How can I find a Carmichael number near a huge given number , say $10^{100}$ ?
My best trial was to find suitable $k$ such that $6k+1$ , $12k+1$ , $18k+1$ are prime and the product as near as possible at $10^{100}$. But the results are still very unsatisfying :
$$9999999999999999999999999995194780645298842465772438047052058885837645928421429394846343577780058169$$ and $$10000000000000000000000000000405929367865700162694655745350302085810080768959837103297359653235421369$$
What can I do for significant better results ?