S000712


First n-digit prime in the digits of sqrt(3).

7, 17, 173, 3527, 50587, 756887, 8877293, 15058723, 807568877, 8877293527, 66942805253, 558069794519, 4463415058723, 80558069794519, 669428052538103, 5688772935274463, 87236694280525381, 729352744634150587, 1732050807568877293, 96994509499895247881

1

S000712

The position of these numbers in given in S000713. See S000710 and S000714 for the primes in sqrt(2) and sqrt(Pi).

T. D. Noe, Plot of 300 terms

T. D. Noe, Table of 300 terms

Wikipedia, Square root of 3

(Mma) d = RealDigits[Sqrt[3], 10, 1000]; t = {}; n = 1; While[d1 = Partition[d[[1]], n, 1]; s = Select[d1, Ceiling[Log[10, FromDigits[#]]] == n && PrimeQ[FromDigits[#]] &, 1]; s != {}, AppendTo[t, {FromDigits[s[[1]]], Position[d1, s[[1]], 1, 1][[1, 1]]}]; n++]; Transpose[t][[1]]

Cf. A002194 (digits of sqrt(3)), S000710S000713S000714.

nonn,base

T. D. Noe, Oct 06 2015

© Tony D Noe 2014-2015