1.
don't know; no idea
Casual or dialectal contraction of 知らない (shiranai), meaning "I don't know." Common in western Japanese dialects and casual male speech.
そんなこと知らん。
I don't know about that.
あいつがどこにいるかなんて知らんよ。
I have no idea where that guy is.
いつ届くかは知らんけど、たぶん来週だろう。
I don't know when it'll arrive, but probably next week.
2.
don't care; not my problem
Used to dismiss responsibility or express indifference, often with an abrupt or blunt tone.
もう知らん。勝手にしろ。
I don't care anymore. Do whatever you want.
失敗しても知らんぞ。
Don't blame me if you fail.
自分で決めたことだろう。結果がどうなっても知らんからな。
You decided this yourself. I'm not responsible for whatever happens.
USAGE:
知らん is a contraction of 知らない. It is characteristic of casual male speech and western Japanese dialects (especially Kansai). In standard Japanese, it sounds blunt or rough.
GRAMMAR:
The ん ending is a contraction of ない that appears in many verbs in casual speech: 分からん (分からない), 食べん (食べない), etc. This pattern is especially common in western dialects.
REGISTER:
More casual and blunt than 知らない. Using 知らん with strangers or superiors would sound rude.