FANDOM


A prime p is full-reptend prime (or long prime) if and only if the period length of 1/p is p-1. e.g. 1/5 = 0.249724972497... has period length 4, and 1/7 = 0.186X35186X35... has period length 6. The full-reptend prime below 100 are 5, 7, 15, 27, 35, 37, 45, 57, 85, 87, 95, X7, E5, E7.

A prime p is a full-reptend prime if and only if 10 is a primitive root mod p.

All full-reptend primes end with 5 or 7, since 10 is a quadratic residue (thus not a primitive root) of all primes end with 1 or E (thus, no safe primes are full-reptend primes, except 5 and 7, since all safe primes end with E, except 5 and 7), besides, about 3/8 (=0.46 or 46%) of the primes are full-reptend primes, if Artin’s conjecture is true, then the density of the set of full-reptend primes related to the set of primes is Artin’s constant, since 10 is not a perfect power, and the squarefree part of 10 is 3, which is not congruent to 1 mod 4.