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
21.465321.6025.90FR2016120433​241358​119​19·​613215​172​331·​10614
31.404421.1220.08FR20150801230​54​4735​175​293​54137·​112​13·​2311​127
41.405324.3224.13FR2014081529105·​135​194​232​2332​301591235​310​117​53
51.409022.3622.00FR20130603436​672​29209318​79​29·​37329​58​177​234
61.407620.2019.20FR2013052572​675​2632​487231​17·​236​29316​515​112
71.480526.3635.16FR20101107522​79·​4594932​1318​613223​174​2512​17333
81.452023.0826.93FR20100809220​233537·​598​47292324​56​19·​23·​2512
91.411722.7622.74FR20100625221​317​3152​418​170532119​61·​712​4313
101.460627.7835.12IC201006127·​167·​8114​91934​132​2312​674231​53​112​175​1074
111.412825.7926.78FR2010052225​55​75​113​292​347238​978​109121312​197​2939
121.449426.5631.88FR2010042354​1913​103213​139​29·​2441·​76732319​114​4635
131.401926.5126.54FR2010030511·​198​23·​675​1877312​473​835​1133217​522​10192
141.422923.5924.86FR201002253117​6029245​56​839238​73​176​432​1573
151.412129.3831.48FR20100212237​312​91093513​1315​2939723​11·​793345871
161.412629.2531.37FR20100128214​36​424873514​2912​8378​113​477​46109111
171.415027.0428.67JW20090502312​617​3889323​117​1513​173223​56​73​833​3493
181.407726.2826.87JW2009042275​61213​137​173​42293313​58​113​53·​732​892​103
191.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
201.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
211.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
221.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
231.450124.3628.64FR20081220233​536​3167228​329​11399257​74​1312​523
241.450228.1434.40IC20080509238​374228​37​114​193​61·​127·​1732518​174​432​48172
251.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
261.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
271.447428.0333.90FR20070907224​55​475​18121314​19·​103·​5712​4261728​17·​372
281.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
291.419227.5329.82FR2007082559​172​234​372​43·​4817314​118​612​1734252​196​1272
301.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
311.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
321.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
331.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
341.451923.7627.92FR20070803313​6151710​832​2719·​151012·​33​517​712
351.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
361.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
371.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
381.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
391.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
401.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
411.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
421.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
431.421012.8911.25JD2005112323938​132​23558​1512​863
441.415823.9224.63TD2003080427​54​722194​37·​474​536314​11·​139​191·​7829
451.414626.3127.65TD20030804718​233325​518​73​173​981439338​134​5233
461.442822.6125.37TD20030804198​434​1492215​523​101313​13·​292​376​911
471.415724.6925.63TD20030804322​97872510​11·​2910​109237​893​1672​1823
481.423121.4722.06TD20030804317​113·​4912513​11·​13·​1982·​36​718​1249
491.409421.1720.54TD20030804211​34​1014​292211319515​17·​530932
501.404819.1317.70TD2003080457​237​1493318​39072252​32​331
511.415820.6820.43TD20030804520​4021240​13·​173​676336​77​113​296
521.404919.5418.20TD2003080435​516​19375​232​2334​1321248​432​67
531.433623.2225.37TD2003080411·​1038245​37​29·​37·​1997511​710​79·​3892
541.402420.0418.62TD20030804211​317​132​19229·​412​83854​472​53·​1076
551.422018.8018.52TD2003080434​236​10132247​53​1927·​1317​1373
561.438119.1720.18TD20030804226​114​763956​2311318​474​7879
571.423420.8821.31TD20030804213​318​2069133​297​2713514​233​31872
581.410322.6722.51TD2003080454​532​594​10124​11·​2315314​712​463·​1531
591.407116.2814.49TD20030804113​315​101·​4791078231​34​56​7
601.420817.0916.28TD20030804213​712​3373713​11172321​133​732
611.403121.2420.11TD2003080422​34​1633​10061514313119​294​1013
621.509419.4926.17TD200308041310​37237​195​714​223226​512​1873
631.437915.6515.47TD2003080478​13·​893313​53​114​14992·​1912
641.438220.0021.32TD200308043·​56​78​5316792·​116​1934​20551
651.416315.6214.24TD20030804172​475​73231​593·​137​47232
661.436519.3220.26TD20030804174​1964110​1559212​315​5·​29·​15672
671.412325.1625.91TD20030804294​221323·​132​2312​89·​1471729​516​119​79
681.420813.6012.07TD200308042334​439215​31958​175​71
691.401724.2423.67TD2003080436​74​43·​16421512​4396259​41·​73939
701.401316.0513.89TD2003080479​134210​233​1734312​5·​116​2371
711.412316.4014.94TD2003080454​17·​3493717​109235​35​3037
721.424615.5314.59TD20030804227​80957​76​135323​36251
731.434917.5017.71TD20030804317​809227​1195·​74​135​59·​10972
741.433119.1019.71TD20030804711​19512​1019·​71512228​312​113​67
751.411419.2318.30TD20030804311​72​37·​4728​173​1012​191452​3537
761.429417.5817.46TD20030804220​79·​9753​76​111034​137​86632
771.410914.9813.19TD20030804229​13511​269335​72​176​3307
781.429919.9920.65TD2003080472​23538​1112​47032·​52​132​193​296​532
791.432316.8616.71TD20030804217​13373​117​432​5801317​176​23
801.421420.0420.06TD200308043·​5·​13627​75​536​2287113​377​9292
811.428417.3817.13TD20030804294214​33​31·​472​1993712​41532
821.435824.0226.70TD2003080434​72​41225​227759​118​BIG
831.400017.7015.71TD200308041742·​712​293​74339​56​135​23·​191
841.409021.7021.17TD2003080474321​112​134​138493226​57​383·​15792
851.416414.6813.13JB JB19940401414​33941312​197223​59​29
861.430215.3614.68JB JB1994040136​72​13·​1272238​61·​137511​196
871.417612.7310.92JB JB1994040156​160929​314​13315234
881.455110.549.72JB JB1994040132​116235195​13883
891.410712.2910.15JB JB19940401672​2399313​107326​515
901.45099.778.64JB JB1994040135​73213​233​5953​196
911.418211.749.83JB JB1994040113·​349923934​511​139
921.623515.7026.86JB JB1994040119·​13077·​292​31828​322​54
931.428910.829.17JB JB19940401732211​114​133311​55​7·​17
941.407212.7910.55JB JB19940401241212​34​56​1181118​134
951.43849.407.84JB JB19940401119·​5093219​34​59
961.415121.5121.44AN1993031226​52​713​132​46334​43121112​3892​6841
971.416121.2821.23AN19930312322​37·​20474928​527132​316​1034​113
981.457820.5323.64AN19930312512​172​312​16992314​29219​32​11·​1310​47
991.400316.7914.68AN19930312518​635932​476​73327​1910​79
1001.440316.9817.38AN19930312235​72​172​19327​1072515​372​2311
1011.415619.6919.19AN19930312246​2339​55​117​312​431911​59·​7207
1021.442015.5115.53AN1993031225​112​199515​372​4737​711​743
1031.414417.4416.31AN1993031237​514​72251​112295​73·​4192​1039
1041.402924.0623.56AN199303125·​673​1272​192191318​37·​2772·​315​72​3110
1051.429917.9918.02AN1993031229​37·​97555​7·​897320​174​3323
1061.441517.3417.93AN1993031273​295​151224​516​97·​919327​134
1071.406416.6314.85AN19930312219​3673517​197·​281132​2516
1081.522217.0822.92AN19930312318​23·​2269173​29·​318210​52​715
1091.410015.2113.42AN19930312213​313​11313·​29·​436​673520​17
1101.431613.2812.18AN19930312174​793​211229​23·​292519
1111.402013.4911.09AN199303123·​514​19972​115​174​41230​134
1121.544420.7931.54AN1993031272​412​31131116​132​792·​33​523​953
1131.431316.8716.66AN19930312227​75326​11·​19·​13952​136​434​179
1141.413213.6311.75JB JB AN1993031236​1573​2832310230​52​112​13
1151.457813.0213.03AN1993031236​512216​13·​594711​47·​113
1161.400313.3210.84AN19930312214​313​57·​296​712119​132​53
1171.481312.9714.04AN19930312514​1925​3·​713117​372​353
1181.434015.9315.62AN19930312119​4324​236​47·​2772514​72​134
1191.428411.7710.25AN19930312514​1136​75​132​251221​234
1201.404016.5714.64AN19930312512​22728​3·​73​237​4111·​195​675
1211.402014.3312.02AN19930312233​539​76​312​97112​193​1274
1221.441811.5710.52AN19930312316​232213​292​37359​114​13
1231.465512.3612.48AN19930312712214​673​461313​11·​194
1241.433515.3714.87AN1993031225​31856​710​232119​691·​1433
1251.429010.448.74AN1993031232172​116​1992·​138​17
1261.402210.678.12AN19930312312​5679​31229​115​571
1271.405410.678.23AN19930312224​355·​195​592710​167
1281.401213.9311.54AN19930312229​732​312​734​349515​532
1291.406120.7319.73AN19930312135​1932·​1112​1123·​76081338​397
1301.421012.0810.32AN1993031229​373​8939​59​311036
1311.416812.8110.98AN1993031239​433513​532327​73​236
1321.400814.9212.61AN19930312234​712714​123124​52​112​297
1331.456213.9814.24AN19930312225​193·​515​1033117​133​472
1341.52709.7811.02AN1993031213·​196230​5313​112​31
1351.409718.6117.43AN1993031251222​321​432​52859710​133​172​1512
1361.40618.956.49AN19930312216​41·​71315​72197
1371.419313.5911.99AN19930312194​37234​514​7928​315​732
1381.42049.097.01AN1993031278​19215​52​3723·​177
1391.44629.858.59AN1993031232​57​79229​13117​192
1401.489211.4912.24AN19930312224117​19·​292311​53​73​41
1411.427514.7013.72AN19930312614220​413​832322​5·​19·​167
1421.410814.0412.12AN1993031213·​2943·​710​19425​5·​432​1394
1431.453316.3217.29AN199303121362·​34​74​119​2357​1034​2399
1441.40718.395.96JB JB AN1993031239​16323​116​17512
1451.432914.1313.29AN1993031222176​17·​82092512​7432
1461.404014.9612.81AN1993031239​10328​112​135​412​47514​533
1471.420313.7212.18AN19930312313221​54​199278​832​1307
1481.416111.949.96JB JB AN199303123·​54​59911·​238222​593
1491.433516.8116.72AN1993031253​81111912​29219​33​174​2332
1501.443516.0216.28AN1993031222​114​17517​1357734​239​71
1511.43629.557.94AN199303122·​13576​1732313​472
1521.42968.346.44AN1993031239​2976​432224​13
1531.411616.6915.25JB JB AN199303123·​132​1049239​292​107193​1396
1541.411710.328.05AN1993031279336​7·​11·​135218​433
1551.431112.4911.20AN1993031229​192596​7333​57​72​313
1561.42167.445.33AN1993031257115​132215​72​17
1571.44337.696.04JB JB AN1993031232​193511217​373
1581.42718.126.15AN1993031231078​2329​5092
1591.41376.684.45JB JB AN1993031226​5·​137314136
1601.44107.465.74JB JB AN1993031234​232315215​53​7
1611.44149.608.15AN199303123132·​17·​4153·​57​75
1621.400610.057.43AN19930312134176​463221​732
1631.47138.337.44JB JB AN1993031234​19911823​57​73
1641.420010.688.71AN1993031223339​57​3127​73​13·​174
1651.448014.4214.42AN19930312112​4359​72​134​9723​3·​737
1661.408916.9715.40AN19930312212315​192​732​33435·​413​1935
1671.40585.853.56AN1993031213329​37232​57
1681.407414.4712.43AN1993031232​233237​2932215​52​135​312
1691.45136.024.39JB JB AN1993031235​756​67220
1701.43308.686.89JB JB AN1993031231235​5925​234​53
1711.42189.677.66JB JB AN1993031224​59512​1933​112​175
1721.404511.459.01AN19930312631226​5·​29233​710​37
1731.403510.698.18AN1993031233​1325​11·​192​73352​711
1741.415611.349.29AN1993031273513​18124​3·​11·​132​195
1751.44515.593.86JB JB AN199303122·​132583·​194
1761.58089.9213.01JB JB AN19930312283511​13228​38​173
1771.42349.687.73JB JB AN1993031252​11133​14832229​32
1781.40617.134.73JB JB AN199303125·​72132​433211​38
1791.50289.289.55JB JB AN1993031223958​173210​374
1801.457110.8610.19AN1993031232​5224​173​314710​257
1811.430413.2112.04AN199303121932·​56​192​1193239​138
1821.44779.187.84AN19930312897·​118220​33​53
1831.491615.7818.79AN1993031273213​77​9412316​1033​127
1841.42769.607.75JB JB AN1993031273115​157222​310​75
1851.407812.8610.65AN1993031222​1373​415​181314​5·​673
1861.41899.637.54JB JB AN1993031272217​181238​8092
1871.40909.607.22JB JB AN199303127283522​312​17·​109
1881.47417.506.48JB JB AN1993031272210​11·​53234​58
1891.492419.1524.26AN1993031222​1132​1310​17·​151·​442359​1396
1901.426811.059.36JB JB AN199303123125​510​1923·​75​113​412
1911.41336.684.44JB JB AN199303125237​13328​1372
1921.42836.985.00JB JB AN199303121173​16722·​314
1931.450010.819.88AN19930312133​53​77​23213​114​13·​41
1941.47448.487.70AN199303121316​723​11·​23·​533
1951.40438.285.79AN19930312139​72​19727​57​19
1961.45269.438.28BdW19880106219​13·​103711311​53​112
1971.497610.9911.82BdW1988010652​7937713218​37​132
1981.43504.933.10BdW19880106210​75738​13
1991.46196.685.29BdW1988010627​5276​41136
2001.54714.774.17BdW1988010673310211​29
2011.48895.414.25BdW1988010611239​13211​53
2021.48294.523.18BdW198801063721538​5
2031.41275.253.13BdW198801065311210​173
2041.42662.110.76BdW1988010635327
2051.43917.285.52BdW19880106124​37​54758​72
2061.44335.713.95BdW198801061212​5335​72​43
2071.56793.642.89BdW1988010612·​3754​7
2081.45573.381.86BdW19880106125​3·​5274
2091.62996.818.64ER198701012310​109235
2101.62607.6810.18BdW1985092011232​56​73221​23
2111.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
2121.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
2131.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
2141.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
2151.503317.3722.12TS MH 27​238199​8572322​13·​472​263
2161.401316.0013.83KV 36​112​47·​35921713221​54​27492
2171.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
2181.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
2191.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
2201.454414.3914.70TS AR 78​2707210​510​293318​114​43
2211.455014.4814.86TS 232​315225​7·​1093319​52​192​29
2221.401411.719.17TS AR 310​54​401136​473229​312
2231.432116.4916.23TS 317​6777​113​2272​547214​57​176
2241.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
2251.406318.8317.45TS 221​1031178​235​151314​52​432​3133
2261.431815.3514.76TS 614​149223​13·​29538​5·​74​734
2271.421415.1513.94TS 67·​2633310​59​233210​76​132​413
2281.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
2291.444213.0312.44HtR PM 219​26383·​167554​297
2301.447615.7816.21TS 317221​56​23·​7993472​3075
2311.41458.816.56XG 311​547·​116​43217​173
2321.40659.206.75NE JK 7932​57​133216​192​67
2331.465714.2715.11HtR PM 174​67219​1374315​53​13·​892
2341.401313.9411.55TS 2227·​676​1373·​54​135​3532
2351.422114.5013.20KV 17·​19433​510​72​293213​137​613
2361.415310.588.45HtR PM 3·​234513​312·​74​1993
2371.412917.5416.33KV 13·​73339​55​895219​72​315​467
2381.431211.239.72KV 21139​73​113​1929·​2774
2391.536713.0516.74HtR PM 5329​317​132115​17·​313​137
2401.44977.325.76GF 13·​55​472218​79

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