Is there a Carmichael-number divisible by $3\times 5\times 17=255$?

Question

I am searching a Carmichael-number of the form $N=3\times 5\times 17\times k$.

$N$ must have the form $N=4080m+3825$ because $N$ must satisfy $N\equiv 0\ (\ mod\ 255\ )$ and $N\equiv 1\ (\ mod\ 16)$. According to my calculation , such a Carmichael-number, if it exists, must be greater than $2.5\times 10^{11}$.

Is it even possible that such a Carmichael-number exist, or is there some reason (perhaps a congruence) preventing this ?

Answer 1

The are Carmichael number that are divisible by 255: e.g. 1886616373665, 158353658932305, 881715504450705, 3193231538989185, 6128613921672705.