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.
2.
don't care; not my problem
Used to dismiss responsibility or express indifference, often with an abrupt or blunt tone.
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.
Common patterns
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.