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The first n-digit prime in the decimal expansion of gamma, the Euler-Mascheroni constant.
3

%I #13 Sep 15 2017 23:15:43

%S 5,53,577,3359,64901,939923,2402431,72156649,215664901,7215664901,

%T 24310421593,721566490153,2359880576723,42159335939923,

%U 359399235988057,6749514631447249,98805767234884867,402431042159335939

%N The first n-digit prime in the decimal expansion of gamma, the Euler-Mascheroni constant.

%C Euler-Mascheroni Gamma = 0.577215664901532860606512090082402431042...

%e Positions in A001620: 1, 13, 1, 43, 8, 46, 30, 3, 4, 3, 33, 3, 50, 38, 44, 96, 53, 31, 40, 64, ...

%p Digits := 10000: p0 := evalf(gamma)*10:for d from 1 to 20 do: id:=0:for i from

%p 0 to 50000 while(id=0) do :q0:=trunc(p0*10^(i+d-1)): x:= irem(q0,10^d): if type(x,prime)=true

%p and length(x)=d then printf(`%d, `,x):id:=1: else fi:od:od:~

%t With[{eg=RealDigits[EulerGamma,10,250][[1]]},Table[First[Select[ FromDigits/@Partition[eg,n,1],PrimeQ[#]&&IntegerLength[#]==n&]], {n,20}]] (* _Harvey P. Dale_, Sep 29 2011 *)

%Y Cf. A001620.

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Feb 15 2011