Do you really need the entire range of an NSUInteger? On iOS that’s an unsigned 32 bit value, which can get very large. It will find into a signed 64 bit.
But you probably don’t need that much precision anyway. The maximum for a uint32_t is UINT32_MAX which is 4,294,967,295 (4 billion). If you increment once a second, it’ll take you more than 136 years to reach that value. Your user’s iPhone won’t be around by then… 🙂