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
11.480526.3635.16FR20101107522​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
201.401926.5126.54FR2010030511·​198​23·​675​1877312​473​835​1133217​522​10192
211.509419.4926.17TD200308041310​37237​195​714​223226​512​1873
221.412325.1625.91TD20030804294​221323·​132​2312​89·​1471729​516​119​79
231.465321.6025.90FR2016120433​241358​119​19·​613215​172​331·​10614
241.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
251.415724.6925.63TD20030804322​97872510​11·​2910​109237​893​1672​1823
261.433623.2225.37TD2003080411·​1038245​37​29·​37·​1997511​710​79·​3892
271.442822.6125.37TD20030804198​434​1492215​523​101313​13·​292​376​911
281.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
291.422923.5924.86FR201002253117​6029245​56​839238​73​176​432​1573
301.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
311.415823.9224.63TD2003080427​54​722194​37·​474​536314​11·​139​191·​7829
321.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
331.492419.1524.26AN1993031222​1132​1310​17·​151·​442359​1396
341.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
351.405324.3224.13FR2014081529105·​135​194​232​2332​301591235​310​117​53
361.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
371.401724.2423.67TD2003080436​74​43·​16421512​4396259​41·​73939
381.457820.5323.64AN19930312512​172​312​16992314​29219​32​11·​1310​47
391.402924.0623.56AN199303125·​673​1272​192191318​37·​2772·​315​72​3110
401.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
411.522217.0822.92AN19930312318​23·​2269173​29·​318210​52​715
421.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
431.411722.7622.74FR20100625221​317​3152​418​170532119​61·​712​4313
441.410322.6722.51TD2003080454​532​594​10124​11·​2315314​712​463·​1531
451.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
461.503317.3722.12TS MH 27​238199​8572322​13·​472​263
471.423121.4722.06TD20030804317​113·​4912513​11·​13·​1982·​36​718​1249
481.409022.3622.00FR20130603436​672​29209318​79​29·​37329​58​177​234
491.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
501.415121.5121.44AN1993031226​52​713​132​46334​43121112​3892​6841
511.438220.0021.32TD200308043·​56​78​5316792·​116​1934​20551
521.423420.8821.31TD20030804213​318​2069133​297​2713514​233​31872
531.416121.2821.23AN19930312322​37·​20474928​527132​316​1034​113
541.409021.7021.17TD2003080474321​112​134​138493226​57​383·​15792
551.429919.9920.65TD2003080472​23538​1112​47032·​52​132​193​296​532
561.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
571.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
581.409421.1720.54TD20030804211​34​1014​292211319515​17·​530932
591.415820.6820.43TD20030804520​4021240​13·​173​676336​77​113​296
601.436519.3220.26TD20030804174​1964110​1559212​315​5·​29·​15672
611.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
621.438119.1720.18TD20030804226​114​763956​2311318​474​7879
631.403121.2420.11TD2003080422​34​1633​10061514313119​294​1013
641.404421.1220.08FR20150801230​54​4735​175​293​54137·​112​13·​2311​127
651.421420.0420.06TD200308043·​5·​13627​75​536​2287113​377​9292
661.406120.7319.73AN19930312135​1932·​1112​1123·​76081338​397
671.433119.1019.71TD20030804711​19512​1019·​71512228​312​113​67
681.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
691.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
701.407620.2019.20FR2013052572​675​2632​487231​17·​236​29316​515​112
711.415619.6919.19AN19930312246​2339​55​117​312​431911​59·​7207
721.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
731.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
741.491615.7818.79AN1993031273213​77​9412316​1033​127
751.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
761.402420.0418.62TD20030804211​317​132​19229·​412​83854​472​53·​1076
771.422018.8018.52TD2003080434​236​10132247​53​1927·​1317​1373
781.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
791.411419.2318.30TD20030804311​72​37·​4728​173​1012​191452​3537
801.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
811.404919.5418.20TD2003080435​516​19375​232​2334​1321248​432​67
821.429917.9918.02AN1993031229​37·​97555​7·​897320​174​3323
831.441517.3417.93AN1993031273​295​151224​516​97·​919327​134
841.434917.5017.71TD20030804317​809227​1195·​74​135​59·​10972
851.404819.1317.70TD2003080457​237​1493318​39072252​32​331
861.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
871.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
881.429417.5817.46TD20030804220​79·​9753​76​111034​137​86632
891.406318.8317.45TS 221​1031178​235​151314​52​432​3133
901.409718.6117.43AN1993031251222​321​432​52859710​133​172​1512
911.440316.9817.38AN19930312235​72​172​19327​1072515​372​2311
921.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
931.453316.3217.29AN199303121362·​34​74​119​2357​1034​2399
941.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
951.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
961.428417.3817.13TD20030804294214​33​31·​472​1993712​41532
971.536713.0516.74HtR PM 5329​317​132115​17·​313​137
981.433516.8116.72AN1993031253​81111912​29219​33​174​2332
991.432316.8616.71TD20030804217​13373​117​432​5801317​176​23
1001.431316.8716.66AN19930312227​75326​11·​19·​13952​136​434​179
1011.412917.5416.33KV 13·​73339​55​895219​72​315​467
1021.414417.4416.31AN1993031237​514​72251​112295​73·​4192​1039
1031.420817.0916.28TD20030804213​712​3373713​11172321​133​732
1041.443516.0216.28AN1993031222​114​17517​1357734​239​71
1051.432116.4916.23TS 317​6777​113​2272​547214​57​176
1061.447615.7816.21TS 317221​56​23·​7993472​3075
1071.400017.7015.71TD200308041742·​712​293​74339​56​135​23·​191
1081.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
1091.434015.9315.62AN19930312119​4324​236​47·​2772514​72​134
1101.442015.5115.53AN1993031225​112​199515​372​4737​711​743
1111.437915.6515.47TD2003080478​13·​893313​53​114​14992·​1912
1121.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
1131.408916.9715.40AN19930312212315​192​732​33435·​413​1935
1141.411616.6915.25JB JB AN199303123·​132​1049239​292​107193​1396
1151.465714.2715.11HtR PM 174​67219​1374315​53​13·​892
1161.412316.4014.94TD2003080454​17·​3493717​109235​35​3037
1171.433515.3714.87AN1993031225​31856​710​232119​691·​1433
1181.455014.4814.86TS 232​315225​7·​1093319​52​192​29
1191.406416.6314.85AN19930312219​3673517​197·​281132​2516
1201.431815.3514.76TS 614​149223​13·​29538​5·​74​734
1211.454414.3914.70TS AR 78​2707210​510​293318​114​43
1221.430215.3614.68JB JB1994040136​72​13·​1272238​61·​137511​196
1231.400316.7914.68AN19930312518​635932​476​73327​1910​79
1241.404016.5714.64AN19930312512​22728​3·​73​237​4111·​195​675
1251.424615.5314.59TD20030804227​80957​76​135323​36251
1261.407116.2814.49TD20030804113​315​101·​4791078231​34​56​7
1271.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
1281.448014.4214.42AN19930312112​4359​72​134​9723​3·​737
1291.416315.6214.24TD20030804172​475​73231​593·​137​47232
1301.456213.9814.24AN19930312225​193·​515​1033117​133​472
1311.481312.9714.04AN19930312514​1925​3·​713117​372​353
1321.421415.1513.94TS 67·​2633310​59​233210​76​132​413
1331.401316.0513.89TD2003080479​134210​233​1734312​5·​116​2371
1341.401316.0013.83KV 36​112​47·​35921713221​54​27492
1351.427514.7013.72AN19930312614220​413​832322​5·​19·​167
1361.410015.2113.42AN19930312213​313​11313·​29·​436​673520​17
1371.432914.1313.29AN1993031222176​17·​82092512​7432
1381.422114.5013.20KV 17·​19433​510​72​293213​137​613
1391.410914.9813.19TD20030804229​13511​269335​72​176​3307
1401.416414.6813.13JB JB19940401414​33941312​197223​59​29
1411.457813.0213.03AN1993031236​512216​13·​594711​47·​113
1421.58089.9213.01JB JB AN19930312283511​13228​38​173
1431.404014.9612.81AN1993031239​10328​112​135​412​47514​533
1441.400814.9212.61AN19930312234​712714​123124​52​112​297
1451.465512.3612.48AN19930312712214​673​461313​11·​194
1461.444213.0312.44HtR PM 219​26383·​167554​297
1471.407414.4712.43AN1993031232​233237​2932215​52​135​312
1481.489211.4912.24AN19930312224117​19·​292311​53​73​41
1491.420313.7212.18AN19930312313221​54​199278​832​1307
1501.431613.2812.18AN19930312174​793​211229​23·​292519
1511.410814.0412.12AN1993031213·​2943·​710​19425​5·​432​1394
1521.420813.6012.07TD200308042334​439215​31958​175​71
1531.430413.2112.04AN199303121932·​56​192​1193239​138
1541.402014.3312.02AN19930312233​539​76​312​97112​193​1274
1551.419313.5911.99AN19930312194​37234​514​7928​315​732
1561.497610.9911.82BdW1988010652​7937713218​37​132
1571.413213.6311.75JB JB AN1993031236​1573​2832310230​52​112​13
1581.401313.9411.55TS 2227·​676​1373·​54​135​3532
1591.401213.9311.54AN19930312229​732​312​734​349515​532
1601.421012.8911.25JD2005112323938​132​23558​1512​863
1611.431112.4911.20AN1993031229​192596​7333​57​72​313
1621.402013.4911.09AN199303123·​514​19972​115​174​41230​134
1631.52709.7811.02AN1993031213·​196230​5313​112​31
1641.416812.8110.98AN1993031239​433513​532327​73​236
1651.417612.7310.92JB JB1994040156​160929​314​13315234
1661.400313.3210.84AN19930312214​313​57·​296​712119​132​53
1671.407812.8610.65AN1993031222​1373​415​181314​5·​673
1681.407212.7910.55JB JB19940401241212​34​56​1181118​134
1691.441811.5710.52AN19930312316​232213​292​37359​114​13
1701.421012.0810.32AN1993031229​373​8939​59​311036
1711.428411.7710.25AN19930312514​1136​75​132​251221​234
1721.457110.8610.19AN1993031232​5224​173​314710​257
1731.62607.6810.18BdW1985092011232​56​73221​23
1741.410712.2910.15JB JB19940401672​2399313​107326​515
1751.416111.949.96JB JB AN199303123·​54​59911·​238222​593
1761.450010.819.88AN19930312133​53​77​23213​114​13·​41
1771.418211.749.83JB JB1994040113·​349923934​511​139
1781.431211.239.72KV 21139​73​113​1929·​2774
1791.455110.549.72JB JB1994040132​116235195​13883
1801.50289.289.55JB JB AN1993031223958​173210​374
1811.426811.059.36JB JB AN199303123125​510​1923·​75​113​412
1821.415611.349.29AN1993031273513​18124​3·​11·​132​195
1831.401411.719.17TS AR 310​54​401136​473229​312
1841.428910.829.17JB JB19940401732211​114​133311​55​7·​17
1851.404511.459.01AN19930312631226​5·​29233​710​37
1861.429010.448.74AN1993031232172​116​1992·​138​17
1871.420010.688.71AN1993031223339​57​3127​73​13·​174
1881.62996.818.64ER198701012310​109235
1891.45099.778.64JB JB1994040135​73213​233​5953​196
1901.44629.858.59AN1993031232​57​79229​13117​192
1911.415310.588.45HtR PM 3·​234513​312·​74​1993
1921.45269.438.28BdW19880106219​13·​103711311​53​112
1931.405410.678.23AN19930312224​355·​195​592710​167
1941.403510.698.18AN1993031233​1325​11·​192​73352​711
1951.44149.608.15AN199303123132·​17·​4153·​57​75
1961.402210.678.12AN19930312312​5679​31229​115​571
1971.411710.328.05AN1993031279336​7·​11·​135218​433
1981.43629.557.94AN199303122·​13576​1732313​472
1991.44779.187.84AN19930312897·​118220​33​53
2001.43849.407.84JB JB19940401119·​5093219​34​59
2011.42769.607.75JB JB AN1993031273115​157222​310​75
2021.42349.687.73JB JB AN1993031252​11133​14832229​32
2031.47448.487.70AN199303121316​723​11·​23·​533
2041.42189.677.66JB JB AN1993031224​59512​1933​112​175
2051.41899.637.54JB JB AN1993031272217​181238​8092
2061.47138.337.44JB JB AN1993031234​19911823​57​73
2071.400610.057.43AN19930312134176​463221​732
2081.40909.607.22JB JB AN199303127283522​312​17·​109
2091.42049.097.01AN1993031278​19215​52​3723·​177
2101.43308.686.89JB JB AN1993031231235​5925​234​53
2111.40659.206.75NE JK 7932​57​133216​192​67
2121.41458.816.56XG 311​547·​116​43217​173
2131.40618.956.49AN19930312216​41·​71315​72197
2141.47417.506.48JB JB AN1993031272210​11·​53234​58
2151.42968.346.44AN1993031239​2976​432224​13
2161.42718.126.15AN1993031231078​2329​5092
2171.44337.696.04JB JB AN1993031232​193511217​373
2181.40718.395.96JB JB AN1993031239​16323​116​17512
2191.40438.285.79AN19930312139​72​19727​57​19
2201.44977.325.76GF 13·​55​472218​79
2211.44107.465.74JB JB AN1993031234​232315215​53​7
2221.43917.285.52BdW19880106124​37​54758​72
2231.42167.445.33AN1993031257115​132215​72​17
2241.46196.685.29BdW1988010627​5276​41136
2251.42836.985.00JB JB AN199303121173​16722·​314
2261.40617.134.73JB JB AN199303125·​72132​433211​38
2271.41376.684.45JB JB AN1993031226​5·​137314136
2281.41336.684.44JB JB AN199303125237​13328​1372
2291.45136.024.39JB JB AN1993031235​756​67220
2301.48895.414.25BdW1988010611239​13211​53
2311.54714.774.17BdW1988010673310211​29
2321.44335.713.95BdW198801061212​5335​72​43
2331.44515.593.86JB JB AN199303122·​132583·​194
2341.40585.853.56AN1993031213329​37232​57
2351.48294.523.18BdW198801063721538​5
2361.41275.253.13BdW198801065311210​173
2371.43504.933.10BdW19880106210​75738​13
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.