There are currently 239 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 239 known triples with q>1.4:last update: 2016-12-04

qualitysizemeritbyona bc
11.62996.818.64ER198701012310​109235
21.62607.6810.18BdW1985092011232​56​73221​23
31.623515.7026.86JB JB1994040119·​13077·​292​31828​322​54
41.58089.9213.01JB JB AN19930312283511​13228​38​173
51.56793.642.89BdW1988010612·​3754​7
61.54714.774.17BdW1988010673310211​29
71.544420.7931.54AN1993031272​412​31131116​132​792·​33​523​953
81.536713.0516.74HtR PM 5329​317​132115​17·​313​137
91.52709.7811.02AN1993031213·​196230​5313​112​31
101.522217.0822.92AN19930312318​23·​2269173​29·​318210​52​715
111.509419.4926.17TD200308041310​37237​195​714​223226​512​1873
121.503317.3722.12TS MH 27​238199​8572322​13·​472​263
131.50289.289.55JB JB AN1993031223958​173210​374
141.497610.9911.82BdW1988010652​7937713218​37​132
151.492419.1524.26AN1993031222​1132​1310​17·​151·​442359​1396
161.491615.7818.79AN1993031273213​77​9412316​1033​127
171.489211.4912.24AN19930312224117​19·​292311​53​73​41
181.48895.414.25BdW1988010611239​13211​53
191.48294.523.18BdW198801063721538​5
201.481312.9714.04AN19930312514​1925​3·​713117​372​353
211.480526.3635.16FR20101107522​79·​4594932​1318​613223​174​2512​17333
221.47448.487.70AN199303121316​723​11·​23·​533
231.47417.506.48JB JB AN1993031272210​11·​53234​58
241.47138.337.44JB JB AN1993031234​19911823​57​73
251.465714.2715.11HtR PM 174​67219​1374315​53​13·​892
261.465512.3612.48AN19930312712214​673​461313​11·​194
271.465321.6025.90FR2016120433​241358​119​19·​613215​172​331·​10614
281.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
291.46196.685.29BdW1988010627​5276​41136
301.460627.7835.12IC201006127·​167·​8114​91934​132​2312​674231​53​112​175​1074
311.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
321.457820.5323.64AN19930312512​172​312​16992314​29219​32​11·​1310​47
331.457813.0213.03AN1993031236​512216​13·​594711​47·​113
341.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
351.457110.8610.19AN1993031232​5224​173​314710​257
361.456213.9814.24AN19930312225​193·​515​1033117​133​472
371.45573.381.86BdW19880106125​3·​5274
381.455110.549.72JB JB1994040132​116235195​13883
391.455014.4814.86TS 232​315225​7·​1093319​52​192​29
401.454414.3914.70TS AR 78​2707210​510​293318​114​43
411.453316.3217.29AN199303121362·​34​74​119​2357​1034​2399
421.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
431.45269.438.28BdW19880106219​13·​103711311​53​112
441.452023.0826.93FR20100809220​233537·​598​47292324​56​19·​23·​2512
451.451923.7627.92FR20070803313​6151710​832​2719·​151012·​33​517​712
461.45136.024.39JB JB AN1993031235​756​67220
471.45099.778.64JB JB1994040135​73213​233​5953​196
481.450228.1434.40IC20080509238​374228​37​114​193​61·​127·​1732518​174​432​48172
491.450124.3628.64FR20081220233​536​3167228​329​11399257​74​1312​523
501.450010.819.88AN19930312133​53​77​23213​114​13·​41
511.44977.325.76GF 13·​55​472218​79
521.449426.5631.88FR2010042354​1913​103213​139​29·​2441·​76732319​114​4635
531.448014.4214.42AN19930312112​4359​72​134​9723​3·​737
541.44779.187.84AN19930312897·​118220​33​53
551.447615.7816.21TS 317221​56​23·​7993472​3075
561.447428.0333.90FR20070907224​55​475​18121314​19·​103·​5712​4261728​17·​372
571.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
581.44629.858.59AN1993031232​57​79229​13117​192
591.44515.593.86JB JB AN199303122·​132583·​194
601.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
611.444213.0312.44HtR PM 219​26383·​167554​297
621.443516.0216.28AN1993031222​114​17517​1357734​239​71
631.44335.713.95BdW198801061212​5335​72​43
641.44337.696.04JB JB AN1993031232​193511217​373
651.442822.6125.37TD20030804198​434​1492215​523​101313​13·​292​376​911
661.442015.5115.53AN1993031225​112​199515​372​4737​711​743
671.441811.5710.52AN19930312316​232213​292​37359​114​13
681.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
691.441517.3417.93AN1993031273​295​151224​516​97·​919327​134
701.44149.608.15AN199303123132·​17·​4153·​57​75
711.44107.465.74JB JB AN1993031234​232315215​53​7
721.440316.9817.38AN19930312235​72​172​19327​1072515​372​2311
731.43917.285.52BdW19880106124​37​54758​72
741.43849.407.84JB JB19940401119·​5093219​34​59
751.438220.0021.32TD200308043·​56​78​5316792·​116​1934​20551
761.438119.1720.18TD20030804226​114​763956​2311318​474​7879
771.437915.6515.47TD2003080478​13·​893313​53​114​14992·​1912
781.436519.3220.26TD20030804174​1964110​1559212​315​5·​29·​15672
791.43629.557.94AN199303122·​13576​1732313​472
801.435824.0226.70TD2003080434​72​41225​227759​118​BIG
811.43504.933.10BdW19880106210​75738​13
821.434917.5017.71TD20030804317​809227​1195·​74​135​59·​10972
831.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
841.434015.9315.62AN19930312119​4324​236​47·​2772514​72​134
851.433623.2225.37TD2003080411·​1038245​37​29·​37·​1997511​710​79·​3892
861.433515.3714.87AN1993031225​31856​710​232119​691·​1433
871.433516.8116.72AN1993031253​81111912​29219​33​174​2332
881.433119.1019.71TD20030804711​19512​1019·​71512228​312​113​67
891.43308.686.89JB JB AN1993031231235​5925​234​53
901.432914.1313.29AN1993031222176​17·​82092512​7432
911.432316.8616.71TD20030804217​13373​117​432​5801317​176​23
921.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
931.432116.4916.23TS 317​6777​113​2272​547214​57​176
941.431815.3514.76TS 614​149223​13·​29538​5·​74​734
951.431613.2812.18AN19930312174​793​211229​23·​292519
961.431316.8716.66AN19930312227​75326​11·​19·​13952​136​434​179
971.431211.239.72KV 21139​73​113​1929·​2774
981.431112.4911.20AN1993031229​192596​7333​57​72​313
991.430413.2112.04AN199303121932·​56​192​1193239​138
1001.430215.3614.68JB JB1994040136​72​13·​1272238​61·​137511​196
1011.429919.9920.65TD2003080472​23538​1112​47032·​52​132​193​296​532
1021.429917.9918.02AN1993031229​37·​97555​7·​897320​174​3323
1031.42968.346.44AN1993031239​2976​432224​13
1041.429417.5817.46TD20030804220​79·​9753​76​111034​137​86632
1051.429010.448.74AN1993031232172​116​1992·​138​17
1061.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
1071.428910.829.17JB JB19940401732211​114​133311​55​7·​17
1081.428411.7710.25AN19930312514​1136​75​132​251221​234
1091.428417.3817.13TD20030804294214​33​31·​472​1993712​41532
1101.42836.985.00JB JB AN199303121173​16722·​314
1111.42769.607.75JB JB AN1993031273115​157222​310​75
1121.427514.7013.72AN19930312614220​413​832322​5·​19·​167
1131.42718.126.15AN1993031231078​2329​5092
1141.426811.059.36JB JB AN199303123125​510​1923·​75​113​412
1151.42662.110.76BdW1988010635327
1161.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
1171.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
1181.424615.5314.59TD20030804227​80957​76​135323​36251
1191.423420.8821.31TD20030804213​318​2069133​297​2713514​233​31872
1201.42349.687.73JB JB AN1993031252​11133​14832229​32
1211.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
1221.423121.4722.06TD20030804317​113·​4912513​11·​13·​1982·​36​718​1249
1231.422923.5924.86FR201002253117​6029245​56​839238​73​176​432​1573
1241.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
1251.422114.5013.20KV 17·​19433​510​72​293213​137​613
1261.422018.8018.52TD2003080434​236​10132247​53​1927·​1317​1373
1271.42189.677.66JB JB AN1993031224​59512​1933​112​175
1281.42167.445.33AN1993031257115​132215​72​17
1291.421420.0420.06TD200308043·​5·​13627​75​536​2287113​377​9292
1301.421415.1513.94TS 67·​2633310​59​233210​76​132​413
1311.421012.8911.25JD2005112323938​132​23558​1512​863
1321.421012.0810.32AN1993031229​373​8939​59​311036
1331.420813.6012.07TD200308042334​439215​31958​175​71
1341.420817.0916.28TD20030804213​712​3373713​11172321​133​732
1351.42049.097.01AN1993031278​19215​52​3723·​177
1361.420313.7212.18AN19930312313221​54​199278​832​1307
1371.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
1381.420010.688.71AN1993031223339​57​3127​73​13·​174
1391.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
1401.419313.5911.99AN19930312194​37234​514​7928​315​732
1411.419227.5329.82FR2007082559​172​234​372​43·​4817314​118​612​1734252​196​1272
1421.41899.637.54JB JB AN1993031272217​181238​8092
1431.418211.749.83JB JB1994040113·​349923934​511​139
1441.417612.7310.92JB JB1994040156​160929​314​13315234
1451.416812.8110.98AN1993031239​433513​532327​73​236
1461.416414.6813.13JB JB19940401414​33941312​197223​59​29
1471.416315.6214.24TD20030804172​475​73231​593·​137​47232
1481.416121.2821.23AN19930312322​37·​20474928​527132​316​1034​113
1491.416111.949.96JB JB AN199303123·​54​59911·​238222​593
1501.415823.9224.63TD2003080427​54​722194​37·​474​536314​11·​139​191·​7829
1511.415820.6820.43TD20030804520​4021240​13·​173​676336​77​113​296
1521.415724.6925.63TD20030804322​97872510​11·​2910​109237​893​1672​1823
1531.415619.6919.19AN19930312246​2339​55​117​312​431911​59·​7207
1541.415611.349.29AN1993031273513​18124​3·​11·​132​195
1551.415310.588.45HtR PM 3·​234513​312·​74​1993
1561.415121.5121.44AN1993031226​52​713​132​46334​43121112​3892​6841
1571.415027.0428.67JW20090502312​617​3889323​117​1513​173223​56​73​833​3493
1581.414626.3127.65TD20030804718​233325​518​73​173​981439338​134​5233
1591.41458.816.56XG 311​547·​116​43217​173
1601.414417.4416.31AN1993031237​514​72251​112295​73·​4192​1039
1611.41376.684.45JB JB AN1993031226​5·​137314136
1621.41336.684.44JB JB AN199303125237​13328​1372
1631.413213.6311.75JB JB AN1993031236​1573​2832310230​52​112​13
1641.412917.5416.33KV 13·​73339​55​895219​72​315​467
1651.412825.7926.78FR2010052225​55​75​113​292​347238​978​109121312​197​2939
1661.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
1671.41275.253.13BdW198801065311210​173
1681.412629.2531.37FR20100128214​36​424873514​2912​8378​113​477​46109111
1691.412325.1625.91TD20030804294​221323·​132​2312​89·​1471729​516​119​79
1701.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
1711.412316.4014.94TD2003080454​17·​3493717​109235​35​3037
1721.412129.3831.48FR20100212237​312​91093513​1315​2939723​11·​793345871
1731.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
1741.411710.328.05AN1993031279336​7·​11·​135218​433
1751.411722.7622.74FR20100625221​317​3152​418​170532119​61·​712​4313
1761.411616.6915.25JB JB AN199303123·​132​1049239​292​107193​1396
1771.411419.2318.30TD20030804311​72​37·​4728​173​1012​191452​3537
1781.410914.9813.19TD20030804229​13511​269335​72​176​3307
1791.410814.0412.12AN1993031213·​2943·​710​19425​5·​432​1394
1801.410712.2910.15JB JB19940401672​2399313​107326​515
1811.410322.6722.51TD2003080454​532​594​10124​11·​2315314​712​463·​1531
1821.410015.2113.42AN19930312213​313​11313·​29·​436​673520​17
1831.409718.6117.43AN1993031251222​321​432​52859710​133​172​1512
1841.409421.1720.54TD20030804211​34​1014​292211319515​17·​530932
1851.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
1861.409022.3622.00FR20130603436​672​29209318​79​29·​37329​58​177​234
1871.409021.7021.17TD2003080474321​112​134​138493226​57​383·​15792
1881.40909.607.22JB JB AN199303127283522​312​17·​109
1891.408916.9715.40AN19930312212315​192​732​33435·​413​1935
1901.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
1911.407812.8610.65AN1993031222​1373​415​181314​5·​673
1921.407726.2826.87JW2009042275​61213​137​173​42293313​58​113​53·​732​892​103
1931.407620.2019.20FR2013052572​675​2632​487231​17·​236​29316​515​112
1941.407414.4712.43AN1993031232​233237​2932215​52​135​312
1951.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
1961.407212.7910.55JB JB19940401241212​34​56​1181118​134
1971.407116.2814.49TD20030804113​315​101·​4791078231​34​56​7
1981.40718.395.96JB JB AN1993031239​16323​116​17512
1991.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
2001.40659.206.75NE JK 7932​57​133216​192​67
2011.406416.6314.85AN19930312219​3673517​197·​281132​2516
2021.406318.8317.45TS 221​1031178​235​151314​52​432​3133
2031.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
2041.40618.956.49AN19930312216​41·​71315​72197
2051.406120.7319.73AN19930312135​1932·​1112​1123·​76081338​397
2061.40617.134.73JB JB AN199303125·​72132​433211​38
2071.40585.853.56AN1993031213329​37232​57
2081.405410.678.23AN19930312224​355·​195​592710​167
2091.405324.3224.13FR2014081529105·​135​194​232​2332​301591235​310​117​53
2101.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
2111.404919.5418.20TD2003080435​516​19375​232​2334​1321248​432​67
2121.404819.1317.70TD2003080457​237​1493318​39072252​32​331
2131.404511.459.01AN19930312631226​5·​29233​710​37
2141.404421.1220.08FR20150801230​54​4735​175​293​54137·​112​13·​2311​127
2151.40438.285.79AN19930312139​72​19727​57​19
2161.404016.5714.64AN19930312512​22728​3·​73​237​4111·​195​675
2171.404014.9612.81AN1993031239​10328​112​135​412​47514​533
2181.403510.698.18AN1993031233​1325​11·​192​73352​711
2191.403121.2420.11TD2003080422​34​1633​10061514313119​294​1013
2201.402924.0623.56AN199303125·​673​1272​192191318​37·​2772·​315​72​3110
2211.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
2221.402420.0418.62TD20030804211​317​132​19229·​412​83854​472​53·​1076
2231.402210.678.12AN19930312312​5679​31229​115​571
2241.402013.4911.09AN199303123·​514​19972​115​174​41230​134
2251.402014.3312.02AN19930312233​539​76​312​97112​193​1274
2261.401926.5126.54FR2010030511·​198​23·​675​1877312​473​835​1133217​522​10192
2271.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
2281.401724.2423.67TD2003080436​74​43·​16421512​4396259​41·​73939
2291.401411.719.17TS AR 310​54​401136​473229​312
2301.401313.9411.55TS 2227·​676​1373·​54​135​3532
2311.401316.0513.89TD2003080479​134210​233​1734312​5·​116​2371
2321.401316.0013.83KV 36​112​47·​35921713221​54​27492
2331.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
2341.401213.9311.54AN19930312229​732​312​734​349515​532
2351.400814.9212.61AN19930312234​712714​123124​52​112​297
2361.400610.057.43AN19930312134176​463221​732
2371.400313.3210.84AN19930312214​313​57·​296​712119​132​53
2381.400316.7914.68AN19930312518​635932​476​73327​1910​79
2391.400017.7015.71TD200308041742·​712​293​74339​56​135​23·​191

AN  Abderrahmane Nitaj  100
AR  Andrej Rosenheinrich  4
BdW  Benne de Weger  14
ER  Eric Reyssat  1
FR  Frank Rubin  29
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