$abc$-triples of high quality
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Numbers
$q$
value
1.629911
$a$:
2
1.629911
$b$:
6436341
1.629911
$c$:
6436343
1.625990
$a$:
121
1.625990
$b$:
48234375
1.625990
$c$:
48234496
1.623490
$a$:
24833
1.623490
$b$:
5020969537415167
1.623490
$c$:
5020969537440000
1.580756
$a$:
283
1.580756
$b$:
8251953125
1.580756
$c$:
8251953408
1.567887
$a$:
1
1.567887
$b$:
4374
1.567887
$c$:
4375
1.547075
$a$:
343
1.547075
$b$:
59049
1.547075
$c$:
59392
1.544433
$a$:
2477678547239
1.544433
$b$:
613474843408551921511
1.544433
$c$:
613474845886230468750
1.536713
$a$:
125
1.536713
$b$:
11174240024064
1.536713
$c$:
11174240024189
1.526999
$a$:
611596453
1.526999
$b$:
5368709120
1.526999
$c$:
5980305573
1.522160
$a$:
20218313059443
1.522160
$b$:
121517356341481357
1.522160
$c$:
121537574654540800
1.509432
$a$:
188728275341281
1.509432
$b$:
30687043271724658719
1.509432
$c$:
30687232000000000000
1.503317
$a$:
10023806115968
1.503317
$b$:
236997656946088771
1.503317
$c$:
237007680752204739
1.502838
$a$:
239
1.502838
$b$:
1919140625
1.502838
$c$:
1919140864
1.497620
$a$:
198425
1.497620
$b$:
96889010407
1.497620
$c$:
96889208832
1.492431
$a$:
44
1.492431
$b$:
14087010572580078081
1.492431
$c$:
14087010572580078125
1.491590
$a$:
73
1.491590
$b$:
5973865915867136
1.491590
$c$:
5973865915867209
1.489245
$a$:
16777216
1.489245
$b$:
311385505409
1.489245
$c$:
311402282625
1.488865
$a$:
121
1.488865
$b$:
255879
1.488865
$c$:
256000
1.482910
$a$:
37
1.482910
$b$:
32768
1.482910
$c$:
32805
1.481322
$a$:
115966796875
1.481322
$b$:
9301344999072
1.481322
$c$:
9417311795947
1.480533
$a$:
8654525279998779296875
1.480533
$b$:
229727166528260169448321941
1.480533
$c$:
229735821053540168227618816
1.474449
$a$:
1
1.474449
$b$:
301327047
1.474449
$c$:
301327048
1.474137
$a$:
49
1.474137
$b$:
31640576
1.474137
$c$:
31640625
1.471298
$a$:
16119
1.471298
$b$:
214358881
1.471298
$c$:
214375000
1.465676
$a$:
5595907
1.465676
$b$:
184693744467968
1.465676
$c$:
184693750063875
1.465520
$a$:
13841287201
1.465520
$b$:
2271670157312
1.465520
$c$:
2285511444513
1.465274
$a$:
377933067
1.465274
$b$:
3972256707877558203125
1.465274
$c$:
3972256707877936136192
1.464604
$a$:
110330191652531040475
1.464604
$b$:
3651621299988620198933
1.464604
$c$:
3761951491641151239408
1.461923
$a$:
3200
1.461923
$b$:
4823609
1.461923
$c$:
4826809
1.460622
$a$:
464743623105438551
1.460622
$b$:
6045120559074418176746593449
1.460622
$c$:
6045120559539161799852032000
1.459424
$a$:
289111328125
1.459424
$b$:
1628886484491098486528
1.459424
$c$:
1628886484780209814653
1.457793
$a$:
115200578857421875
1.457793
$b$:
336192253411623744461
1.457793
$c$:
336307453990481166336
1.457789
$a$:
177978515625
1.457789
$b$:
10323603816448
1.457789
$c$:
10501582332073
1.457481
$a$:
96301474167
1.457481
$b$:
212192535400390625
1.457481
$c$:
212192631701864792
1.457065
$a$:
225
1.457065
$b$:
72596138768
1.457065
$c$:
72596138993
1.456202
$a$:
637534208
1.456202
$b$:
94573974609375
1.456202
$c$:
94574612143583
1.455673
$a$:
1
1.455673
$b$:
2400
1.455673
$c$:
2401
1.455126
$a$:
15944049
1.455126
$b$:
34359738368
1.455126
$c$:
34375682417
1.455024
$a$:
15144820879
1.455024
$b$:
304177737629696
1.455024
$c$:
304192882450575
1.454434
$a$:
15605316307
1.454434
$b$:
243890000000000
1.454434
$c$:
243905605316307
1.453343
$a$:
4826809
1.453343
$b$:
21094497145095066
1.453343
$c$:
21094497149921875
1.453195
$a$:
925190931432103
1.453195
$b$:
1133649264795189248
1.453195
$c$:
1134574455726621351
1.452613
$a$:
702021632
1.452613
$b$:
1977326743
1.452613
$c$:
2679348375
1.452000
$a$:
720077960137146368
1.452000
$b$:
121494451649631319056757
1.452000
$c$:
121495171727591456203125
1.451917
$a$:
25161368403091
1.451917
$b$:
570243460709396737065659
1.451917
$c$:
570243460734558105468750
1.451343
$a$:
1701
1.451343
$b$:
1046875
1.451343
$c$:
1048576
1.450858
$a$:
83349
1.450858
$b$:
5880651776
1.450858
$c$:
5880735125
1.450216
$a$:
146767394485224241
1.450216
$b$:
13669290314405085785446416384
1.450216
$c$:
13669290314551853179931640625
1.450097
$a$:
2704798098231340213727
1.450097
$b$:
2282915619421863094395648
1.450097
$c$:
2285620417520094434609375
1.450025
$a$:
1
1.450025
$b$:
63927525375
1.450025
$c$:
63927525376
1.449651
$a$:
1
1.449651
$b$:
20709375
1.449651
$c$:
20709376
1.449354
$a$:
2707160810382798173125
1.449354
$b$:
362056449426413786635575296
1.449354
$c$:
362059156587224169433748421
1.447977
$a$:
5203
1.447977
$b$:
265137564453125
1.447977
$c$:
265137564458328
1.447742
$a$:
89
1.447742
$b$:
1500512167
1.447742
$c$:
1500512256
1.447590
$a$:
129140163
1.447590
$b$:
6024036352000000
1.447590
$c$:
6024036481140163
1.447420
$a$:
393927551841835417600000
1.447420
$b$:
10704872737453891276395489673
1.447420
$c$:
10705266665005733111813089673
1.446873
$a$:
27982932961
1.446873
$b$:
43309818510835712
1.446873
$c$:
43309846493768673
1.446246
$a$:
55546875
1.446246
$b$:
6979321856
1.446246
$c$:
7034868731
1.445064
$a$:
338
1.445064
$b$:
390625
1.445064
$c$:
390963
1.444595
$a$:
292638540234375
1.444595
$b$:
272250614375973241
1.444595
$c$:
272543252916207616
1.444199
$a$:
137887744
1.444199
$b$:
10781034805381
1.444199
$c$:
10781172693125
1.443501
$a$:
995588
1.443501
$b$:
10358428955078125
1.443501
$c$:
10358428956073713
1.443306
$a$:
1
1.443306
$b$:
512000
1.443306
$c$:
512001
1.443284
$a$:
61731
1.443284
$b$:
48828125
1.443284
$c$:
48889856
1.442803
$a$:
1289066038662879404041
1.442803
$b$:
39453125000000000000000
1.442803
$c$:
40742191038662879404041
1.442013
$a$:
1249446765800288
1.442013
$b$:
1963592529296875
1.442013
$c$:
3213039295097163
1.441813
$a$:
22771715409
1.441813
$b$:
348972425216
1.441813
$c$:
371744140625
1.441775
$a$:
8387035209728
1.441775
$b$:
99252466918352690625
1.441775
$c$:
99252475305387900353
1.441518
$a$:
160412424963707
1.441518
$b$:
217634277343750000
1.441518
$c$:
217794689768713707
1.441440
$a$:
29791
1.441440
$b$:
3939110834
1.441440
$c$:
3939140625
1.440968
$a$:
42849
1.440968
$b$:
28629151
1.440968
$c$:
28672000
1.440263
$a$:
9244796845555712
1.440263
$b$:
87305465605616163
1.440263
$c$:
96550262451171875
1.439062
$a$:
1
1.439062
$b$:
19140624
1.439062
$c$:
19140625
1.438356
$a$:
1
1.438356
$b$:
2505572351
1.438356
$c$:
2505572352
1.438238
$a$:
14321927484375
1.438238
$b$:
101029508532509551847
1.438238
$c$:
101029522854437036222
1.438138
$a$:
7505629765697536
1.438138
$b$:
14887652467405109375
1.438138
$c$:
14895158097170806911
1.437859
$a$:
52832077950197
1.437859
$b$:
4373797760182125
1.437859
$c$:
4426629838132322
1.436544
$a$:
3929319027001
1.436544
$b$:
20925925864527593159
1.436544
$c$:
20925929793846620160
1.436180
$a$:
742586
1.436180
$b$:
3521116921
1.436180
$c$:
3521859507
1.435750
$a$:
162729
1.435750
$b$:
1042151581574097478352896
1.435750
$c$:
1042151581574097478515625
1.435005
$a$:
7168
1.435005
$b$:
78125
1.435005
$c$:
85293
1.434858
$a$:
104474391867
1.434858
$b$:
316478381828866048
1.434858
$c$:
316478486303257915
1.434151
$a$:
1013888
1.434151
$b$:
226092951133905625
1.434151
$c$:
226092951134919513
1.433956
$a$:
101391750713
1.433956
$b$:
8541701586764912
1.433956
$c$:
8541802978515625
1.433601
$a$:
139344708952637771
1.433601
$b$:
164883187567419514159104
1.433601
$c$:
164883326912128466796875
1.433463
$a$:
12397455648
1.433463
$b$:
2334834480015625
1.433463
$c$:
2334846877471273
1.433451
$a$:
1013875
1.433451
$b$:
64186132652918669
1.433451
$c$:
64186132653932544
1.433093
$a$:
37569208117
1.433093
$b$:
12721777397216796875
1.433093
$c$:
12721777434786004992
1.433042
$a$:
961
1.433042
$b$:
474609375
1.433042
$c$:
474610336
1.432904
$a$:
2097152
1.432904
$b$:
134777585793473
1.432904
$c$:
134777587890625
1.432347
$a$:
287965184
1.432347
$b$:
71693980398960997
1.432347
$c$:
71693980686926181
1.432320
$a$:
1670815292588032
1.432320
$b$:
1360104322866807375
1.432320
$c$:
1361775138159395407
1.432142
$a$:
8652390921
1.432142
$b$:
30896079667609079
1.432142
$c$:
30896088320000000
1.431814
$a$:
2063030309
1.431814
$b$:
2236779851677696
1.431814
$c$:
2236781914708005
1.431623
$a$:
8688792277309
1.431623
$b$:
10384694050816
1.431623
$c$:
19073486328125
1.431260
$a$:
2255797354496
1.431260
$b$:
73843744178785779
1.431260
$c$:
73845999976140275
1.431183
$a$:
2048
1.431183
$b$:
170732841741
1.431183
$c$:
170732843789
1.431091
$a$:
184832
1.431091
$b$:
3079178955793
1.431091
$c$:
3079179140625
1.430417
$a$:
193
1.430417
$b$:
16056027781250
1.430417
$c$:
16056027781443
1.430175
$a$:
7489872117
1.430175
$b$:
2297154668331008
1.430175
$c$:
2297162158203125
1.429915
$a$:
315380807
1.429915
$b$:
96840548010171460143
1.429915
$c$:
96840548010486840950
1.429873
$a$:
162678573828608
1.429873
$b$:
967560450839696875
1.429873
$c$:
967723129413525483
1.429552
$a$:
570807
1.429552
$b$:
217533001
1.429552
$c$:
218103808
1.429428
$a$:
8035237888
1.429428
$b$:
381439008360381125
1.429428
$c$:
381439016395619013
1.429007
$a$:
10460353203
1.429007
$b$:
17274491311
1.429007
$c$:
27734844514
1.428912
$a$:
82800367216340571
1.428912
$b$:
78295316104448477385125
1.428912
$c$:
78295398904815693725696
1.428908
$a$:
5329
1.428908
$b$:
65876535296
1.428908
$c$:
65876540625
1.428401
$a$:
67138671875
1.428401
$b$:
519730440957
1.428401
$c$:
586869112832
1.428361
$a$:
707281
1.428361
$b$:
238726341441404928
1.428361
$c$:
238726341442112209
1.428323
$a$:
11
1.428323
$b$:
9565927
1.428323
$c$:
9565938
1.427566
$a$:
73
1.427566
$b$:
3969746099
1.427566
$c$:
3969746172
1.427488
$a$:
13845841
1.427488
$b$:
497860496850944
1.427488
$c$:
497860510696785
1.427115
$a$:
59049
1.427115
$b$:
132590423
1.427115
$c$:
132649472
1.426752
$a$:
31
1.426752
$b$:
112812500000
1.426752
$c$:
112812500031
1.426565
$a$:
3
1.426565
$b$:
125
1.426565
$c$:
128
1.425727
$a$:
61677818554527009
1.425727
$b$:
11320974204017382972991
1.425727
$c$:
11321035881835937500000
1.425181
$a$:
8251953125
1.425181
$b$:
5925963089217250048
1.425181
$c$:
5925963097469203173
1.424607
$a$:
108582141952
1.424607
$b$:
3412675793515625
1.424607
$c$:
3412784375657577
1.423406
$a$:
6566485948342272
1.423406
$b$:
754264929015760642103
1.423406
$c$:
754271495501708984375
1.423380
$a$:
275
1.423380
$b$:
4831837933
1.423380
$c$:
4831838208
1.423191
$a$:
557832031250
1.423191
$b$:
126612145087527382220763
1.423191
$c$:
126612145088085214252013
1.423086
$a$:
749502843041820983
1.423086
$b$:
2964660052322998046875
1.423086
$c$:
2965409555166039867858
1.422876
$a$:
1696555248485695128859
1.422876
$b$:
386984662267854848000000
1.422876
$c$:
388681217516340543128859
1.422606
$a$:
8466594201171275
1.422606
$b$:
77680637267625423929344
1.422606
$c$:
77680645734219625100619
1.422082
$a$:
2215457
1.422082
$b$:
315103974609375
1.422082
$c$:
315103976824832
1.422015
$a$:
12304697054518521
1.422015
$b$:
6350779162034176000
1.422015
$c$:
6363083859088694521
1.421827
$a$:
944
1.421827
$b$:
4638671875
1.421827
$c$:
4638672819
1.421575
$a$:
78125
1.421575
$b$:
27217619
1.421575
$c$:
27295744
1.421378
$a$:
72402135
1.421378
$b$:
109048965991846471808
1.421378
$c$:
109048965991918873943
1.421370
$a$:
1218826949
1.421370
$b$:
1403221060546875
1.421370
$c$:
1403222279373824
1.421045
$a$:
549755813888
1.421045
$b$:
7136675045487
1.421045
$c$:
7686430859375
1.421008
$a$:
2308155904
1.421008
$b$:
1191744140625
1.421008
$c$:
1194052296529
1.420813
$a$:
1293862733719
1.420813
$b$:
38084983750656
1.420813
$c$:
39378846484375
1.420751
$a$:
1580506708975616
1.420751
$b$:
120887352505699423
1.420751
$c$:
122467859214675039
1.420582
$a$:
223270703038574259899031
1.420582
$b$:
649307365977022004946459915625
1.420582
$c$:
649307589247725043520719814656
1.420437
$a$:
109531219
1.420437
$b$:
1121484800
1.420437
$c$:
1231016019
1.420320
$a$:
1594323
1.420320
$b$:
51905822720000
1.420320
$c$:
51905824314323
1.420232
$a$:
19177936109568
1.420232
$b$:
1490096941448656057
1.420232
$c$:
1490116119384765625
1.420035
$a$:
12167
1.420035
$b$:
47669765625
1.420035
$c$:
47669777792
1.419559
$a$:
13651536370466816
1.419559
$b$:
875615065424903125
1.419559
$c$:
889266601795369941
1.419292
$a$:
178409449
1.419292
$b$:
39056396484375
1.419292
$c$:
39056574893824
1.419183
$a$:
44790692380548068359375
1.419183
$b$:
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1.400261
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1.400261
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1.400041
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501636678168234375
Definition
The list contains all known $abc$-triples quality at least $1.4$, as givin in [2]. An $abc$-triple is a solution of the equation $a+b=c$ with coprime integers $0 < a \leq b < c$. The quality of an $abc$-triple is defined as $q = \log(c)/\log\text{rad}(abc)$, where $\text{rad}(abc)$ is the radical of $abc$, that is, the product over all prime divisors of $abc$.
Parameters
$q$
—   real number ($q > 1.4$)
Comments
(1)
The abc-conjecture [3] states that $\limsup q = 1$, that is, for every $\varepsilon > 0$ there are only finitely many $abc$-triples of quality $q > 1+\varepsilon$.
Links
Data properties
Entries are of type: integer
Table is complete: unknown
Sources of data: [2] and the references therein
Reliability: The quality $q$ is correct up to one ulp (unit of least precision); see https://www.numberdb.org/help#section-number-types.