MAYOR NÚMERO DE CARMICHAEL CON 6 FACTORES CONOCIDO: 6C20961

New record 6 Carmichael number with 20961 digits

Publicado en https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;3395cbea.1706

I have found 6 Carmichael number with 20961 digits.

The  6 Carmichael number is  N = P . Q . R . S .T .U , where
P = 6.M + 1 ,  Q = 12.M + 1 , R= (P. Q-1)/x  + 1  , x = 1965359

S= L . y +1  ,   where  L = LCM ( P-1 , Q-1 ,R-1) , y=17074247590

T = (P.Q.R.S -1)/z +1 ,   z= 40788370861 , U = ( P. Q.R.S. T -1)/v +1 ,   v= 438106.

M = ( (t .c - 1) ^ a ) /4  ,

a = 5 ,   t = 3.5.7.11.13.17.19.23.29.31.37.... 409 =  409  # / 2  , c = 955911733


C = P . Q . R  is a 3 Carmichael with 3494 digits.

D = C.  S   is a 4 Carmichael with 5247 digits.

E = D  .T   is a 5 Carmichael with 10484 digits.

F  =    E . U   is   a 6 Carmichael with 20961 digits.

I inform you that I have obtained the primality certificates  for P , Q  , R , S , T , U  with primo - 411 . lx64 program .

These certificates can be viewed  on :

P  is prime  in https://drive.google.com/open?id=0B8ZBlKf4gdL2LVR1Z2U4WXgwQ2c

 Q  is prime  in  https://drive.google.com/open?id=0B8ZBlKf4gdL2SlVaTmRIQnd5N2M

R   is prime in  https://drive.google.com/open?id=0B8ZBlKf4gdL2bnpHcVJUOW1MR00

S   is prime in  https://drive.google.com/open?id=0B8ZBlKf4gdL2UXNna0FtaXJFVmM


T  is prime in https://drive.google.com/open?id=0B8ZBlKf4gdL2U2JFSEE5YkdtMG8


U   is prime in https://drive.google.com/open?id=0B8ZBlKf4gdL2SXZQdENMTUFYSUU


Previous record :
In   http://mathworld.wolfram.com/CarmichaelNumber.html       you can see :
“  The largest known Carmichael numbers having a given number of factors are summarized in the following table (updated from Dubner 1989 , 1998).
Factors     digits    discoverer
3              60351   Broadhurst (2002)
4             29094   Broadhurst 2003 (Broadhurst 2015b)
5              1105    Caldwell and Dubner
6               19140  Broadhurst 2003 (Broadhurst 2015a)   “

Any help will be welcome!

Juan Navarro Muñoz
Barcelona ( Spain)