A248919 "Stubborn primes" (see comments in A232210).

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

Offset: 1

Author

Vladimir Shevelev, Oct 16 2014

Keywords

• nonn
• base
• more

Comments

Terms a(2)-a(5) were obtained by Peter J. C. Moses.

Terms a(6)-a(7) were obtained by Hans Havermann (cf. b-file in A232210).

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.

Links

• Vladimir Shevelev, "Stubborn primes"

Crossrefs

Cf. A000040, A232210.