​61213​137​173​42293313​58​113​53·​732​892​103
171.623515.7026.86JB JB1994040119·​13077·​292​31828​322​54
181.412825.7926.78FR2010052225​55​75​113​292​347238​978​109121312​197​2939
191.435824.0226.70TD2003080434​72​41225​227759​118​BIG
201.410225.8826.62FR2019030225​678​107·​2238154​536​3535322​714​43·​83
211.401926.5126.54FR2010030511·​198​23·​675​1877312​473​835​1133217​522​10192
221.509419.4926.17TD200308041310​37237​195​714​223226​512​1873
231.412325.1625.91TD20030804294​221323·​132​2312​89·​1471729​516​119​79
241.465321.6025.90FR2016120433​241358​119​19·​613215​172​331·​10614
251.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
261.415724.6925.63TD20030804322​97872510​11·​2910​109237​893​1672​1823
271.433623.2225.37TD2003080411·​1038245​37​29·​37·​1997511​710​79·​3892
281.442822.6125.37TD20030804198​434​1492215​523​101313​13·​292​376​911
291.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
301.422923.5924.86FR201002253117​6029245​56​839238​73​176​432​1573
311.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
321.415823.9224.63TD2003080427​54​722194​37·​474​536314​11·​139​191·​7829
331.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
341.492419.1524.26AN1993031222​1132​1310​17·​151·​442359​1396
351.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
361.405324.3224.13FR2014081529105·​135​194​232​2332​301591235​310​117​53
371.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
381.401724.2423.67TD2003080436​74​43·​16421512​4396259​41·​73939
391.457820.5323.64AN19930312512​172​312​16992314​29219​32​11·​1310​47
401.402924.0623.56AN199303125·​673​1272​192191318​37·​2772·​315​72​3110
411.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
421.522217.0822.92AN19930312318​23·​2269173​29·​318210​52​715
431.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
441.411722.7622.74FR20100625221​317​3152​418​170532119​61·​712​4313
451.410322.6722.51TD2003080454​532​594​10124​11·​2315314​712​463·​1531
461.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
471.503317.3722.12TS MH 27​238199​8572322​13·​472​263
481.423121.4722.06TD20030804317​113·​4912513​11·​13·​1982·​36​718​1249
491.409022.3622.00FR20130603436​672​29209318​79​29·​37329​58​177​234
501.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
511.415121.5121.44AN1993031226​52​713​132​46334​43121112​3892​6841
521.438220.0021.32TD200308043·​56​78​5316792·​116​1934​20551
531.423420.8821.31TD20030804213​318​2069133​297​2713514​233​31872
541.416121.2821.23AN19930312322​37·​20474928​527132​316​1034​113
551.409021.7021.17TD2003080474321​112​134​138493226​57​383·​15792
561.429919.9920.65TD2003080472​23538​1112​47032·​52​132​193​296​532
571.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
581.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
591.409421.1720.54TD20030804211​34​1014​292211319515​17·​530932
601.415820.6820.43TD20030804520​4021240​13·​173​676336​77​113​296
611.436519.3220.26TD20030804174​1964110​1559212​315​5·​29·​15672
621.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
631.438119.1720.18TD20030804226​114​763956​2311318​474​7879
641.403121.2420.11TD2003080422​34​1633​10061514313119​294​1013
651.404421.1220.08FR20150801230​54​4735​175​293​54137·​112​13·​2311​127
661.421420.0420.06TD200308043·​5·​13627​75​536​2287113​377​9292
671.406120.7319.73AN19930312135​1932·​1112​1123·​76081338​397
681.433119.1019.71TD20030804711​19512​1019·​71512228​312​113​67
691.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
701.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
711.407620.2019.20FR2013052572​675​2632​487231​17·​236​29316​515​112
721.415619.6919.19AN19930312246​2339​55​117​312​431911​59·​7207
731.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
741.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
751.491615.7818.79AN1993031273213​77​9412316​1033​127
761.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
771.402420.0418.62TD20030804211​317​132​19229·​412​83854​472​53·​1076
781.422018.8018.52TD2003080434​236​10132247​53​1927·​1317​1373
791.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
801.411419.2318.30TD20030804311​72​37·​4728​173​1012​191452​3537
811.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
821.404919.5418.20TD2003080435​516​19375​232​2334​1321248​432​67
831.429917.9918.02AN1993031229​37·​97555​7·​897320​174​3323
841.441517.3417.93AN1993031273​295​151224​516​97·​919327​134
851.434917.5017.71TD20030804317​809227​1195·​74​135​59·​10972
861.404819.1317.70TD2003080457​237​1493318​39072252​32​331
871.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
881.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
891.429417.5817.46TD20030804220​79·​9753​76​111034​137​86632
901.406318.8317.45TS 221​1031178​235​151314​52​432​3133
911.409718.6117.43AN1993031251222​321​432​52859710​133​172​1512
921.440316.9817.38AN19930312235​72​172​19327​1072515​372​2311
931.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
941.453316.3217.29AN199303121362·​34​74​119​2357​1034​2399
951.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
961.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
971.428417.3817.13TD20030804294214​33​31·​472​1993712​41532
981.536713.0516.74HtR PM 5329​317​132115​17·​313​137
991.433516.8116.72AN1993031253​81111912​29219​33​174​2332
1001.432316.8616.71TD20030804217​13373​117​432​5801317​176​23
1011.431316.8716.66AN19930312227​75326​11·​19·​13952​136​434​179
1021.412917.5416.33KV 13·​73339​55​895219​72​315​467
1031.414417.4416.31AN1993031237​514​72251​112295​73·​4192​1039
1041.420817.0916.28TD20030804213​712​3373713​11172321​133​732
1051.443516.0216.28AN1993031222​114​17517​1357734​239​71
1061.432116.4916.23TS 317​6777​113​2272​547214​57​176
1071.447615.7816.21TS 317221​56​23·​7993472​3075
1081.400017.7015.71TD200308041742·​712​293​74339​56​135​23·​191
1091.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
1101.434015.9315.62AN19930312119​4324​236​47·​2772514​72​134
1111.442015.5115.53AN1993031225​112​199515​372​4737​711​743
1121.437915.6515.47TD2003080478​13·​893313​53​114​14992·​1912
1131.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
1141.408916.9715.40AN19930312212315​192​732​33435·​413​1935
1151.411616.6915.25JB JB AN199303123·​132​1049239​292​107193​1396
1161.465714.2715.11HtR PM 174​67219​1374315​53​13·​892
1171.412316.4014.94TD2003080454​17·​3493717​109235​35​3037
1181.433515.3714.87AN1993031225​31856​710​232119​691·​1433
1191.455014.4814.86TS 232​315225​7·​1093319​52​192​29
1201.406416.6314.85AN19930312219​3673517​197·​281132​2516
1211.431815.3514.76TS 614​149223​13·​29538​5·​74​734
1221.454414.3914.70TS AR 78​2707210​510​293318​114​43
1231.430215.3614.68JB JB1994040136​72​13·​1272238​61·​137511​196
1241.400316.7914.68AN19930312518​635932​476​73327​1910​79
1251.404016.5714.64AN19930312512​22728​3·​73​237​4111·​195​675
1261.424615.5314.59TD20030804227​80957​76​135323​36251
1271.407116.2814.49TD20030804113​315​101·​4791078231​34​56​7
1281.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
1291.448014.4214.42AN19930312112​4359​72​134​9723​3·​737
1301.416315.6214.24TD20030804172​475​73231​593·​137​47232
1311.456213.9814.24AN19930312225​193·​515​1033117​133​472
1321.481312.9714.04AN19930312514​1925​3·​713117​372​353
1331.421415.1513.94TS 67·​2633310​59​233210​76​132​413
1341.401316.0513.89TD2003080479​134210​233​1734312​5·​116​2371
1351.401316.0013.83KV 36​112​47·​35921713221​54​27492
1361.427514.7013.72AN19930312614220​413​832322​5·​19·​167
1371.410015.2113.42AN19930312213​313​11313·​29·​436​673520​17
1381.432914.1313.29AN1993031222176​17·​82092512​7432
1391.422114.5013.20KV 17·​19433​510​72​293213​137​613
1401.410914.9813.19TD20030804229​13511​269335​72​176​3307
1411.416414.6813.13JB JB19940401414​33941312​197223​59​29
1421.457813.0213.03AN1993031236​512216​13·​594711​47·​113
1431.58089.9213.01JB JB AN19930312283511​13228​38​173
1441.404014.9612.81AN1993031239​10328​112​135​412​47514​533
1451.400814.9212.61AN19930312234​712714​123124​52​112​297
1461.465512.3612.48AN19930312712214​673​461313​11·​194
1471.444213.0312.44HtR PM 219​26383·​167554​297
1481.407414.4712.43AN1993031232​233237​2932215​52​135​312
1491.489211.4912.24AN19930312224117​19·​292311​53​73​41
1501.420313.7212.18AN19930312313221​54​199278​832​1307
1511.431613.2812.18AN19930312174​793​211229​23·​292519
1521.410814.0412.12AN1993031213·​2943·​710​19425​5·​432​1394
1531.420813.6012.07TD200308042334​439215​31958​175​71
1541.430413.2112.04AN199303121932·​56​192​1193239​138
1551.402014.3312.02AN19930312233​539​76​312​97112​193​1274
1561.419313.5911.99AN19930312194​37234​514​7928​315​732
1571.497610.9911.82BdW1988010652​7937713218​37​132
1581.413213.6311.75JB JB AN1993031236​1573​2832310230​52​112​13
1591.401313.9411.55TS 2227·​676​1373·​54​135​3532
1601.401213.9311.54AN19930312229​732​312​734​349515​532
1611.421012.8911.25JD2005112323938​132​23558​1512​863
1621.431112.4911.20AN1993031229​192596​7333​57​72​313
1631.402013.4911.09AN199303123·​514​19972​115​174​41230​134
1641.52709.7811.02AN1993031213·​196230​5313​112​31
1651.416812.8110.98AN1993031239​433513​532327​73​236
1661.417612.7310.92JB JB1994040156​160929​314​13315234
1671.400313.3210.84AN19930312214​313​57·​296​712119​132​53
1681.407812.8610.65AN1993031222​1373​415​181314​5·​673
1691.407212.7910.55JB JB19940401241212​34​56​1181118​134
1701.441811.5710.52AN19930312316​232213​292​37359​114​13
1711.421012.0810.32AN1993031229​373​8939​59​311036
1721.428411.7710.25AN19930312514​1136​75​132​251221​234
1731.457110.8610.19AN1993031232​5224​173​314710​257
1741.62607.6810.18BdW1985092011232​56​73221​23
1751.410712.2910.15JB JB19940401672​2399313​107326​515
1761.416111.949.96JB JB AN199303123·​54​59911·​238222​593
1771.450010.819.88AN19930312133​53​77​23213​114​13·​41
1781.418211.749.83JB JB1994040113·​349923934​511​139
1791.431211.239.72KV 21139​73​113​1929·​2774
1801.455110.549.72JB JB1994040132​116235195​13883
1811.50289.289.55JB JB AN1993031223958​173210​374
1821.426811.059.36JB JB AN199303123125​510​1923·​75​113​412
1831.415611.349.29AN1993031273513​18124​3·​11·​132​195
1841.401411.719.17TS AR 310​54​401136​473229​312
1851.428910.829.17JB JB19940401732211​114​133311​55​7·​17
1861.404511.459.01AN19930312631226​5·​29233​710​37
1871.429010.448.74AN1993031232172​116​1992·​138​17
1881.420010.688.71AN1993031223339​57​3127​73​13·​174
1891.62996.818.64ER198701012310​109235
1901.45099.778.64JB JB1994040135​73213​233​5953​196
1911.44629.858.59AN1993031232​57​79229​13117​192
1921.415310.588.45HtR PM 3·​234513​312·​74​1993
1931.45269.438.28BdW19880106219​13·​103711311​53​112
1941.405410.678.23AN19930312224​355·​195​592710​167
1951.403510.698.18AN1993031233​1325​11·​192​73352​711
1961.44149.608.15AN199303123132·​17·​4153·​57​75
1971.402210.678.12AN19930312312​5679​31229​115​571
1981.411710.328.05AN1993031279336​7·​11·​135218​433
1991.43629.557.94AN199303122·​13576​1732313​472
2001.44779.187.84AN19930312897·​118220​33​53
2011.43849.407.84JB JB19940401119·​5093219​34​59
2021.42769.607.75JB JB AN1993031273115​157222​310​75
2031.42349.687.73JB JB AN1993031252​11133​14832229​32
2041.47448.487.70AN199303121316​723​11·​23·​533
2051.42189.677.66JB JB AN1993031224​59512​1933​112​175
2061.41899.637.54JB JB AN1993031272217​181238​8092
2071.47138.337.44JB JB AN1993031234​19911823​57​73
2081.400610.057.43AN19930312134176​463221​732
2091.40909.607.22JB JB AN199303127283522​312​17·​109
2101.42049.097.01AN1993031278​19215​52​3723·​177
2111.43308.686.89JB JB AN1993031231235​5925​234​53
2121.40659.206.75NE JK 7932​57​133216​192​67
2131.41458.816.56XG 311​547·​116​43217​173
2141.40618.956.49AN19930312216​41·​71315​72197
2151.47417.506.48JB JB AN1993031272210​11·​53234​58
2161.42968.346.44AN1993031239​2976​432224​13
2171.42718.126.15AN1993031231078​2329​5092
2181.44337.696.04JB JB AN1993031232​193511217​373
2191.40718.395.96JB JB AN1993031239​16323​116​17512
2201.40438.285.79AN19930312139​72​19727​57​19
2211.44977.325.76GF 13·​55​472218​79
2221.44107.465.74JB JB AN1993031234​232315215​53​7
2231.43917.285.52BdW19880106124​37​54758​72
2241.42167.445.33AN1993031257115​132215​72​17
2251.46196.685.29BdW1988010627​5276​41136
2261.42836.985.00JB JB AN199303121173​16722·​314
2271.40617.134.73JB JB AN199303125·​72132​433211​38
2281.41376.684.45JB JB AN1993031226​5·​137314136
2291.41336.684.44JB JB AN199303125237​13328​1372
2301.45136.024.39JB JB AN1993031235​756​67220
2311.48895.414.25BdW1988010611239​13211​53
2321.54714.774.17BdW1988010673310211​29
2331.44335.713.95BdW198801061212​5335​72​43
2341.44515.593.86JB JB AN199303122·​132583·​194
2351.40585.853.56AN1993031213329​37232​57
2361.48294.523.18BdW198801063721538​5
2371.41275.253.13BdW198801065311210​173
2381.43504.933.10BdW19880106210​75738​13
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.