After 8 years, the 26th prime Eisenstein Mersenne Norm is found: 3^2237561+3^1118781+1.

The 25th prime Eisenstein Mersenne Norm was found by Boris Iskra in 2005.

More compactly, this number may be written as

Phi(3, 3^{^1118781} + 1)/3, and this form makes it apparent that this is also a Generalized Unique prime (as are all of the prime E.-M. Norms).

http://primes.utm.edu/primes/page.php?id=117512 It has 1,067,588 decimal digits.

To accelerate the search process, I have implemented the primality test using FFT modulo (3^3p+1); each test takes less than half of the standard N-1 test (with zero-padded general FFT).