1, 2, 1, 9, 2, 2, 1, 1, 10, 6, 6, 1, 2, 6, 1, 2, 1, 2, 2, 1, 3, 2, 1, 2, 1, 1, ... However, studies show that three-fourths of primes of the form 8k + n, where n ∈ {3, 5} are full reptend primes in base 2 (For example, there are 87 primes below 1000 congruent to 3 or 5 modulo 8, and 67 of them are full-reptend in base 2, it is total 77%). For some sequences, the preponderance of full reptend primes is much greater. For instance, 1078 of the 1206 primes of form 24k + 5 below 100000 are full reptend primes in base 2, with 1013 being the first that is not full reptend in base 2. Furthermore, all primes of the form 4p + 1 for p is prime are full-reptend primes in base 2. n-th level reptend prime An n-th level reptend prime is a prime p having n different cycles in expansions of (k is an integer, 1 ≤ k ≤ p−1). In base 10, smallest n-th level reptend prime are 7, 3, 103, 53, 11, 79, 211, 41, 73, 281, 353, 37, 2393, 449, 3061, 1889, 137, 2467, 16189, 641, 3109, 4973, 11087, 1321, 101, 7151, 7669, 757, 38629, 1231, 49663, 12289, 859, 239, 27581, 9613, 18131, 13757, 33931, 9161, 118901, 6763, 18233, 1409, 88741, 4003, 5171, 19489, 86143, 23201, ... In base 2, smallest n-th level reptend prime are 3, 7, 43, 113, 251, 31, 1163, 73, 397, 151, 331, 1753, 4421, 631, 3061, 257, 1429, 127, 6043, 3121, 29611, 1321, 18539, 601, 15451, 14327, 2971, 2857, 72269, 3391, 683, 2593, 17029, 2687, 42701, 11161, 13099, 1103, 71293, 13121, 17467, 2143, 83077, 25609, 5581, 5153, 26227, 2113, 51941, 2351, ... Full reptend primes in various bases Artin also conjectured: There are infinitely many full-reptend primes in all bases except squares. Full-reptend primes in all bases except perfect powers and numbers whose squarefree part are congruent to 1 modulo 4 comprise 37.395...% of all primes. (See ) The smallest full-reptend primes in base n are: 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 5, 2, 3, 2, 0, 2, 5, 2, 3, 2, 5, 2, 7, 2, 3, 2, 5, 2, 11, 2, 3, 2, 19, 2, 0, 2, 3, 2, 7, 2, 5, 2, 3, 2, 11, 2, 5, 2, 3, 2, 5,