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%I #10 May 14 2024 20:17:21
%S 29,59,599,2999,8999,29999999
%N Primes of the form p = k*10^m - 1 where k is 3, 6 or 9, such that p+2 is also a prime.
%C There are no more terms for m <= 34936. - Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 29 2007
%H M. Kamada, <a href="https://stdkmd.net/nrr/">Factorizations of near-repdigit numbers</a>
%e a(1)= because 3*10^1-1 = 29 and 3*10^1+1 = 31 are primes.
%e a(2)= because 6*10^1-1 = 59 and 6*10^1+1 = 61 are primes.
%e a(3)= because 6*10^2-1 = 599 and 6*10^2+1 = 601 are primes.
%e a(4)= because 3*10^3-1 = 2999 and 3*10^3+1 = 3001 are primes.
%e a(5)= because 9*10^3-1 = 8999 and 9*10^3+1 = 9001 are primes.
%e a(6)= because 3*10^7-1 = 29999999 and 3*10^7+1 = 30000001 are primes.
%t Select[FromDigits/@Flatten[Table[PadRight[{k},n,9],{k,{2,5,8}},{n,2,10}],1],AllTrue[ #+{0,2},PrimeQ]&]//Union (* _Harvey P. Dale_, May 14 2024 *)
%K more,nonn
%O 1,1
%A _Lekraj Beedassy_, Dec 21 2006
%E Edited by _N. J. A. Sloane_, Jan 01 2007
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