Geodesic
Catalan's equation has no new solution with either exponent less than 10651.
Experimental mathematics, Tome 4 (1995) no. 4, pp. 259-268

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Keywords: Catalan's equation, linear forms in two logarithms, class numbers 
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     author = {Mignotte, Maurice and Roy, Yves},
     title = {Catalan's equation has no new solution with either exponent less than 10651.},
     journal = {Experimental mathematics},
     pages = {259--268},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {1995},
     zbl = {0857.11012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EXMA_1995__4_4_228795/}
}
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Mignotte, Maurice; Roy, Yves. Catalan's equation has no new solution with either exponent less than 10651.. Experimental mathematics, Tome 4 (1995) no. 4, pp. 259-268. http://geodesic.mathdoc.fr/item/EXMA_1995__4_4_228795/