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the 26th prime Eisenstein Mersenne Norm

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  • batalovs
    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
    Message 1 of 2 , Mar 30, 2014
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      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).
    • mikeoakes2
      That s great work, Serge. Many congrats ! Mike
      Message 2 of 2 , Mar 30, 2014
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        That's great work, Serge.
        Many congrats !
        Mike
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