First n-digit prime in the digits of sqrt(Pi).
7, 17, 509, 2729, 83341, 602729, 4538509, 81674833, 128213807, 7724538509, 50905516027, 612238712821, 6122387128213, 85090551602729, 218137495065673, 2453850905516027, 98529112845910321, 754945612238712821, 9055160272981674833, 53850905516027298167
1
The position of these numbers in given in S000715. See S000710 and S000712 for the primes in sqrt(2) and sqrt(3).
T. D. Noe, Plot of 300 terms
T. D. Noe, Table of 300 terms
Wikipedia, Pi
(Mma) d = RealDigits[Sqrt[Pi], 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. A002161 (digits of sqrt(Pi)), S000710, S000712, S000715.
nonn,base
T. D. Noe, Oct 06 2015