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
11.410225.8826.62FR2019030225​678​107·​2238154​536​3535322​714​43·​83
21.420629.8133.15FR20170515313​375​44939255​723​19·​463·​863220​538​61·​1134
31.465321.6025.90FR2016120433​241358​119​19·​613215​172​331·​10614
41.404421.1220.08FR20150801230​54​4735​175​293​54137·​112​13·​2311​127
51.405324.3224.13FR2014081529105·​135​194​232​2332​301591235​310​117​53
61.409022.3622.00FR20130603436​672​29209318​79​29·​37329​58​177​234
71.407620.2019.20FR2013052572​675​2632​487231​17·​236​29316​515​112
81.480526.3635.16FR20101107522​79·​4594932​1318​613223​174​2512​17333
91.452023.0826.93FR20100809220​233537·​598​47292324​56​19·​23·​2512
101.411722.7622.74FR20100625221​317​3152​418​170532119​61·​712​4313
111.460627.7835.12IC201006127·​167·​8114​91934​132​2312​674231​53​112​175​1074
121.412825.7926.78FR2010052225​55​75​113​292​347238​978​109121312​197​2939
131.449426.5631.88FR2010042354​1913​103213​139​29·​2441·​76732319​114​4635
141.401926.5126.54FR2010030511·​198​23·​675​1877312​473​835​1133217​522​10192
151.422923.5924.86FR201002253117​6029245​56​839238​73​176​432​1573
161.412129.3831.48FR20100212237​312​91093513​1315​2939723​11·​793345871
171.412629.2531.37FR20100128214​36​424873514​2912​8378​113​477​46109111
181.415027.0428.67JW20090502312​617​3889323​117​1513​173223​56​73​833​3493
191.407726.2826.87JW2009042275​61213​137​173​42293313​58​113​53·​732​892​103
201.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
211.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
221.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
231.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
241.450124.3628.64FR20081220233​536​3167228​329​11399257​74​1312​523
251.450228.1434.40IC20080509238​374228​37​114​193​61·​127·​1732518​174​432​48172
261.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
271.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
281.447428.0333.90FR20070907224​55​475​18121314​19·​103·​5712​4261728​17·​372
291.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
301.419227.5329.82FR2007082559​172​234​372​43·​4817314​118​612​1734252​196​1272
311.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
321.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
331.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
341.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
351.451923.7627.92FR20070803313​6151710​832​2719·​151012·​33​517​712
361.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
371.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
381.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
391.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
401.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
411.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
421.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
431.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
441.421012.8911.25JD2005112323938​132​23558​1512​863
451.415823.9224.63TD2003080427​54​722194​37·​474​536314​11·​139​191·​7829
461.414626.3127.65TD20030804718​233325​518​73​173​981439338​134​5233
471.442822.6125.37TD20030804198​434​1492215​523​101313​13·​292​376​911
481.415724.6925.63TD20030804322​97872510​11·​2910​109237​893​1672​1823
491.423121.4722.06TD20030804317​113·​4912513​11·​13·​1982·​36​718​1249
501.409421.1720.54TD20030804211​34​1014​292211319515​17·​530932
511.404819.1317.70TD2003080457​237​1493318​39072252​32​331
521.415820.6820.43TD20030804520​4021240​13·​173​676336​77​113​296
531.404919.5418.20TD2003080435​516​19375​232​2334​1321248​432​67
541.433623.2225.37TD2003080411·​1038245​37​29·​37·​1997511​710​79·​3892
551.402420.0418.62TD20030804211​317​132​19229·​412​83854​472​53·​1076
561.422018.8018.52TD2003080434​236​10132247​53​1927·​1317​1373
571.438119.1720.18TD20030804226​114​763956​2311318​474​7879
581.423420.8821.31TD20030804213​318​2069133​297​2713514​233​31872
591.410322.6722.51TD2003080454​532​594​10124​11·​2315314​712​463·​1531
601.407116.2814.49TD20030804113​315​101·​4791078231​34​56​7
611.420817.0916.28TD20030804213​712​3373713​11172321​133​732
621.403121.2420.11TD2003080422​34​1633​10061514313119​294​1013
631.509419.4926.17TD200308041310​37237​195​714​223226​512​1873
641.437915.6515.47TD2003080478​13·​893313​53​114​14992·​1912
651.438220.0021.32TD200308043·​56​78​5316792·​116​1934​20551
661.416315.6214.24TD20030804172​475​73231​593·​137​47232
671.436519.3220.26TD20030804174​1964110​1559212​315​5·​29·​15672
681.412325.1625.91TD20030804294​221323·​132​2312​89·​1471729​516​119​79
691.420813.6012.07TD200308042334​439215​31958​175​71
701.401724.2423.67TD2003080436​74​43·​16421512​4396259​41·​73939
711.401316.0513.89TD2003080479​134210​233​1734312​5·​116​2371
721.412316.4014.94TD2003080454​17·​3493717​109235​35​3037
731.424615.5314.59TD20030804227​80957​76​135323​36251
741.434917.5017.71TD20030804317​809227​1195·​74​135​59·​10972
751.433119.1019.71TD20030804711​19512​1019·​71512228​312​113​67
761.411419.2318.30TD20030804311​72​37·​4728​173​1012​191452​3537
771.429417.5817.46TD20030804220​79·​9753​76​111034​137​86632
781.410914.9813.19TD20030804229​13511​269335​72​176​3307
791.429919.9920.65TD2003080472​23538​1112​47032·​52​132​193​296​532
801.432316.8616.71TD20030804217​13373​117​432​5801317​176​23
811.421420.0420.06TD200308043·​5·​13627​75​536​2287113​377​9292
821.428417.3817.13TD20030804294214​33​31·​472​1993712​41532
831.435824.0226.70TD2003080434​72​41225​227759​118​BIG
841.400017.7015.71TD200308041742·​712​293​74339​56​135​23·​191
851.409021.7021.17TD2003080474321​112​134​138493226​57​383·​15792
861.416414.6813.13JB JB19940401414​33941312​197223​59​29
871.430215.3614.68JB JB1994040136​72​13·​1272238​61·​137511​196
881.417612.7310.92JB JB1994040156​160929​314​13315234
891.455110.549.72JB JB1994040132​116235195​13883
901.410712.2910.15JB JB19940401672​2399313​107326​515
911.45099.778.64JB JB1994040135​73213​233​5953​196
921.418211.749.83JB JB1994040113·​349923934​511​139
931.623515.7026.86JB JB1994040119·​13077·​292​31828​322​54
941.428910.829.17JB JB19940401732211​114​133311​55​7·​17
951.407212.7910.55JB JB19940401241212​34​56​1181118​134
961.43849.407.84JB JB19940401119·​5093219​34​59
971.415121.5121.44AN1993031226​52​713​132​46334​43121112​3892​6841
981.416121.2821.23AN19930312322​37·​20474928​527132​316​1034​113
991.457820.5323.64AN19930312512​172​312​16992314​29219​32​11·​1310​47
1001.400316.7914.68AN19930312518​635932​476​73327​1910​79
1011.440316.9817.38AN19930312235​72​172​19327​1072515​372​2311
1021.415619.6919.19AN19930312246​2339​55​117​312​431911​59·​7207
1031.442015.5115.53AN1993031225​112​199515​372​4737​711​743
1041.414417.4416.31AN1993031237​514​72251​112295​73·​4192​1039
1051.402924.0623.56AN199303125·​673​1272​192191318​37·​2772·​315​72​3110
1061.429917.9918.02AN1993031229​37·​97555​7·​897320​174​3323
1071.441517.3417.93AN1993031273​295​151224​516​97·​919327​134
1081.406416.6314.85AN19930312219​3673517​197·​281132​2516
1091.522217.0822.92AN19930312318​23·​2269173​29·​318210​52​715
1101.410015.2113.42AN19930312213​313​11313·​29·​436​673520​17
1111.431613.2812.18AN19930312174​793​211229​23·​292519
1121.402013.4911.09AN199303123·​514​19972​115​174​41230​134
1131.544420.7931.54AN1993031272​412​31131116​132​792·​33​523​953
1141.431316.8716.66AN19930312227​75326​11·​19·​13952​136​434​179
1151.413213.6311.75JB JB AN1993031236​1573​2832310230​52​112​13
1161.457813.0213.03AN1993031236​512216​13·​594711​47·​113
1171.400313.3210.84AN19930312214​313​57·​296​712119​132​53
1181.481312.9714.04AN19930312514​1925​3·​713117​372​353
1191.434015.9315.62AN19930312119​4324​236​47·​2772514​72​134
1201.428411.7710.25AN19930312514​1136​75​132​251221​234
1211.404016.5714.64AN19930312512​22728​3·​73​237​4111·​195​675
1221.402014.3312.02AN19930312233​539​76​312​97112​193​1274
1231.441811.5710.52AN19930312316​232213​292​37359​114​13
1241.465512.3612.48AN19930312712214​673​461313​11·​194
1251.433515.3714.87AN1993031225​31856​710​232119​691·​1433
1261.429010.448.74AN1993031232172​116​1992·​138​17
1271.402210.678.12AN19930312312​5679​31229​115​571
1281.405410.678.23AN19930312224​355·​195​592710​167
1291.401213.9311.54AN19930312229​732​312​734​349515​532
1301.406120.7319.73AN19930312135​1932·​1112​1123·​76081338​397
1311.421012.0810.32AN1993031229​373​8939​59​311036
1321.416812.8110.98AN1993031239​433513​532327​73​236
1331.400814.9212.61AN19930312234​712714​123124​52​112​297
1341.456213.9814.24AN19930312225​193·​515​1033117​133​472
1351.52709.7811.02AN1993031213·​196230​5313​112​31
1361.409718.6117.43AN1993031251222​321​432​52859710​133​172​1512
1371.40618.956.49AN19930312216​41·​71315​72197
1381.419313.5911.99AN19930312194​37234​514​7928​315​732
1391.42049.097.01AN1993031278​19215​52​3723·​177
1401.44629.858.59AN1993031232​57​79229​13117​192
1411.489211.4912.24AN19930312224117​19·​292311​53​73​41
1421.427514.7013.72AN19930312614220​413​832322​5·​19·​167
1431.410814.0412.12AN1993031213·​2943·​710​19425​5·​432​1394
1441.453316.3217.29AN199303121362·​34​74​119​2357​1034​2399
1451.40718.395.96JB JB AN1993031239​16323​116​17512
1461.432914.1313.29AN1993031222176​17·​82092512​7432
1471.404014.9612.81AN1993031239​10328​112​135​412​47514​533
1481.420313.7212.18AN19930312313221​54​199278​832​1307
1491.416111.949.96JB JB AN199303123·​54​59911·​238222​593
1501.433516.8116.72AN1993031253​81111912​29219​33​174​2332
1511.443516.0216.28AN1993031222​114​17517​1357734​239​71
1521.43629.557.94AN199303122·​13576​1732313​472
1531.42968.346.44AN1993031239​2976​432224​13
1541.411616.6915.25JB JB AN199303123·​132​1049239​292​107193​1396
1551.411710.328.05AN1993031279336​7·​11·​135218​433
1561.431112.4911.20AN1993031229​192596​7333​57​72​313
1571.42167.445.33AN1993031257115​132215​72​17
1581.44337.696.04JB JB AN1993031232​193511217​373
1591.42718.126.15AN1993031231078​2329​5092
1601.41376.684.45JB JB AN1993031226​5·​137314136
1611.44107.465.74JB JB AN1993031234​232315215​53​7
1621.44149.608.15AN199303123132·​17·​4153·​57​75
1631.400610.057.43AN19930312134176​463221​732
1641.47138.337.44JB JB AN1993031234​19911823​57​73
1651.420010.688.71AN1993031223339​57​3127​73​13·​174
1661.448014.4214.42AN19930312112​4359​72​134​9723​3·​737
1671.408916.9715.40AN19930312212315​192​732​33435·​413​1935
1681.40585.853.56AN1993031213329​37232​57
1691.407414.4712.43AN1993031232​233237​2932215​52​135​312
1701.45136.024.39JB JB AN1993031235​756​67220
1711.43308.686.89JB JB AN1993031231235​5925​234​53
1721.42189.677.66JB JB AN1993031224​59512​1933​112​175
1731.404511.459.01AN19930312631226​5·​29233​710​37
1741.403510.698.18AN1993031233​1325​11·​192​73352​711
1751.415611.349.29AN1993031273513​18124​3·​11·​132​195
1761.44515.593.86JB JB AN199303122·​132583·​194
1771.58089.9213.01JB JB AN19930312283511​13228​38​173
1781.42349.687.73JB JB AN1993031252​11133​14832229​32
1791.40617.134.73JB JB AN199303125·​72132​433211​38
1801.50289.289.55JB JB AN1993031223958​173210​374
1811.457110.8610.19AN1993031232​5224​173​314710​257
1821.430413.2112.04AN199303121932·​56​192​1193239​138
1831.44779.187.84AN19930312897·​118220​33​53
1841.491615.7818.79AN1993031273213​77​9412316​1033​127
1851.42769.607.75JB JB AN1993031273115​157222​310​75
1861.407812.8610.65AN1993031222​1373​415​181314​5·​673
1871.41899.637.54JB JB AN1993031272217​181238​8092
1881.40909.607.22JB JB AN199303127283522​312​17·​109
1891.47417.506.48JB JB AN1993031272210​11·​53234​58
1901.492419.1524.26AN1993031222​1132​1310​17·​151·​442359​1396
1911.426811.059.36JB JB AN199303123125​510​1923·​75​113​412
1921.41336.684.44JB JB AN199303125237​13328​1372
1931.42836.985.00JB JB AN199303121173​16722·​314
1941.450010.819.88AN19930312133​53​77​23213​114​13·​41
1951.47448.487.70AN199303121316​723​11·​23·​533
1961.40438.285.79AN19930312139​72​19727​57​19
1971.45269.438.28BdW19880106219​13·​103711311​53​112
1981.497610.9911.82BdW1988010652​7937713218​37​132
1991.43504.933.10BdW19880106210​75738​13
2001.46196.685.29BdW1988010627​5276​41136
2011.54714.774.17BdW1988010673310211​29
2021.48895.414.25BdW1988010611239​13211​53
2031.48294.523.18BdW198801063721538​5
2041.41275.253.13BdW198801065311210​173
2051.42662.110.76BdW1988010635327
2061.43917.285.52BdW19880106124​37​54758​72
2071.44335.713.95BdW198801061212​5335​72​43
2081.56793.642.89BdW1988010612·​3754​7
2091.45573.381.86BdW19880106125​3·​5274
2101.62996.818.64ER198701012310​109235
2111.62607.6810.18BdW1985092011232​56​73221​23
2121.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
2131.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
2141.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
2151.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
2161.503317.3722.12TS MH 27​238199​8572322​13·​472​263
2171.401316.0013.83KV 36​112​47·​35921713221​54​27492
2181.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
2191.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
2201.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
2211.454414.3914.70TS AR 78​2707210​510​293318​114​43
2221.455014.4814.86TS 232​315225​7·​1093319​52​192​29
2231.401411.719.17TS AR 310​54​401136​473229​312
2241.432116.4916.23TS 317​6777​113​2272​547214​57​176
2251.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
2261.406318.8317.45TS 221​1031178​235​151314​52​432​3133
2271.431815.3514.76TS 614​149223​13·​29538​5·​74​734
2281.421415.1513.94TS 67·​2633310​59​233210​76​132​413
2291.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
2301.444213.0312.44HtR PM 219​26383·​167554​297
2311.447615.7816.21TS 317221​56​23·​7993472​3075
2321.41458.816.56XG 311​547·​116​43217​173
2331.40659.206.75NE JK 7932​57​133216​192​67
2341.465714.2715.11HtR PM 174​67219​1374315​53​13·​892
2351.401313.9411.55TS 2227·​676​1373·​54​135​3532
2361.422114.5013.20KV 17·​19433​510​72​293213​137​613
2371.415310.588.45HtR PM 3·​234513​312·​74​1993
2381.412917.5416.33KV 13·​73339​55​895219​72​315​467
2391.431211.239.72KV 21139​73​113​1929·​2774
2401.536713.0516.74HtR PM 5329​317​132115​17·​313​137
2411.44977.325.76GF 13·​55​472218​79

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.