Smallest prime of the form xxxx…xxx n for odd n and digit x, or 0 if there is none.

11, 3, 5, 7, 19, 11, 13, 0, 17, 19, 421, 23, 0, 127, 29, 31, 233, 0, 37, 139, 41, 43, 0, 47, 149, 151, 53, 0, 157, 59, 61, 163, 0, 67, 269, 71, 73, 0, 277, 79, 181, 83, 0, 487, 89, 191, 193, 0, 97, 199, 101, 103, 0, 107, 109, 2111, 113, 0, 1117, 3119, 3121, 1123

1

This sequence was inspired by the paper of Wu. However, this work is does not appear there. Searching the first 10^6 terms, it appears that the only zero terms correspond of multiples of 5.

T. D. Noe, Plot of 1000 terms

T. D. Noe, Table of 1000 terms

Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv 1503.0883 (Mar 31 2015)

(Mma) mx = 100; Table[nDigits = IntegerDigits[n]; s = n; len = 0; i = 0; If[n > 5 && Mod[n, 5] == 0, 0, While[len < mx && ! PrimeQ[s], i++; If[i > 9, i = 1; len++]; s = FromDigits[Join[Table[i, {len}], nDigits]]]; If[len < mx, s, 0]], {n, 1, 200, 2}]

nonn,base,nice

T. D. Noe, Apr 09 2015