8663

This number is a prime.

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8663 is a prime (p) with this rare property: there is another smaller prime q such that the sum of the cubes of p and q is equal to a square. In this case q = 2137 and 8663^3 + 2137^3 = 659896275600 = 812340^2. 37 is the only prime smaller than 8663 with this property: 11^3 + 37^3 = 51984 = 228^2. [Keith]