Full reptend prime
In number theory, a full reptend prime, full repetend prime, proper prime or long prime in base b is an odd prime number p such that the Fermat quotient q p ( b ) = b p − 1 − 1 p {\displaystyle q_{p}(b)={\frac {b^{p-1}-1}{p}}} (where p does not divide b) gives a cyclic number. Therefore, the base b expansion of 1 / p {\displaystyle 1/p} repeats the digits of the corresponding cyclic number infinitely, as does that of a / p {\displaystyle a/p} with rotation of the digits for any a between 1 and p − 1.