What is 3rd century BC?

Hannibal

its the 4th century!

It is grammatically correct to spell out the word for numbers of ten and less, hence, "second century B.C." is correct.

Hannibal son of Hamilcar Barca invaded Italy and occupied it from 218 to 202 BC during the Second Punic War.

The 6th century ad comes after the 3rd century ad.