25523the 26th prime Eisenstein Mersenne Norm
- Mar 30, 2014After 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).
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).
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