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Pillai conjecture is for every natural number n, there are only finitely many pairs of perfect powers with difference n. The list below shows, for n≤100, all solutions for perfect powers less than 108:

n perfect powers differ by n n perfect powers differ by n n perfect powers differ by n n perfect powers differ by n
1 (8 = 23, 9 = 32), 31 (23 = 33, 54 = 26), (230 = 162, 261 = 172), (497E923 = 313, 497E954 = 22382), 61 (8 = 23, 69 = 34), (23 = 33, 84 = X2), (160 = 63, 201 = 152), (900 = 64, 961 = 312), (160000 = 603, 160061 = 42E2), (13139E68 = 2583, 1313X009 = 3X792), 91 (14 = 24, X5 = 53), (1830 = 462, 1901 = 472), (1030230 = 10162, 1030301 = 1013),
2 (21 = 52, 23 = 33), 32 (92E = E3, 961 = 312), 62 (121 = 112, 183 = 35), (3X9581 = 6X12, 3X9623 = 833), 92
3 (X5 = 53, X8 = 27), 33 (21 = 52, 54 = 26), (261 = 172, 294 = 182), (681 = 272, 6E4 = X3), (6181 = 872, 61E4 = 1X3), 63 (21 = 52, 84 = X2), (X1 = E2, 144 = 122), (961 = 312, X04 = 322), 93 (201 = 152, 294 = 182), (1901 = 472, 1994 = 482),
4 (4 = 22, 8 = 23), (28 = 25, 30 = 62), (X1 = E2, X5 = 53), 34 (9 = 32, 41 = 72), (69 = 34, X1 = E2), (160 = 63, 194 = 28), (1694 = 442, 1708 = 123), 64 (41 = 72, X5 = 53), (230 = 162, 294 = 182), (418241 = 7072, 4182X5 = 853), 94 (9 = 32, X1 = E2), (14 = 24, X8 = 27), (28 = 25, 100 = 102), (100 = 102, 194 = 28), (294 = 182, 368 = 29), (509 = 36, 5X1 = 252), (1154 = 382, 1228 = 2E), (213414 = 5042, 2134X8 = 217),
5 (4 = 22, 9 = 32), (23 = 33, 28 = 25), 35 (8 = 23, 41 = 72), (X8 = 27, 121 = 112), (294 = 182, 309 = 192), 65 (4 = 22, 69 = 34), (X04 = 322, X69 = 332), 95 (8 = 23, X1 = E2), (368 = 29, 441 = 54), (92E = E3, X04 = 322), (1994 = 482, 1X69 = 492), (X208 = 223, X2X1 = E12), (21202508 = 2E23, 212025X1 = 50252),
6 36 66 96
7 (9 = 32, 14 = 24), (21 = 52, 28 = 25), (X1 = E2, X8 = 27), (16E61 = 1312, 16E68 = 213), 37 (309 = 192, 344 = 1X2), 67 (41 = 72, X8 = 27), (X69 = 332, E14 = 342), (4701 = 752, 4768 = 183), (44899 = 393, 44944 = 2122), 97 (69 = 34, 144 = 122), (X8 = 27, 183 = 35), (1X69 = 492, 1E44 = 4X2),
8 (8 = 23, 14 = 24), (483E4 = 3X3, 48400 = 2202), 38 (69 = 34, X5 = 53), (84 = X2, 100 = 102), (X5 = 53, 121 = 112), 68 (54 = 26, 100 = 102), (261 = 172, 309 = 192), (41368 = 383, 41414 = 2042), 98 (9 = 32, X5 = 53), (84 = X2, 160 = 63), (554 = 242, 630 = 262), (27830 = 1762, 27908 = 323), (13X2630 = 11962, 13X2708 = 1123),
9 (14 = 24, 21 = 52), (23 = 33, 30 = 62), (160 = 63, 169 = 132), (31054 = 343, 31061 = 1912), 39 (4 = 22, 41 = 72), (30 = 62, 69 = 34), (344 = 1X2, 381 = 1E2), (5400 = 802, 5439 = 193), 69 (100 = 102, 169 = 132), (183 = 35, 230 = 162), (E14 = 342, E81 = 352), (1284 = 3X2, 1331 = 113), 99 (4 = 22, X1 = E2), (8 = 23, X5 = 53), (23 = 33, 100 = 102), (230 = 162, 309 = 192), (1323 = 37, 1400 = 402), (1E44 = 4X2, 2021 = 4E2),
X (1323 = 37, 1331 = 113), 3X (183 = 35, 201 = 152), 6X 9X (X5 = 53, 183 = 35), (169 = 132, 247 = 73), (183 = 35, 261 = 172),
E (14 = 24, 23 = 33), (21 = 52, 30 = 62), (1985 = 55, 1994 = 482), (1E44 = 4X2, 1E53 = 133), 3E (69 = 34, X8 = 27), (121 = 112, 160 = 63), (144 = 122, 183 = 35), (381 = 1E2, 400 = 202), (E81 = 352, 1000 = 103), (100814 = 3582, 100853 = 533), 6E (E81 = 352, 1030 = 362), (E414 = E82, E483 = 39), 9E (9 = 32, X8 = 27), (21 = 52, 100 = 102), (2021 = 4E2, 2100 = 502), (721X5 = 453, 72284 = 2822),
10 (4 = 22, 14 = 24), (1331 = 113, 1341 = 3E2), 40 (14 = 24, 54 = 26), (X1 = E2, 121 = 112), (10814 = 1042, 10854 = 243), 70 (14 = 24, 84 = X2), (294 = 182, 344 = 1X2), X0 (8 = 23, X8 = 27), (41 = 72, 121 = 112), (121 = 112, 201 = 152), (5X1 = 252, 681 = 272),
11 (30 = 62, 41 = 72), (183 = 35, 194 = 28), (2X04 = 5X2, 2X15 = 153), 41 (28 = 25, 69 = 34), (400 = 202, 441 = 54), (112X94 = 3782, 112E15 = 553), 71 (30 = 62, X1 = E2), (1030 = 362, 10X1 = 372), X1 (4 = 22, X5 = 53), (1000 = 103, 10X1 = 372), (2100 = 502, 21X1 = 512),
12 42 72 X2 (X1 = E2, 183 = 35),
13 (41 = 72, 54 = 26), (525531 = 913, 525544 = 7XX2), 43 (41 = 72, 84 = X2), (441 = 54, 484 = 222), 73 (121 = 112, 194 = 28), (194 = 28, 247 = 73), (10X1 = 372, 1154 = 382), X3 (261 = 172, 344 = 1X2), (21X1 = 512, 2284 = 522),
14 (9 = 32, 21 = 52), (14 = 24, 28 = 25), (X8 = 27, 100 = 102), 44 (100 = 102, 144 = 122), 74 (69 = 34, 121 = 112), (X8 = 27, 160 = 63), (309 = 192, 381 = 1E2), X4 (4 = 22, X8 = 27), (630 = 262, 714 = 2X), (1985 = 55, 1X69 = 492),
15 (8 = 23, 21 = 52), (28 = 25, 41 = 72), (54 = 26, 69 = 34), (368 = 29, 381 = 1E2), (3X017 = 373, 3X030 = 1E62), (69454 = 443, 69469 = 2732), 45 (484 = 222, 509 = 36), (12100 = 1102, 12145 = 253), 75 (28 = 25, X1 = E2), (30 = 62, X5 = 53), (6E4 = X3, 769 = 292), (1154 = 382, 1209 = 392), (48X8 = 211, 4961 = 772), (80347 = 473, 80400 = 2X02), X5 (84 = X2, 169 = 132), (2284 = 522, 2369 = 532),
16 (9 = 32, 23 = 33), (169 = 132, 183 = 35), (247 = 73, 261 = 172), 46 (23 = 33, 69 = 34), (201 = 152, 247 = 73), 76 X6 (1X69 = 492, 1E53 = 133),
17 (8 = 23, 23 = 33), (69 = 34, 84 = X2), (X5 = 53, 100 = 102), (230 = 162, 247 = 73), 47 (9 = 32, 54 = 26), (509 = 36, 554 = 242), (85721 = 2XE2, 85768 = 483), 77 (9 = 32, 84 = X2), (X5 = 53, 160 = 63), (1209 = 392, 1284 = 3X2), X7 (160 = 63, 247 = 73), (2369 = 532, 2454 = 210),
18 (14 = 24, 30 = 62), (144 = 122, 160 = 63), 48 (8 = 23, 54 = 26), (21 = 52, 69 = 34), (121 = 112, 169 = 132), (3414 = 642, 3460 = 163), 78 (8 = 23, 84 = X2), (30 = 62, X8 = 27), (344 = 1X2, 400 = 202), (4830 = 762, 48X8 = 211), X8 (14 = 24, 100 = 102), (X8 = 27, 194 = 28), (144 = 122, 230 = 162), (681 = 272, 769 = 292), (E14 = 342, 1000 = 103), (2X15 = 153, 2E01 = 5E2),
19 (4 = 22, 21 = 52), (84 = X2, X1 = E2), 49 (54 = 26, X1 = E2), (247 = 73, 294 = 182), (554 = 242, 5X1 = 252), 79 (28 = 25, X5 = 53), (144 = 122, 201 = 152), (1284 = 3X2, 1341 = 3E2), (9887 = 75, 9944 = XX2), X9 (294 = 182, 381 = 1E2), (2454 = 210, 2541 = 552),
1X (23 = 33, 41 = 72), (1323 = 37, 1341 = 3E2), 4X 7X (23 = 33, X1 = E2), (86623 = 3E, 866X1 = 2E12), XX
1E (4 = 22, 23 = 33), (9 = 32, 28 = 25), (X1 = E2, 100 = 102), (1209 = 392, 1228 = 2E), 4E (5X1 = 252, 630 = 262), 7E (41 = 72, 100 = 102), (X1 = E2, 160 = 63), (1341 = 3E2, 1400 = 402), (115E41 = 1E4, 116000 = 67), XE (X5 = 53, 194 = 28), (2541 = 552, 2630 = 562),
20 (8 = 23, 28 = 25), (21 = 52, 41 = 72), (6E4 = X3, 714 = 2X), 50 (4 = 22, 54 = 26), (144 = 122, 194 = 28), (X13804 = E022, X13854 = E43), 80 (4 = 22, 84 = X2), (21 = 52, X1 = E2), (28 = 25, X8 = 27), (84 = X2, 144 = 122), (381 = 1E2, 441 = 54), E0 (54 = 26, 144 = 122), (714 = 2X, 804 = 2X2),
21 (84 = X2, X5 = 53), (100 = 102, 121 = 112), 51 (54 = 26, X5 = 53), (630 = 262, 681 = 272), 81 (X8 = 27, 169 = 132), (1400 = 402, 1481 = 74), (3460 = 163, 3521 = 652), E1 (30 = 62, 121 = 112), (2630 = 562, 2721 = 572),
22 (20969 = 1532, 2098E = 2E3), (21X489E = 1E5, 21X4901 = 15752), 52 82 (23 = 33, X5 = 53), (247 = 73, 309 = 192), E2
23 (9 = 32, 30 = 62), (121 = 112, 144 = 122), (160 = 63, 183 = 35), 53 (69 = 34, 100 = 102), (681 = 272, 714 = 2X), (51453801 = 7X012, 51453854 = 3E43), 83 (100 = 102, 183 = 35), (169 = 132, 230 = 162), (1481 = 74, 1544 = 422), E3 (9 = 32, 100 = 102), (69 = 34, 160 = 63), (X1 = E2, 194 = 28), (309 = 192, 400 = 202), (2721 = 572, 2814 = 582), (3X84 = 6X2, 3E77 = 173), (7E09 = 992, 8000 = 203),
24 (4 = 22, 28 = 25), (8 = 23, 30 = 62), (30 = 62, 54 = 26), (84 = X2, X8 = 27), (344 = 1X2, 368 = 29), (25369 = 134, 25391 = 313), (63X04 = 2622, 63X28 = 215), 54 (30 = 62, 84 = X2), (54 = 26, X8 = 27), (169 = 132, 201 = 152), (368 = 29, 400 = 202), 84 (21 = 52, X5 = 53), (X5 = 53, 169 = 132), (183 = 35, 247 = 73), (400 = 202, 484 = 222), (630 = 262, 6E4 = X3), (1901 = 472, 1985 = 55), (4768 = 183, 4830 = 762), (8000 = 203, 8084 = 9X2), (1X830 = 1462, 1X8E4 = 2X3), E4 (8 = 23, 100 = 102), (169 = 132, 261 = 172), (769 = 292, 861 = 2E2),
25 (144 = 122, 169 = 132), 55 (14 = 24, 69 = 34), (714 = 2X, 769 = 292), (1708 = 123, 1761 = 452), (56854368 = 4083, 56854401 = 82012), 85 (23 = 33, X8 = 27), (1544 = 422, 1609 = 432), (3541EE = 7E3, 354284 = 6522), E5 (28 = 25, 121 = 112), (2814 = 582, 2909 = 592),
26 (3E77 = 173, 3EX1 = 6E2), 56 86 E6 (152X7 = 273, 153X1 = 1252),
27 (169 = 132, 194 = 28), 57 (769 = 292, 804 = 2X2), (7004 = 922, 705E = 1E3), 87 (21 = 52, X8 = 27), (1609 = 432, 1694 = 442), E7 (1228 = 2E, 1323 = 37), (2909 = 592, 2X04 = 5X2), (50004 = 22X2, 500EE = 3E3),
28 (4 = 22, 30 = 62), (28 = 25, 54 = 26), (41 = 72, 69 = 34), (4594 = 742, 4600 = 65), 58 (28 = 25, 84 = X2), (X8 = 27, 144 = 122), (194 = 28, 230 = 162), (1228 = 2E, 1284 = 3X2), (1214368 = 1083, 1214404 = 11022), 88 (X1 = E2, 169 = 132), (441 = 54, 509 = 36), (13694 = 1182, 13760 = 263), (36994 = 1X82, 36X60 = 363), E8 (4 = 22, 100 = 102), (804 = 2X2, 900 = 64),
29 (14 = 24, 41 = 72), (194 = 28, 201 = 152), 59 (84 = X2, 121 = 112), (804 = 2X2, 861 = 2E2), 89 (14 = 24, X1 = E2), (54 = 26, 121 = 112), (194 = 28, 261 = 172), (1694 = 442, 1761 = 452), E9 (247 = 73, 344 = 1X2), (344 = 1X2, 441 = 54), (2X04 = 5X2, 2E01 = 5E2),
2X 5X 8X (861 = 2E2, 92E = E3), (1E53 = 133, 2021 = 4E2), EX (23 = 33, 121 = 112),
2E (201 = 152, 230 = 162), (900 = 64, 92E = E3), 5E (X5 = 53, 144 = 122), (309 = 192, 368 = 29), (861 = 2E2, 900 = 64), (1284 = 3X2, 1323 = 37), 8E (1331 = 113, 1400 = 402), (1761 = 452, 1830 = 462), (E90230 = EX62, E902EE = EE3), EE (84 = X2, 183 = 35), (1609 = 432, 1708 = 123), (2E01 = 5E2, 3000 = 602),
30 (54 = 26, 84 = X2), (1000 = 103, 1030 = 362), 60 (9 = 32, 69 = 34), (41 = 72, X1 = E2), (100 = 102, 160 = 63), (201 = 152, 261 = 172), 90 (30 = 62, 100 = 102), (160 = 63, 230 = 162), (484 = 222, 554 = 242), (14504760 = 2663, 14504830 = 40762), 100 (21 = 52, 121 = 112), (69 = 34, 169 = 132), (194 = 28, 294 = 182), (861 = 2E2, 961 = 312), (49954 = 2242, 49X54 = X5),
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