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%I #8 Aug 21 2017 16:12:37
%S 3,61,887,9887,39887,339887,1618033,65638117,398874989,1772030917,
%T 38622235369,803398874989,1618033988749,61803398874989,
%U 586834365638117,8343656381177203,69317931800607667,484754088075386891
%N The first n-digit prime in the decimal expansion of the golden ratio.
%C The Golden ratio is (1+sqrt(5))/2 = 1.618033988749894848204586834....
%p Digits := 10000: p0 := evalf((1+sqrt(5))/2):for d from 1 to 20 do: id:=0:for
%p i from 0 to 50000 while(id=0) do :q0:=trunc(p0*10^(i+d-1)): x:= irem(q0,10^d):
%p if type(x,prime)=true and length(x)=d then printf(`%d, `,x):id:=1: else fi:od:od:
%t With[{c=RealDigits[GoldenRatio,10,100000][[1]]},FromDigits/@Table[ SelectFirst[ Partition[c,n,1],PrimeQ[FromDigits[#]] && IntegerLength[ FromDigits[#]]==n&],{n,18}]] (* _Harvey P. Dale_, Aug 21 2017 *)
%Y Cf. A001622.
%K nonn,base
%O 1,1
%A _Michel Lagneau_, Feb 15 2011
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