Prime Number for Android
You can choose to show divisors or not. Not showing divisors can speed up checking for super-long numbers.
This app will also tell you the next and the previous Prime Number if available.
Testing shows that (with "Show divisors" options enabled) the app can determine numbers whose length is shorter than 8 in a flash. Length equals to 8 in less than 1 seconds. And determining those with 9 characters in less than 5 seconds. This can vary from device to device.