A processor includes a processor core coupled to an address translation storage structure. The address translation storage structure includes a plurality of entries, each corresponding to a memory page. Each entry also includes a physical address of a memory page, and a private page indication that indicates whether any other processors have an entry, in either a respective address translation storage structure or a respective cache memory, that maps to the memory page. The processor also includes a memory controller that may inhibit issuance of a probe message to other processors in response to receiving a write memory request to a given memory page. The write request includes a private page attribute that is associated with the private page indication, and indicates that no other processor has an entry, in either the respective address translation storage structure or the respective cache memory, that maps to the memory page.