Full reptend prime
From Number
Definition
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.
Facts
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
.