# Deterministic elliptic curve primality proving for a special sequence of numbers

@article{Abatzoglou2013DeterministicEC,
title={Deterministic elliptic curve primality proving for a special sequence of numbers},
author={Alexander Abatzoglou and Alice Silverberg and Andrew V. Sutherland and Angela Wong},
journal={arXiv: Number Theory},
year={2013},
volume={1},
pages={1-20}
}
We give a deterministic algorithm that very quickly proves the primality or compositeness of the integers N in a certain sequence, using an elliptic curve E/Q with complex multiplication by the ring of integers of Q(sqrt(-7)). The algorithm uses O(log N) arithmetic operations in the ring Z/NZ, implying a bit complexity that is quasi-quadratic in log N. Notably, neither of the classical "N-1" or "N+1" primality tests apply to the integers in our sequence. We discuss how this algorithm may be… Expand
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