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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 1000 are 5, 7, 15, 27, 35, 37, 45, 57, 85, 87, 95, X7, E5, E7, 105, 107, 117, 125, 145, 167, 195, 1X5, 1E5, 1E7, 205, 225, 255, 267, 277, 285, 295, 315, 325, 365, 377, 397, 3X5, 3E5, 3E7, 415, 427, 435, 437, 447, 455, 465, 497, 4X5, 517, 527, 535, 545, 557, 565, 575, 585, 5E5, 615, 655, 675, 687, 695, 6X7, 705, 735, 737, 745, 767, 775, 785, 797, 817, 825, 835, 855, 865, 8E5, 8E7, 907, 927, 955, 965, 995, 9X7, 9E5, X07, X17, X35, X37, X45, X77, X87, X95, XE7, E25, E37, E45, E95, E97, EX5, EE5, EE7.

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 45.X242% 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.