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COMMENTS
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Hypothetically, a(8) = 26293 = A232210(2889).
However, there are two conjectures: 1) for every n, prime a(n) exists (Shevelev); 2) already prime a(8) does not exist (Havermann).
M. F. Hasler showed that, if a prime of the form 262933...3 > 26293 exists, then it has at least several thousand digits.
Note that, for a(n), n=1,...,7, the number of digits of the smallest prime of the form a(n)*10^k+3...3 (k 3's) respectively equals 16, 26, 53, 255, 4756, 6525, 9677. Judging from the ratio 4756/255 > 18.65, the smallest prime of the form 262933...3 could have more than 180000 digits.
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