Elliptic curve primality proving, abbreviated ECPP, is class of algorithms that provide certificates of primality using sophisticated results from the theory of elliptic
curves. A detailed description and list of references are given by Atkin and
Morain (1990, 1993).
ECPP is the fastest known general-purpose primality testing algorithm. ECPP has a running time of . As of 2004, the program PRIMO can certify
a 4769-digit prime in approximately 2000 hours of computation (or nearly three months
of uninterrupted computation) on a 1 GHz processor using this technique. As of 2009,
the largest prime certified using this technique was the 11th Mills'
which has decimal digits. The proof was performed using a distributed
computation that started in September 2005 and ended in June 2006 and required a
cumulative CPU-time corresponding to 2.39 GHz for 2219 days (just over 6 years).
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