%I #30 Aug 02 2021 02:10:00

%S 0,41,442249570307408382321638310780109588391,41,3,3,3,2,2,2,2,2,2,2,

%T 19,189207115002721,181,17,167,

%U 16158634964154228180872122424567684345543663819,15601,15085130035827878542455979623747888891433345604817588712723282399687865427853871,1460552582234841803

%N Smallest prime formed by the digit string after decimal point of n^(1/n), or 0 if no such prime exists.

%C Conjecture: a(n) is nonzero for all n>1. Generates surprisingly large primes that are easily certified using Elliptic curve techniques (Mathematica's NumberTheory`PrimeQ`). For n=24 no certifiable prime was found with fewer than 1024 digits. - _Wouter Meeussen_, Jun 04 2004

%C a(24) is a 3932-digit number; see the a-file from _Robert G. Wilson v_ in the Links section. - _Jon E. Schoenfield_, Jul 31 2021

%H Robert G. Wilson v, <a href="/A095189/b095189.txt">Table of n, a(n) for n = 1..23</a>

%H Robert G. Wilson v, <a href="/A095189/a095189.txt">Table of n, a(n) with a(n) = 'Unknown' where not known</a>

%e a(7) = 3 as 7^(1/7) = 1.3204692477561... and the least prime is 3.

%t << NumberTheory`PrimeQ`; Table[{n, k = 1; While[temp = Floor[10^k FractionalPart[n^(1/n)]]; k < 256 && (temp === 1 || ! ProvablePrimeQ[temp]), k++ ]; temp, k}, {n, 2, 23}]

%t f[n_] := f[n] = Block[{k = 1, c = FractionalPart[n^(1/n)]}, While[d = FromDigits[ RealDigits[c, 10, k][[1]]]; k < 10001 && ! PrimeQ[d], k++; j = k]; If[k == 10001, 0, d]]; f[1] = 0; Array[f, 23] (* _Robert G. Wilson v_, Oct 11 2014 *)

%Y Cf. A095188.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Jun 02 2004

%E Corrected and extended by _Wouter Meeussen_, Jun 04 2004