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Theodorus-primes: primes formed from the concatenation of the initial decimal digits of Theodorus's constant, sqrt(3).
5

%I #10 Aug 15 2015 14:51:51

%S 17,173,1732050807568877293

%N Theodorus-primes: primes formed from the concatenation of the initial decimal digits of Theodorus's constant, sqrt(3).

%C The next term (a(4)) has 111 digits. - _Harvey P. Dale_, Oct 24 2014

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Theodorus-Prime.html">Theodorus-Prime</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>

%e sqrt(3) = 1.732050807568877..., 17--the concatenation of the first 2 decimal digits--is prime, so a(1)=17.

%t nn=300;With[{ds3=RealDigits[Sqrt[3],10,nn][[1]]},Select[ Table[ FromDigits[ Take[ds3,n]],{n,nn}],PrimeQ]] (* _Harvey P. Dale_, Oct 24 2014 *)

%Y Cf. A119344.

%K nonn,bref,base

%O 1,1

%A _Eric W. Weisstein_, May 15 2006

%E Edited by _Charles R Greathouse IV_, Apr 27 2010