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On the twisted Fermat cubic, an elliptic divisibility sequence arises as thesequence of denominators of the multiples of a single rational point. We provethat the number of prime terms in the sequence is uniformly bounded. When therational point is the image of another rational point under a certain3-isogeny, all terms beyond the first fail to be primes.

The Uniform Primality Conjecture for the Twisted Fermat Cubic