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Inverting Carmichael Primes

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  • miltbrown@earthlink.net
    Three Factor Carmichael Primes can be inverted to much smaller primes by the test ((2*T)^q) mod p = 1 Below is a listing of these primes:
    Message 1 of 1 , Dec 30, 2006
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      Three Factor Carmichael Primes can be inverted
      to much smaller primes by the test

      ((2*T)^q) mod p = 1

      Below is a listing of these primes:

      T---------------p-----------q

      5,43,127-------561--------17*11*3
      5,23,67--------1729-------19*13*5
      5,3,59---------2821-------31*13*7

      11,-,103-------6601-------41*23*7
      13,101,101-----8911-------67*19*7
      3,7,7----------29341------61*37*13

      3,3,-,---------46657------97*37*13
      37,23,-,-------52633------103*73*7
      3,113,-,-------115921-----241*37*13

      19,-,-,--------162401-----233*41*17
      61,-,-,--------334153-----409*43*19
      7,5,7----------399001-----211*61*31

      157,89,5-------410041-----137*73*41
      3,13,71--------488881-----181*73*37
      7,5,-, --------512461-----271*61*31

      3,127,-,-------530881-----421*97*13
      5,7,17---------1152271----211*127*43
      3,3,3----------1461241----541*73*37

      23,83,-,-------1857241----331*181*31
      5,73,-,--------1909001----461*101*41
      5,-,-,---------2508013----599*79*53

      61,113,-,------3828001----251*151*101
      7,5,211--------4335241----521*157*53
      19,3,-,--------5481451----1171*151*31

      3,31,-,--------7519441----761*241*41
      3,37,-,--------5444489----953*197*29
      3,17,23--------23382529---1249*193*97

      29,139,-,------29111881---491*281*211
      71,-,-,--------34657141---431*421*191
      13,11,53-------64377991---811*487*163

      31,13,-,-------851703301-—4451*1069*179
      31,23,59-------2436691321-6781*1583*227

      Milton L. Brown
      miltbrown AT earthlink.net
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