There are currently 236 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 Reken mee met ABC finds all ABC triples up to a certain bound. By a run of an 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 236 known triples with q>1.4:last update: 2013-06-03

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
271.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
281.46196.685.29BdW1988010627​5276​41136
291.460627.7835.12IC201006127·​167·​8114​91934​132​2312​674231​53​112​175​1074
301.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
311.457820.5323.64AN19930312512​172​312​16992314​29219​32​11·​1310​47
321.457813.0213.03AN1993031236​512216​13·​594711​47·​113
331.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
341.457110.8610.19AN1993031232​5224​173​314710​257
351.456213.9814.24AN19930312225​193·​515​1033117​133​472
361.45573.381.86BdW19880106125​3·​5274
371.455110.549.72JB JB1994040132​116235195​13883
381.455014.4814.86TS 232​315225​7·​1093319​52​192​29
391.454414.3914.70TS AR 78​2707210​510​293318​114​43
401.453316.3217.29AN199303121362·​34​74​119​2357​1034​2399
411.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
421.45269.438.28BdW19880106219​13·​103711311​53​112
431.452023.0826.93FR20100809220​233537·​598​47292324​56​19·​23·​2512
441.451923.7627.92FR20070803313​6151710​832​2719·​151012·​33​517​712
451.45136.024.39JB JB AN1993031235​756​67220
461.45099.778.64JB JB1994040135​73213​233​5953​196
471.450228.1434.40IC20080509238​374228​37​114​193​61·​127·​1732518​174​432​48172
481.450124.3628.64FR20081220233​536​3167228​329​11399257​74​1312​523
491.450010.819.88AN19930312133​53​77​23213​114​13·​41
501.44977.325.76GF 13·​55​472218​79
511.449426.5631.88FR2010042354​1913​103213​139​29·​2441·​76732319​114​4635
521.448014.4214.42AN19930312112​4359​72​134​9723​3·​737
531.44779.187.84AN19930312897·​118220​33​53
541.447615.7816.21TS 317221​56​23·​7993472​3075
551.447428.0333.90FR20070907224​55​475​18121314​19·​103·​5712​4261728​17·​372
561.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
571.44629.858.59AN1993031232​57​79229​13117​192
581.44515.593.86JB JB AN199303122·​132583·​194
591.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
601.444213.0312.44HtR PM 219​26383·​167554​297
611.443516.0216.28AN1993031222​114​17517​1357734​239​71
621.44335.713.95BdW198801061212​5335​72​43
631.44337.696.04JB JB AN1993031232​193511217​373
641.442822.6125.37TD20030804198​434​1492215​523​101313​13·​292​376​911
651.442015.5115.53AN1993031225​112​199515​372​4737​711​743
661.441811.5710.52AN19930312316​232213​292​37359​114​13
671.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
681.441517.3417.93AN1993031273​295​151224​516​97·​919327​134
691.44149.608.15AN199303123132·​17·​4153·​57​75
701.44107.465.74JB JB AN1993031234​232315215​53​7
711.440316.9817.38AN19930312235​72​172​19327​1072515​372​2311
721.43917.285.52BdW19880106124​37​54758​72
731.43849.407.84JB JB19940401119·​5093219​34​59
741.438220.0021.32TD200308043·​56​78​5316792·​116​1934​20551
751.438119.1720.18TD20030804226​114​763956​2311318​474​7879
761.437915.6515.47TD2003080478​13·​893313​53​114​14992·​1912
771.436519.3220.26TD20030804174​1964110​1559212​315​5·​29·​15672
781.43629.557.94AN199303122·​13576​1732313​472
791.435824.0226.70TD2003080434​72​41225​227759​118​BIG
801.43504.933.10BdW19880106210​75738​13
811.434917.5017.71TD20030804317​809227​1195·​74​135​59·​10972
821.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
831.434015.9315.62AN19930312119​4324​236​47·​2772514​72​134
841.433623.2225.37TD2003080411·​1038245​37​29·​37·​1997511​710​79·​3892
851.433515.3714.87AN1993031225​31856​710​232119​691·​1433
861.433516.8116.72AN1993031253​81111912​29219​33​174​2332
871.433119.1019.71TD20030804711​19512​1019·​71512228​312​113​67
881.43308.686.89JB JB AN1993031231235​5925​234​53
891.432914.1313.29AN1993031222176​17·​82092512​7432
901.432316.8616.71TD20030804217​13373​117​432​5801317​176​23
911.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
921.432116.4916.23TS 317​6777​113​2272​547214​57​176
931.431815.3514.76TS 614​149223​13·​29538​5·​74​734
941.431613.2812.18AN19930312174​793​211229​23·​292519
951.431316.8716.66AN19930312227​75326​11·​19·​13952​136​434​179
961.431211.239.72KV 21139​73​113​1929·​2774
971.431112.4911.20AN1993031229​192596​7333​57​72​313
981.430413.2112.04AN199303121932·​56​192​1193239​138
991.430215.3614.68JB JB1994040136​72​13·​1272238​61·​137511​196
1001.429919.9920.65TD2003080472​23538​1112​47032·​52​132​193​296​532
1011.429917.9918.02AN1993031229​37·​97555​7·​897320​174​3323
1021.42968.346.44AN1993031239​2976​432224​13
1031.429417.5817.46TD20030804220​79·​9753​76​111034​137​86632
1041.429010.448.74AN1993031232172​116​1992·​138​17
1051.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
1061.428910.829.17JB JB19940401732211​114​133311​55​7·​17
1071.428411.7710.25AN19930312514​1136​75​132​251221​234
1081.428417.3817.13TD20030804294214​33​31·​472​1993712​41532
1091.42836.985.00JB JB AN199303121173​16722·​314
1101.42769.607.75JB JB AN1993031273115​157222​310​75
1111.427514.7013.72AN19930312614220​413​832322​5·​19·​167
1121.42718.126.15AN1993031231078​2329​5092
1131.426811.059.36JB JB AN199303123125​510​1923·​75​113​412
1141.42662.110.76BdW1988010635327
1151.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
1161.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
1171.424615.5314.59TD20030804227​80957​76​135323​36251
1181.423420.8821.31TD20030804213​318​2069133​297​2713514​233​31872
1191.42349.687.73JB JB AN1993031252​11133​14832229​32
1201.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
1211.423121.4722.06TD20030804317​113·​4912513​11·​13·​1982·​36​718​1249
1221.422923.5924.86FR201002253117​6029245​56​839238​73​176​432​1573
1231.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
1241.422114.5013.20KV 17·​19433​510​72​293213​137​613
1251.422018.8018.52TD2003080434​236​10132247​53​1927·​1317​1373
1261.42189.677.66JB JB AN1993031224​59512​1933​112​175
1271.42167.445.33AN1993031257115​132215​72​17
1281.421420.0420.06TD200308043·​5·​13627​75​536​2287113​377​9292
1291.421415.1513.94TS 67·​2633310​59​233210​76​132​413
1301.421012.8911.25JD2005112323938​132​23558​1512​863
1311.421012.0810.32AN1993031229​373​8939​59​311036
1321.420813.6012.07TD200308042334​439215​31958​175​71
1331.420817.0916.28TD20030804213​712​3373713​11172321​133​732
1341.42049.097.01AN1993031278​19215​52​3723·​177
1351.420313.7212.18AN19930312313221​54​199278​832​1307
1361.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
1371.420010.688.71AN1993031223339​57​3127​73​13·​174
1381.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
1391.419313.5911.99AN19930312194​37234​514​7928​315​732
1401.419227.5329.82FR2007082559​172​234​372​43·​4817314​118​612​1734252​196​1272
1411.41899.637.54JB JB AN1993031272217​181238​8092
1421.418211.749.83JB JB1994040113·​349923934​511​139
1431.417612.7310.92JB JB1994040156​160929​314​13315234
1441.416812.8110.98AN1993031239​433513​532327​73​236
1451.416414.6813.13JB JB19940401414​33941312​197223​59​29
1461.416315.6214.24TD20030804172​475​73231​593·​137​47232
1471.416121.2821.23AN19930312322​37·​20474928​527132​316​1034​113
1481.416111.949.96JB JB AN199303123·​54​59911·​238222​593
1491.415823.9224.63TD2003080427​54​722194​37·​474​536314​11·​139​191·​7829
1501.415820.6820.43TD20030804520​4021240​13·​173​676336​77​113​296
1511.415724.6925.63TD20030804322​97872510​11·​2910​109237​893​1672​1823
1521.415619.6919.19AN19930312246​2339​55​117​312​431911​59·​7207
1531.415611.349.29AN1993031273513​18124​3·​11·​132​195
1541.415310.588.45HtR PM 3·​234513​312·​74​1993
1551.415121.5121.44AN1993031226​52​713​132​46334​43121112​3892​6841
1561.415027.0428.67JW20090502312​617​3889323​117​1513​173223​56​73​833​3493
1571.414626.3127.65TD20030804718​233325​518​73​173​981439338​134​5233
1581.41458.816.56XG 311​547·​116​43217​173
1591.414417.4416.31AN1993031237​514​72251​112295​73·​4192​1039
1601.41376.684.45JB JB AN1993031226​5·​137314136
1611.41336.684.44JB JB AN199303125237​13328​1372
1621.413213.6311.75JB JB AN1993031236​1573​2832310230​52​112​13
1631.412917.5416.33KV 13·​73339​55​895219​72​315​467
1641.412825.7926.78FR2010052225​55​75​113​292​347238​978​109121312​197​2939
1651.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
1661.41275.253.13BdW198801065311210​173
1671.412629.2531.37FR20100128214​36​424873514​2912​8378​113​477​46109111
1681.412325.1625.91TD20030804294​221323·​132​2312​89·​1471729​516​119​79
1691.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
1701.412316.4014.94TD2003080454​17·​3493717​109235​35​3037
1711.412129.3831.48FR20100212237​312​91093513​1315​2939723​11·​793345871
1721.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
1731.411710.328.05AN1993031279336​7·​11·​135218​433
1741.411722.7622.74FR20100625221​317​3152​418​170532119​61·​712​4313
1751.411616.6915.25JB JB AN199303123·​132​1049239​292​107193​1396
1761.411419.2318.30TD20030804311​72​37·​4728​173​1012​191452​3537
1771.410914.9813.19TD20030804229​13511​269335​72​176​3307
1781.410814.0412.12AN1993031213·​2943·​710​19425​5·​432​1394
1791.410712.2910.15JB JB19940401672​2399313​107326​515
1801.410322.6722.51TD2003080454​532​594​10124​11·​2315314​712​463·​1531
1811.410015.2113.42AN19930312213​313​11313·​29·​436​673520​17
1821.409718.6117.43AN1993031251222​321​432​52859710​133​172​1512
1831.409421.1720.54TD20030804211​34​1014​292211319515​17·​530932
1841.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
1851.409022.3622.00FR20130603436​672​29209318​79​29·​37329​58​177​234
1861.409021.7021.17TD2003080474321​112​134​138493226​57​383·​15792
1871.40909.607.22JB JB AN199303127283522​312​17·​109
1881.408916.9715.40AN19930312212315​192​732​33435·​413​1935
1891.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
1901.407812.8610.65AN1993031222​1373​415​181314​5·​673
1911.407726.2826.87JW2009042275​61213​137​173​42293313​58​113​53·​732​892​103
1921.407620.2019.20FR2013052572​675​2632​487231​17·​236​29316​515​112
1931.407414.4712.43AN1993031232​233237​2932215​52​135​312
1941.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
1951.407212.7910.55JB JB19940401241212​34​56​1181118​134
1961.407116.2814.49TD20030804113​315​101·​4791078231​34​56​7
1971.40718.395.96JB JB AN1993031239​16323​116​17512
1981.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
1991.40659.206.75NE JK 7932​57​133216​192​67
2001.406416.6314.85AN19930312219​3673517​197·​281132​2516
2011.406318.8317.45TS 221​1031178​235​151314​52​432​3133
2021.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
2031.40618.956.49AN19930312216​41·​71315​72197
2041.406120.7319.73AN19930312135​1932·​1112​1123·​76081338​397
2051.40617.134.73JB JB AN199303125·​72132​433211​38
2061.40585.853.56AN1993031213329​37232​57
2071.405410.678.23AN19930312224​355·​195​592710​167
2081.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
2091.404919.5418.20TD2003080435​516​19375​232​2334​1321248​432​67
2101.404819.1317.70TD2003080457​237​1493318​39072252​32​331
2111.404511.459.01AN19930312631226​5·​29233​710​37
2121.40438.285.79AN19930312139​72​19727​57​19
2131.404016.5714.64AN19930312512​22728​3·​73​237​4111·​195​675
2141.404014.9612.81AN1993031239​10328​112​135​412​47514​533
2151.403510.698.18AN1993031233​1325​11·​192​73352​711
2161.403121.2420.11TD2003080422​34​1633​10061514313119​294​1013
2171.402924.0623.56AN199303125·​673​1272​192191318​37·​2772·​315​72​3110
2181.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
2191.402420.0418.62TD20030804211​317​132​19229·​412​83854​472​53·​1076
2201.402210.678.12AN19930312312​5679​31229​115​571
2211.402013.4911.09AN199303123·​514​19972​115​174​41230​134
2221.402014.3312.02AN19930312233​539​76​312​97112​193​1274
2231.401926.5126.54FR2010030511·​198​23·​675​1877312​473​835​1133217​522​10192
2241.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
2251.401724.2423.67TD2003080436​74​43·​16421512​4396259​41·​73939
2261.401411.719.17TS AR 310​54​401136​473229​312
2271.401313.9411.55TS 2227·​676​1373·​54​135​3532
2281.401316.0513.89TD2003080479​134210​233​1734312​5·​116​2371
2291.401316.0013.83KV 36​112​47·​35921713221​54​27492
2301.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
2311.401213.9311.54AN19930312229​732​312​734​349515​532
2321.400814.9212.61AN19930312234​712714​123124​52​112​297
2331.400610.057.43AN19930312134176​463221​732
2341.400313.3210.84AN19930312214​313​57·​296​712119​132​53
2351.400316.7914.68AN19930312518​635932​476​73327​1910​79
2361.400017.7015.71TD200308041742·​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  26
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