sory problem of translut (pseudoprime)

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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
Message 1 of 1 , Sep 30, 2009
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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