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What is the current status on Mersenne primes?

The following Mersenne primes are known.

The way to determine if is prime is to use the Lucas-Lehmer test:

         u := 4
         for i from 3 to p do
            u := u^2-2 mod 2^p-1
         if u == 0 then
            2^p-1 is prime
            2^p-1 is composite

All exponents less than 1,481,800 have now been tested at least once.


An introduction to the theory of numbers. G.H. Hardy, E.M. Wright. Fifth edition, 1979, Oxford.

Alex Lopez-Ortiz
Mon Feb 23 16:26:48 EST 1998