1. A method for reducing data traffic among multiple processors with transactional memory for processing data, the method comprising: processing a transaction using a first processor, wherein the transaction includes: reading first data into a private cache of the first processor, upon detecting a preset condition of recent modifications on the first data, performing a write operation on the first data in the private cache of the first processor, and setting a cache line state index string to indicate a special state of the first data written in the private cache of the first processor, the special state signaling that the first data is modified and is to be exclusively written in a last level cache (LLC) when the transaction is committed; committing the transaction to a transactional memory system by writing the first data in the private cache of the first processor into the LLC accessible by the multiple processors, and invalidating the first data in the private cache of the first processor; and modifying the first data by modifying a copy of the first data in the LLC.