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sory problem of translut (pseudoprime)

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  • Lio David
    There s Not Sense for     the search :  the great pseudoprime number or the great superpseudoprime. k composite numbre k is a psudoprime  if  k
    Message 1 of 1 , Sep 30, 2009
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      There's Not Sense for     the search :  the great pseudoprime number or the great
      superpseudoprime.
      k composite numbre

      k is a psudoprime  if  k satisfies
                                                    k=1 mod 2^n-1  and  k=1 mod n   

       2^10-1   = 3*11*31        we have   (11 *31) =  1 mod 2^10-1 and  =  1 mod 10 
      then is  psudoprime
       2^12      = 3*3*5*7*13  no
       2^14      = 3*43*127                      43*127 =   1 mod 14
       2^16      =3*5*17*257                   17*257 =   1 mod 16
       2^18      = 3*7*19*73                    19*73   =   1 mod  18

      to find a psudoprime is  very simple : n even  number ;
                                                                                      \
         if  k=1 mod 2^n-1  and  k=1 mod n     


      ------------ --------- --------- --------- --------- --------- -
      for the superpsudoprime

           2^22-1 =   3*23*89*683     we have (23*89*683) = 1 mod 22
                                                                 and               
      23=  1 mod 22
                                                                                      
      89=  1 mod 22
                                                                                    
      683=  1 mod 22
      then a superpsudoprime k   
         k= 1 mod 2^n-1      and  all factor of k   =   1  mod n 

      There's Not Sense for     the search :  the great psudoprime number or the great
      superpseudoprime.




      rachid




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