There are currently 225 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 16 new good ABC triples in the last few years, the latest on January 28 2010, which is also the largest one (c has 30 digits).


The 225 known triples with q>1.4:last update: 2010-01-28

qualitysizemeritbyona bc
11.62996.818.64ER 2310​109235
21.62607.6810.18BdW 11232​56​73221​23
31.623515.7026.86JB JB 19·​13077·​292​31828​322​54
41.58089.9213.01JB JB AN 283511​13228​38​173
51.56793.642.89BdW 12·​3754​7
61.54714.774.17BdW 73310211​29
71.544420.7931.54AN 72​412​31131116​132​792·​33​523​953
81.536713.0516.74HtR PM 5329​317​132115​17·​313​137
91.52709.7811.02AN 13·​196230​5313​112​31
101.522217.0822.92AN 318​23·​2269173​29·​318210​52​715
111.509419.4926.17TD 1310​37237​195​714​223226​512​1873
121.503317.3722.12TS MH 27​238199​8572322​13·​472​263
131.50289.289.55JB JB AN 23958​173210​374
141.497610.9911.82BdW 52​7937713218​37​132
151.492419.1524.26AN 22​1132​1310​17·​151·​442359​1396
161.491615.7818.79AN 73213​77​9412316​1033​127
171.489211.4912.24AN 224117​19·​292311​53​73​41
181.48895.414.25BdW 11239​13211​53
191.48294.523.18BdW 3721538​5
201.481312.9714.04AN 514​1925​3·​713117​372​353
211.47448.487.70AN 1316​723​11·​23·​533
221.47417.506.48JB JB AN 72210​11·​53234​58
231.47138.337.44JB JB AN 34​19911823​57​73
241.465714.2715.11HtR PM 174​67219​1374315​53​13·​892
251.465512.3612.48AN 712214​673​461313​11·​194
261.464621.5825.80FR2007092052​2310​106531711​113​193424​319​178​29
271.46196.685.29BdW 27​5276​41136
281.459421.2124.80KV 511​31·​19128​713​89·​8592330​134​277
291.457820.5323.64AN 512​172​312​16992314​29219​32​11·​1310​47
301.457813.0213.03AN 36​512216​13·​594711​47·​113
311.457517.3318.96TS 3·​109·​1314522​8923​112​195​974
321.457110.8610.19AN 32​5224​173​314710​257
331.456213.9814.24AN 225​193·​515​1033117​133​472
341.45573.381.86BdW 125​3·​5274
351.455110.549.72JB JB 32​116235195​13883
361.455014.4814.86TS 232​315225​7·​1093319​52​192​29
371.454414.3914.70TS AR 78​2707210​510​293318​114​43
381.453316.3217.29AN 1362·​34​74​119​2357​1034​2399
391.453218.0519.71TS MH 75​232​1014243​359239​13·​196​3072
401.45269.438.28BdW 219​13·​103711311​53​112
411.451923.7627.92FR20070803313​6151710​832​2719·​151012·​33​517​712
421.45136.024.39JB JB AN 35​756​67220
431.45099.778.64JB JB 35​73213​233​5953​196
441.450228.1434.40IC20080509238​374228​37​114​193​61·​127·​1732518​174​432​48172
451.450124.3628.64FR20081220233​536​3167228​329​11399257​74​1312​523
461.450010.819.88AN 133​53​77​23213​114​13·​41
471.44977.325.76GF 13·​55​472218​79
481.448014.4214.42AN 112​4359​72​134​9723​3·​737
491.44779.187.84AN 897·​118220​33​53
501.447615.7816.21TS 317221​56​23·​7993472​3075
511.447428.0333.90FR20070907224​55​475​18121314​19·​103·​5712​4261728​17·​372
521.446916.6417.32TS 4094221​115​17·​19·​39735​75​139
531.44629.858.59AN 32​57​79229​13117​192
541.44515.593.86JB JB AN 2·​132583·​194
551.444617.4418.26TS AR 311​58​4229175​235​313232​72​1093
561.444213.0312.44HtR PM 219​26383·​167554​297
571.443516.0216.28AN 22​114​17517​1357734​239​71
581.44335.713.95BdW 1212​5335​72​43
591.44337.696.04JB JB AN 32​193511217​373
601.442822.6125.37TD 198​434​1492215​523​101313​13·​292​376​911
611.442015.5115.53AN 25​112​199515​372​4737​711​743
621.441811.5710.52AN 316​232213​292​37359​114​13
631.441820.0021.59JD20070516213​74​6532318​55​181·​673211·​1313​313
641.441517.3417.93AN 73​295​151224​516​97·​919327​134
651.44149.608.15AN 3132·​17·​4153·​57​75
661.44107.465.74JB JB AN 34​232315215​53​7
671.440316.9817.38AN 235​72​172​19327​1072515​372​2311
681.43917.285.52BdW 124​37​54758​72
691.43849.407.84JB JB 119·​5093219​34​59
701.438220.0021.32TD 3·​56​78​5316792·​116​1934​20551
711.438119.1720.18TD 226​114​763956​2311318​474​7879
721.437915.6515.47TD 78​13·​893313​53​114​14992·​1912
731.436519.3220.26TD 174​1964110​1559212​315​5·​29·​15672
741.43629.557.94AN 2·​13576​1732313​472
751.435824.0226.70TD 34​72​41225​227759​118​BIG
761.43504.933.10BdW 210​75738​13
771.434917.5017.71TD 317​809227​1195·​74​135​59·​10972
781.434217.3517.47JD2006042727​89254​76​112​714313​193​45472
791.434015.9315.62AN 119​4324​236​47·​2772514​72​134
801.433623.2225.37TD 11·​1038245​37​29·​37·​1997511​710​79·​3892
811.433515.3714.87AN 25​31856​710​232119​691·​1433
821.433516.8116.72AN 53​81111912​29219​33​174​2332
831.433119.1019.71TD 711​19512​1019·​71512228​312​113​67
841.43308.686.89JB JB AN 31235​5925​234​53
851.432914.1313.29AN 22176​17·​82092512​7432
861.432316.8616.71TD 217​13373​117​432​5801317​176​23
871.432318.1318.38JD20060601232​733314​53​11·​135​557713​232​1632
881.432116.4916.23TS 317​6777​113​2272​547214​57​176
891.431815.3514.76TS 614​149223​13·​29538​5·​74​734
901.431613.2812.18AN 174​793​211229​23·​292519
911.431316.8716.66AN 227​75326​11·​19·​13952​136​434​179
921.431211.239.72KV 21139​73​113​1929·​2774
931.431112.4911.20AN 29​192596​7333​57​72​313
941.430413.2112.04AN 1932·​56​192​1193239​138
951.430215.3614.68JB JB 36​72​13·​1272238​61·​137511​196
961.429919.9920.65TD 72​23538​1112​47032·​52​132​193​296​532
971.429917.9918.02AN 29​37·​97555​7·​897320​174​3323
981.42968.346.44AN 39​2976​432224​13
991.429417.5817.46TD 220​79·​9753​76​111034​137​86632
1001.429010.448.74AN 32172​116​1992·​138​17
1011.428922.8924.49FR20070816310​76​541·​2203153​296​10134217​1116​13
1021.428910.829.17JB JB 732211​114​133311​55​7·​17
1031.428411.7710.25AN 514​1136​75​132​251221​234
1041.428417.3817.13TD 294214​33​31·​472​1993712​41532
1051.42836.985.00JB JB AN 1173​16722·​314
1061.42769.607.75JB JB AN 73115​157222​310​75
1071.427514.7013.72AN 614220​413​832322​5·​19·​167
1081.42718.126.15AN 31078​2329​5092
1091.426811.059.36JB JB AN 3125​510​1923·​75​113​412
1101.42662.110.76BdW 35327
1111.425722.0523.06FR2007080336​477​16779​114​234​6847325​515​1035
1121.425218.7718.71JD20060614511​13228​176​235​14937​76​11·​293​2932
1131.424615.5314.59TD 227​80957​76​135323​36251
1141.423420.8821.31TD 213​318​2069133​297​2713514​233​31872
1151.42349.687.73JB JB AN 52​11133​14832229​32
1161.423223.1024.24FR200812252·​510​134315​7·​317​45817118​1092​36773
1171.423121.4722.06TD 317​113·​4912513​11·​13·​1982·​36​718​1249
1181.422622.8923.90FR2007122952​134​174​141971238​237​83318​74​113​894
1191.422114.5013.20KV 17·​19433​510​72​293213​137​613
1201.422018.8018.52TD 34​236​10132247​53​1927·​1317​1373
1211.42189.677.66JB JB AN 24​59512​1933​112​175
1221.42167.445.33AN 57115​132215​72​17
1231.421420.0420.06TD 3·​5·​13627​75​536​2287113​377​9292
1241.421415.1513.94TS 67·​2633310​59​233210​76​132​413
1251.421012.8911.25JD2005112323938​132​23558​1512​863
1261.421012.0810.32AN 29​373​8939​59​311036
1271.420813.6012.07TD 2334​439215​31958​175​71
1281.420817.0916.28TD 213​712​3373713​11172321​133​732
1291.42049.097.01AN 78​19215​52​3723·​177
1301.420313.7212.18AN 313221​54​199278​832​1307
1311.420218.1717.60TS 214​310​43·​461115​294​83·​3972526
1321.420010.688.71AN 23339​57​3127​73​13·​174
1331.419617.9517.28JD20060621247​9755​78​89·​7392317​116​132​23
1341.419313.5911.99AN 194​37234​514​7928​315​732
1351.419227.5329.82FR2007082559​172​234​372​43·​4817314​118​612​1734252​196​1272
1361.41899.637.54JB JB AN 72217​181238​8092
1371.418211.749.83JB JB 13·​349923934​511​139
1381.417612.7310.92JB JB 56​160929​314​13315234
1391.416812.8110.98AN 39​433513​532327​73​236
1401.416414.6813.13JB JB 414​33941312​197223​59​29
1411.416315.6214.24TD 172​475​73231​593·​137​47232
1421.416121.2821.23AN 322​37·​20474928​527132​316​1034​113
1431.416111.949.96JB JB AN 3·​54​59911·​238222​593
1441.415823.9224.63TD 27​54​722194​37·​474​536314​11·​139​191·​7829
1451.415820.6820.43TD 520​4021240​13·​173​676336​77​113​296
1461.415724.6925.63TD 322​97872510​11·​2910​109237​893​1672​1823
1471.415619.6919.19AN 246​2339​55​117​312​431911​59·​7207
1481.415611.349.29AN 73513​18124​3·​11·​132​195
1491.415310.588.45HtR PM 3·​234513​312·​74​1993
1501.415121.5121.44AN 26​52​713​132​46334​43121112​3892​6841
1511.415027.0428.67JW20090502312​617​3889323​117​1513​173223​56​73​833​3493
1521.414626.3127.65TD 718​233325​518​73​173​981439338​134​5233
1531.41458.816.56XG 311​547·​116​43217​173
1541.414417.4416.31AN 37​514​72251​112295​73·​4192​1039
1551.41376.684.45JB JB AN 26​5·​137314136
1561.41336.684.44JB JB AN 5237​13328​1372
1571.413213.6311.75JB JB AN 36​1573​2832310230​52​112​13
1581.412917.5416.33KV 13·​73339​55​895219​72​315​467
1591.412724.4425.00TS 72​179​47225​312​52​37·​509·​5712317​536​672
1601.41275.253.13BdW 5311210​173
1611.412629.2531.37FR20100128214​36​424873514​2912​8378​113​477​46109111
1621.412325.1625.91TD 294​221323·​132​2312​89·​1471729​516​119​79
1631.412322.8322.88FR20081225212​133​2233315​113​975​409515​1794​2141
1641.412316.4014.94TD 54​17·​3493717​109235​35​3037
1651.411921.0120.54FR20070819116​233​4492226​310​13·​172​263253​74​193​298
1661.411710.328.05AN 79336​7·​11·​135218​433
1671.411616.6915.25JB JB AN 3·​132​1049239​292​107193​1396
1681.411419.2318.30TD 311​72​37·​4728​173​1012​191452​3537
1691.410914.9813.19TD 229​13511​269335​72​176​3307
1701.410814.0412.12AN 13·​2943·​710​19425​5·​432​1394
1711.410712.2910.15JB JB 672​2399313​107326​515
1721.410322.6722.51TD 54​532​594​10124​11·​2315314​712​463·​1531
1731.410015.2113.42AN 213​313​11313·​29·​436​673520​17
1741.409718.6117.43AN 51222​321​432​52859710​133​172​1512
1751.409421.1720.54TD 211​34​1014​292211319515​17·​530932
1761.409122.4922.16FR2009010235​515​135710​795​35323211​737​832​197
1771.409021.7021.17TD 74321​112​134​138493226​57​383·​15792
1781.40909.607.22JB JB AN 7283522​312​17·​109
1791.408916.9715.40AN 212315​192​732​33435·​413​1935
1801.408618.5017.22TS AR 2·​7·​11·​13623·​434​4494316​534​972
1811.407812.8610.65AN 22​1373​415​181314​5·​673
1821.407726.2826.87JW2009042275​61213​137​173​42293313​58​113​53·​732​892​103
1831.407414.4712.43AN 32​233237​2932215​52​135​312
1841.407221.0620.23FR20090301412​59238​76​138​1831212​54​766513
1851.407212.7910.55JB JB 241212​34​56​1181118​134
1861.407116.2814.49TD 113​315​101·​4791078231​34​56​7
1871.40718.395.96JB JB AN 39​16323​116​17512
1881.406817.1215.46JD20060331317​89473​61·​3595213​5·​198​191
1891.40659.206.75NE JK 7932​57​133216​192​67
1901.406416.6314.85AN 219​3673517​197·​281132​2516
1911.406318.8317.45TS 221​1031178​235​151314​52​432​3133
1921.406216.2614.42JD20060401227​172711​304123·​53​138​232​113
1931.40618.956.49AN 216​41·​71315​72197
1941.406120.7319.73AN 135​1932·​1112​1123·​76081338​397
1951.40617.134.73JB JB AN 5·​72132​433211​38
1961.40585.853.56AN 13329​37232​57
1971.405410.678.23AN 224​355·​195​592710​167
1981.405120.4819.35FR20070807321​7·​4498001510​4995228​173​475
1991.404919.5418.20TD 35​516​19375​232​2334​1321248​432​67
2001.404819.1317.70TD 57​237​1493318​39072252​32​331
2011.404511.459.01AN 631226​5·​29233​710​37
2021.40438.285.79AN 139​72​19727​57​19
2031.404016.5714.64AN 512​22728​3·​73​237​4111·​195​675
2041.404014.9612.81AN 39​10328​112​135​412​47514​533
2051.403510.698.18AN 33​1325​11·​192​73352​711
2061.403121.2420.11TD 22​34​1633​10061514313119​294​1013
2071.402924.0623.56AN 5·​673​1272​192191318​37·​2772·​315​72​3110
2081.402721.7020.64KV 34​19·​61·​1732244​71052​1494​503·​9293
2091.402420.0418.62TD 211​317​132​19229·​412​83854​472​53·​1076
2101.402210.678.12AN 312​5679​31229​115​571
2111.402013.4911.09AN 3·​514​19972​115​174​41230​134
2121.402014.3312.02AN 233​539​76​312​97112​193​1274
2131.401720.4219.02FR2007082628​47·​103258​192​11714310​710​17·​9672
2141.401724.2423.67TD 36​74​43·​16421512​4396259​41·​73939
2151.401411.719.17TS AR 310​54​401136​473229​312
2161.401313.9411.55TS 2227·​676​1373·​54​135​3532
2171.401316.0513.89TD 79​134210​233​1734312​5·​116​2371
2181.401316.0013.83KV 36​112​47·​35921713221​54​27492
2191.401217.6315.70JD20060602137​75​135​17·​1831230​52​127·​3532
2201.401213.9311.54AN 229​732​312​734​349515​532
2211.400814.9212.61AN 234​712714​123124​52​112​297
2221.400610.057.43AN 134176​463221​732
2231.400313.3210.84AN 214​313​57·​296​712119​132​53
2241.400316.7914.68AN 518​635932​476​73327​1910​79
2251.400017.7015.71TD 1742·​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  16
GF  Gerhard Frey  1
HtR  Herman te Riele  4
IC  Ismael Jiménez Calvo  1
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