  The problem of N-digit sets all permutations of which give primes is
discussed. Such sets may include only digits 1, 3, 7 and 9, and none of 0, 2,
5, 4, 6, 8. Direct calculations show that such full-permutation digit sets
occur at N = 1, 2, 3 and are absent in the 4 - 10 interval of N. On the other
hand the formal full permutation at N = 19, 23, 317 and 1031 (as well at N = 2)
cases is provided by repunits (integers all digits of which are 1). The
existence/nonexistence of other (not repunits) full-permutation digit sets for
arbitrary large N is an open question with probable negative answer. The
maximal-permutation digit sets with maximal number of primes are given for N =
4 - 10.
