Table of good abc-examples, II

Abderrahmane Nitaj

Mars 19, 2003

The Table 2 contains all examples a + b = c, related to the abc-conjecture, satisfying 0 < a < b < c and (a, b) = 1, known to me with ρ ≥ 4.0, where

ρ = ρ(a, b, c) = \frac{log(abc)}{log(r(abc))},

and r(abc) is the radical of abc (i.e. the product of the distinct prime factors of abc).

Authors:

J.B.–J.B.: J. Browkin and J. Brzezinski N.E.–J.K.: N. Elkies and J. Kanapka M.H.–T.S.: M. Hegner and T. Schulmeiss G.F.: G. Frey P.M.–H.R.: P.L. Montgomery and H. te Riele A.N.: A. Nitaj E.R.: E. Reyssat A.R–T.S.: A. Rosenheinrich and T. Schulmeiss T.S.: T. Schulmeiss K.V.: K. Visser B.W.: B.M.M. de Weger G.X.: G. Xiao

Table 2

no. a  b  c  ρ  discoverer

1) 13.19^{6}  2^{30}.5  3^{13}.11^{2}.31  4.41901 Nitaj
2) 2^{5}.11^{2}.19^{9}  5^{15}.37^{2}.47  3^{7}.7^{11}.743  4.26801 Nitaj
3) 2^{19}.13.103  7^{11}  3^{11}.5^{3}.11^{2}  4.24789 B. de Weger
4) 2^{35}.7^{2}.17^{2}.19  3^{27}.107^{2}  5^{15}.37^{2}.2311  4.23069 Nitaj
5) 3^{18}.23.2269  17^{3}.29.31^{8}  2^{10}.5^{2}.7^{15}  4.22979 Nitaj
6) 17^{4}.79^{3}.211  2^{29}.23.29^{2}  5^{19}  4.22960 Nitaj
7) 5^{14}.19  2^{5}.3.7^{13}  11^{7}.37^{2}.353  4.22532 Nitaj
8) 3^{21}  7^{2}.11^{6}.199  2.13^{8}.17  4.20094 Nitaj
9) 3^{6}.5^{12}  2^{16}.13.59^{4}  7^{11}.47.113  4.17428 Nitaj
10) 3^{16}.23^{2}  2^{13}.29^{2}.37^{3} 5^{9}.11^{4}.13  4.17088 Nitaj
11) 5^{14}.11  3^{6}.7^{5}.13^{2}.251 2^{2}1.23^{4}  4.16452 Nitaj
12) 5^{18}.6359  3^{2}.47^{6}.73^{3}  2^{7}.19^{10}.79  4.14883 Nitaj
13) 2^{7}.23^{8}  19^{9}.857^{2}  3^{22}.13.47^{2}.263  4.13152 M.H–T.S.
14) 11^{3}.31^{5}.101.479  107^{8}  2^{31}.3^{4}.5^{6}.7  4.13000 Nitaj
15) 5^{12}.17^{2}.31^{2}.1699  23^{14}.29  2^{19}.3^{2}.11.13^{10}.47 4.12727 Nitaj
16) 3.5^{9}.13^{2}.79^{3}.239^{2}.91249 7^{29}  2^{65}.37.41.103  4.12366 Nitaj
17) 7.11^{6}.43  3^{11}.5^{4}  2^{17}.17^{3}43  4.10757 G. Xiao
18) 3.5^{14}.199  7^{2}.11^{5}.17^{4}.41 2^{30}.13^{4}  4.10410 Nitaj
19) 3^{6}.5^{11}.41  2^{9}.7^{9}.283  13^{10}.53  4.09700 Nitaj
20) 2^{16}.41.71  3^{15}.7^{2}  19^{7}  4.09655 Nitaj
21) 3^{12}.5^{6}  7^{9}.31^{2}  2^{9}.11^{5}.571  4.09647 Nitaj
22) 7^{8}.19  2^{15}.5^{2}.37^{2}  3.17^{7}  4.09080 Nitaj
23) 2^{6}.5^{2}.7^{1}3.13^{2}.463  3^{4}.43^{12}  11^{12}.389^{2}.6841 4.08545 Nitaj
24) 79^{5}.677  2^{42}  3^{12}.7.13^{4}.61  4.08331 Nitaj

Table 2 (continued)

no. a  b  c  ρ  discoverer

25) 5^{18}.8837  7^{9}.19^{3}.79.191^{2}  2^{22}.3^{5}.13^{8}  4.07709 Nitaj
26) 2^{24}.3^{5}  5.19^{5}.59^{2}  7^{10}.167  4.07114 Nitaj
27) 2.11^{2}.107^{4}.359^{2}.20947 5^{3}.7^{3}.29^{11}  3^{35}.23^{3}  4.07038 Nitaj
28) 7^{3}.29^{5}.151^{2}  2^{4}.5^{16}.97.919  3^{27}.13^{4}  4.06406 Nitaj
29) 19.47.71^{6}  3^{21}.193^{2}  2^{7}.5^{12}.127^{2}  4.06347 Nitaj
30) 3^{6}.157^{3}.283  23^{10}  2^{30}.5^{2}.11^{2}.13  4.05990 B-B, Nitaj
31) 7^{8}.17^{3}  2^{32}.3^{2}  11.13^{5}.23^{2}.31  4.05301 Nitaj
32) 2^{13}.3^{13}.11^{3}  13.29.43^{6}.673  5^{20}.17  4.04710 Nitaj
33) 5^{13}.13  2^{17}.19^{3}.23  3^{17}.283  4.04498 Nitaj
34) 3^{7}.5^{14}.7^{2}  2^{51}.11^{2}  29^{5}.73.419^{2}.1039 4.03039 Nitaj
35) 3^{2}.5^{7}.79  2^{29}.13  11^{7}.19^{2}  4.02943 Nitaj
36) 3^{6}.19^{12}  2^{5}.37^{3}.59^{4}.19603 7^{17}.11^{2}.71  4.02904 Nitaj
37) 2^{41}.97^{2}  73^{8}.2347  3^{2}.5^{5}.11^{10}.43.61 4.01847 Nitaj
38) 5^{10}.17^{3}  2^{22}.373^{2}  3^{7}.11^{6}.163  4.01360 Nitaj
39) 2.5^{9}  3^{14}  7^{5}.11.47  4.01342 Nitaj
40) 2^{37}  3^{20}.853  5^{2}.7^{6}.29.191^{2}  4.01312 Nitaj
41) 7^{2}.41^{2}.311^{3}  11^{16}.13^{2}.79  2.3^{3}.5^{23}.953  4.00968 Nitaj
42) 2^{2}.73.89^{5}.347.997  7^{4}.23^{11}  3^{36}.19  4.00764 Nitaj
43) 2^{22}.11.43  3^{2}.17^{7}  7^{2}.41^{5}  4.00751 Nitaj
44) 2^{10}.19^{10}  5^{6}.13^{4}.29^{5}  3^{20}.4425749  4.00292 Nitaj
45) 2^{11}.11^{4}.13^{2}.23  3^{25}  7^{3}.29^{5}.137  4.00238 Nitaj
46) 5^{3}.11^{4}.31^{2}  3^{17}.7^{2}  2^{25}.241  4.00087 Nitaj
47) 37.384^{4}  2^{28}.5^{3}.19^{2}  3^{22}.7.59  4.00042 Nitaj