%I
%S 9901,99990001,999999000001,9999999900000001
%N Primes of the form 100^k  10^k + 1.
%C These primes correspond to k = 2, 4, 6, and 8. There are no other primes of this form for k up to 10000. These primes appear in A187614 because the decimal representation of their reciprocal contains only the digits 0, 1, 8, and 9.
%C Because these numbers are values of the sixth cyclotomic polynomial, by Theorem 1 of Golomb, the only k that can produce primes are the 3smooth numbers, 2^i*3^j (A003586).
%C Next term has k > 1000000.  _Robert Gelhar_, Aug 20 2020
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 85.
%H Solomon W. Golomb, <a href="http://www.jstor.org/stable/2321679">Cyclotomic polynomials and factorization theorems</a>, Amer. Math. Monthly 85 (1978), 734737.
%t Select[Table[100^n  10^n + 1, {n, 1000}], PrimeQ]
%Y Cf. A003586, A168624, A187614.
%K nonn,more
%O 1,1
%A _T. D. Noe_, Mar 14 2011
