Upto $2^{64}$ , there are two Carmichael numbers with only odd digits :
$$53711113=157\cdot 313\cdot 1093$$ and $$3559313513953=29\cdot 113\cdot 337\cdot 673\cdot 4789$$
In the first case, the prime factors give only one even digit (unfortunately, if they would also be all odd , this would be beautiful).
Is there another such Carmichael number ? If yes, what is the third ?
I expect that there are only finite many such Carmichael-numbers. Do we have a chance to prove that ?