Full reptend prime
For arbitrary base
A prime is termed a full reptend prime to base (where is a positive integer greater than 1) if the following equivalent conditions are satisfied:
- is a primitive root modulo .
- The base expansion of has repeating block of length .
- The number is a cyclic number in base .
Default of base 10
By default, the term full reptend prime is used for a prime that is a full reptend prime in base 10.
For a fixed base , there exists a finite number dependent on such that whether or not is a full reptend prime mod depends only on the congruence class of modulo that finite number. When itself is an odd prime, this number is .