%I #32 Jan 02 2023 12:30:50

%S 13,131,653,883,1279,10739,17669

%N "Stubborn primes" (see comments in A232210).

%C Terms a(2)-a(5) were obtained by _Peter J. C. Moses_.

%C Terms a(6)-a(7) were obtained by _Hans Havermann_ (cf. b-file in A232210).

%C Hypothetically, a(8) = 26293 = A232210(2889).

%C However, there are two conjectures: 1) for every n, prime a(n) exists (Shevelev); 2) already prime a(8) does not exist (Havermann).

%C _M. F. Hasler_ showed that, if a prime of the form 262933...3 > 26293 exists, then it has at least several thousand digits.

%C 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.

%H Vladimir Shevelev, <a href="http://list.seqfan.eu/oldermail/seqfan/2014-September/013620.html">"Stubborn primes"</a>

%Y Cf. A000040, A232210.

%K nonn,base,more

%O 1,1

%A _Vladimir Shevelev_, Oct 16 2014