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Numbers k such that 10^k + 3 is prime.
30

%I #60 Mar 01 2022 20:35:02

%S 1,2,5,6,11,17,18,39,56,101,105,107,123,413,426,2607,7668,10470,11021,

%T 17753,26927,60776,98288,300476,509546

%N Numbers k such that 10^k + 3 is prime.

%C A102006 is another version of the same sequence. - _N. J. A. Sloane_, Jan 28 2010

%C Verified existing 21 terms. If another term exists, it is > 39456. - _Robert Price_, Aug 16 2010

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/10003.htm#prime">Prime numbers of the form 100...003</a>.

%H Henri & Renaud Lifchitz, <a href="http://www.primenumbers.net/prptop/searchform.php?form=10%5En%2B3">PRP Records.</a>

%H Sabin Tabirca and Kieran Reynolds, <a href="http://multimedia.ucc.ie/Staff/ST/articles/SNJ03_Tabirca1.ps">Lacunary Prime Numbers</a>.

%F a(n) = A102006(n) + 1.

%e 5 is a term since 10^5 + 3 = 100003 is a prime.

%e 6 is a term since 10^6 + 3 = 1000003 is a prime.

%t Do[ If[ PrimeQ[ 10^n + 3], Print[n]], {n, 0, 18000}] (* _Robert G. Wilson v_ Jun 15 2002 *)

%o (PARI) is(n)=isprime(10^n + 3) \\ _Charles R Greathouse IV_, Apr 28 2015

%Y Cf. A102006, A159352.

%K hard,more,nonn

%O 1,2

%A _G. L. Honaker, Jr._

%E More terms from _Robert G. Wilson v_, Jun 15 2002

%E a(16) from _Ray Chandler_, Oct 09 2003

%E a(17)-a(20) from _Robert G. Wilson v_, Jan 18 2005

%E a(21) from _Jason Earls_, Jan 01 2008

%E a(22) from _Robert Price_, Jan 09 2011

%E a(23) from _Robert Price_, Mar 03 2011

%E a(24) from _Edward A. Trice_, Oct 21 2012

%E a(25) from _Paul Bourdelais_, Jan 28 2021