Prime Curios!: 181

181
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It is conjectured that there is always a prime between x^a and y^b for all integers x, y, a, b > 1, except for the following ten pairs: (2³,3²), (5²,3³), (2⁵,6²), (11²,5³), (3⁷,13³), (5⁵,56²), (181²,2¹⁵), (43³,282²), (46³,312²), and (22434²,55⁵). [Redmond and Sun]

Submitted: 2008-04-02 22:33:20; Last Modified: 2008-04-02 22:36:06.