An elliptic curve test for Mersenne primes

Benedict H. Gross
2005 Journal of Number Theory  
Let 3 be a prime, and let p = 2 − 1 be the corresponding Mersenne number. The Lucas-Lehmer test for the primality of p goes as follows. Define the sequence of integers x k by the recursion
doi:10.1016/j.jnt.2003.11.011 fatcat:tdqa2so5yjfibkppmlpaifgxhq