@neptune's largest known 96,522 decimal digits 3-Carmichael number, with single random base verification

96522.gp

\\ @Neptune's largest known 3-Carmichael number (96522 decimal digits):
\\ https://www.mersenneforum.org/node/22080/page3#post1066763

p = 3*(5752211*43#/2-1)^1069/2+1;
q = 3*(5752211*43#/2-1)^1069+1;
r = 3*((5752211*43#/2-1)^1069+(5752211*43#/2-1)^2138)/1050650772710+1;
n = p*q*r;
print(#digits(n));

n1 = (n-1)/gcd(n-1,p-1);
n2 = n1/gcd(n1,q-1);
n3 = n2/gcd(n2,r-1);
print(#digits(n3));

expr="lift(Mod(2+random(),n)^(n-1))";
gettime();
print(eval(expr));
print("took "gettime()"ms to compute "expr);

hermann@7950x:~$ time gp -q < 96522.gp
96522
48267
1
took 481803ms to compute lift(Mod(2+random(),n)^(n-1))

real	8m5.826s
user	8m1.829s
sys	0m3.969s
hermann@7950x:~$