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Numbers n such that 4*10^n+9 is prime.
1

%I #28 Jan 17 2019 13:44:06

%S 0,2,4,5,8,9,28,191,196,2038,34414,39266,50579,94286,108412,130480,

%T 178091,185355

%N Numbers n such that 4*10^n+9 is prime.

%C a(19) > 2*10^5. - _Robert Price_, May 24 2015

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/4/40009.htm#prime">Prime numbers of the form 400...009</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) = A101715(n-1) + 1.

%e n = 2, 4, 5, 8, 9 are members since 409, 40009, 400009, 400000009 and 4000000009 are all prime.

%t Do[ If[ PrimeQ[4*10^n + 9], Print[n]], {n, 0, 10000}]

%o (PARI) is(n)=ispseudoprime(4*10^n+9) \\ _Charles R Greathouse IV_, Jun 12 2017

%Y Cf. A088275, A056806, A101715.

%K nonn

%O 1,2

%A Julien Peter Benney (jpbenney(AT)ftml.net), Jan 15 2005

%E a(10)=2038 from Joao da Silva (zxawyh66(AT)yahoo.com), Sep 30 2005

%E a(11)-a(12) from Kamada data by _Robert Price_, Dec 13 2010

%E Edited by _Ray Chandler_, Dec 23 2010

%E a(13)-a(18) from _Robert Price_, May 24 2015